The encyclopedia of gambling - University of Calgary PRISM

University of Calgary

PRISM: University of Calgary's Digital Repository

Alberta Gambling Research Institute Alberta Gambling Research Institute

1977

The encyclopedia of gambling : the game, the

odds,the teclmiques, the people and places, the

myths and history

Arnold, Peter

Chartwell Books, Inc.

http://hdl.handle.net/1880/41350

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Form 15

* THE i/^ENCYCLOPEDIA OF/*GAMBLING

Tin game, tlv odds,tlie teclmiques,lhepeople and places

the myt/is and historyPETER ARNOLD

! l T H E ~L/* ENCYCLOPEDIA OF/*GAMBLING

The game, the odds,the techniques, the people and places

the myths and historyPETER ARNOLD

795A75e

CHÛRIVNEILacncinc.

To my wife

A QUARTO BOOK

Published hy Chartwell Books Inc.,A Division of Books Sales Inc.,

110 Enterprise Avenue, Secaucus New Jersey 07094

ISBN 0 89009 179 XLibrary of Congress Catalog Card No. 77 83275

© Copyright 1977 Quarto Limited

This hook was designed and produced hy Quarto PuhlishingLimited,

13 New Burlington Street, London WlArt Editor: Peter Laws

Phototypeset in Britain hynimtype Services Limited, Scarborough, Yorkshire

Printed in Spain byPrinter Industrie Grafica S.A.

Tuset 19, BarcelonaSant Vicenç dels Horts 1977

Deposito Legal B. 39636-1977Mohn-Gordon Limited, London

CONTENTSPart OneThe History, Culture and Psychology of Gambling

Part Two 31The Mathematics and Science of GamblingTheory of Probability 33 / Independent or mutually exclusiveevents 36/Converse probabilities 36/Periodic events 37/The law oflarge numbers 39/Probability curves 40/Pascal's Triangle 40/Combinations and Permutations 40/Equipartition 42/Prospects ofruination 44/Gambling organisation's advantage 44/Pari-mutuel ortotalisator system 44/Bookmakers 45/Casinos 46/Systems 46/Martingale system 46/D'Alembert system 47/Cancellation system47 / Cancellation system backwards 48 / Psychology 48

Part Three 49Sports on Which Gambling Takes PlaceHorse racing 50/Horse racing in Britain 52/Horse racing inFrance 59/Racing in America 61 /Racing in Australia 64/Otherracing 67 / Fighting 70/ Soccer 72 /Other games 78

Part FourFixes and Swindles

81

89Part FiveGames of Chance v

Raffles 90/Lotteries 90/Sweepstakes 97/The numbers game 97/Bingo 99/German lotto 101 /Keno 101 /Slot machines 103/Craps106 / Hazard 113 / Chuck-a-luck 114 / Crown and anchor 114 / Beatthe dealer 114 / Under and over seven 115 / Baccarat 115 / Chemin defer 118/Punto banco 119/Faro 120/Trente et quarante 122/Roulette 123/Forerunners of roulette 135/Boule 137/Vingt-trois 140 /Hoggenheimer 140/Four-five-six 141/Other games of chance 143

Part Six 145Games of SkillBlackjack 146/Variations 151 /Strategy at Blackjack 151 /Splitting155/Insurance 158/Pontoon 161/Poker 162/Straight draw poker162/Strategy 163/Stud poker 166/Strategy 166/Brag 166/Ginrummy 167/Strategy 168/Napoleon 169/Strategy 169/Red dog andshoot 172/Other card games 172/Backgammon 173/Betting and theDoubling Cube 178/Chouette 178/Strategy 179/General 183/Poker dice 184/Liar dice 185/Dominoes 185/Spoof 187/Other games of skill 188

Part SevenSome Famous Casinos

193

233

241

Part EightGambling Oddities

Part NineGlossary

P A R T O N E

, o gamble is to risk anything of value ona game of chance or on the outcome of anyevent involving chance, in the hope of profit.All that can be said about the beginnings ofgambling is that in all civilisations, records ofgames are among the earliest found.

A mural in the British Museum showsAncient Egyptians playing atep, from whichthe modern game of spoof arose, and whichrequired no equipment other than the normalnumber of fingers.

Over 4,000 years ago the Chinese wereplaying wei-ch'i, a game which is still playedin the East, where a gamble is often taken onthe outcome.

As gamblers are attempting to predict whatthe future holds, there is an obvious associa-tion with fortune telling. One of the earliestmethods of fortune telling was pessomancy,the casting of pebbles at random and readinganswers to questions in the scatter. AncientGreeks also used bones, both the flat kindfor yes-no answers and the ankle bones ofcloven-footed animals like sheep which offeredfour distinct faces. These bones were calledastragals and were widely used in Greece andIndia, thousands of years before the birth ofChrist, for gambling. Astragals were cast fromcups, and are the ancestors of today's dice,which, like dominoes, are frequently calledbones. In Greek mythology, the universe wasdivided by casting an astragal: Zeus won theheavens, Hades the underworld and Poseidonthe sea. Board games using a form of die are atleast 5,000 years old. The earliest in existenceare five found in the royal tombs at Ur inMesopotamia. The dice used were of pyramidshape, and the game played on the boardsused counters. It was probably a race game,but nobody knows how it was played. Thefirst six-sided dice were used by the Etruscansand, brought to Rome, where dice made about900 B.C. have been found.

Gaming was popular in early times inBabylonia, China and India. Homer, in theIliad, tells of a quarrel over a game of knuckle-bones. Cheating and the harmful effects ofgambling are mentioned before the birth ofChrist by Aristotle, who talks of loaded dice.Tacitus, in the first century A.D., talks of menstaking their liberty on the throw of dice, andbecoming slaves when they lost. The Old

The ancientGreeks thought thatgambling was inventedbv the gods and was apleasure for the sociallyprivileged only. This -^illustration, incised on theinside of a minor cover inthe British Museum, datesfrom about 350 B.C., andshows the goddess oj love,Aphro'lite, playingknuckleboneswith the god Pan.

H I S T O R Y

P A R T O N E

|

Many nwdvrn women havebeen introduced to theattractions or peril* ofgambling by the currentcraze for organised bingo,but the ladies on theterracotta figurine fromCapua in the BritishMuseum were enjoyingplaying knucklebones inthe fifth centurv B.C.

The man shown on thisRoman mosaic from theNational Museum of Romelooks not unlike a modernjockey. A charioteer, hewears the colours of hissponsor and even a leathercrash helmet ns a protectionagainst possible falls.

i..'.

Testament frequently mentions the casting olots among ancient Jews to ascertain the wisof God or to detect guilt among suspects.

The views of early societies towards gambling differed. Many regarded the drawing olots as a suitable method of determining thguilt or otherwise of a suspected criminal,the suitability of candidates for office, beonly that of huntsman. But this was nolooked upon as gambling, since it was believefthat gods rather than chance were directinthe results. The ancient Greeks saw gamblinfor profit as a threat to the organization of thstate, and punished those who practised iThe Romans passed laws against gamblinibut it nevertheless became a feature of thDecember festival of Saturn, encouraged bthe rulers as part of the general merrymakingIn both Greece and Rome gaming took placin the taverns. l

The invention of playing cards provided 'convenient means of gambling, more sophistcated than the casting of dice, the runningraces, the tossing of coins, or race-gamesboards and counters. Nobody can say f<certain where playing cards were first usej1

One theory is that th^y were first used10

H I S T O R Y

casting olCorea and that the marks on them corres-lin the wiAonded to arrows, which were used for divin-tpects. |ng. Another is that they derived from paperprds ganinoney used in China, another that they wereirawing oflrst used in India. The Indian theory is based

ining tlfm the fact that Indian gods, particularlyiminal, ( lanuman, the monkey-god, are shown hold-

Jffice, bewas n<

las believedirectingamblifl

Lt ionof t lractised igamblin;

lure of tl[uraged Irrymakin]took pin

ng symbols not unlike those used in the suitsJf modern cards: Hanuman held a cup, aword, a ring and a sceptre.

Certainly the rapid development of cardsis the basis for a number of games occurred inEurope from the end of the fourteenth;entury. The first reference to playing cards isn a manuscript dated 1377 in the BritishMuseum. The standard pack of 52 cards wasused, and this was the only pack used for?ames in Britain, where cards were introducedn the first half of the fifteenth century. How-pver, m Europe there was also the Tarot pack,

.providedfrsed for both fortune telling and games.|re sophistf °e earliest Tarot packs contained four suitsrunning |CUPS> swords, money and batons) of 14 cards?ames \vi|fach 'the numbers one to ten, plus kings,in say f|jueens, knights and varlets) and 22 triumph,

I first usefT" trurnp, cards. There is dispute as to whetherst used f e ' ar°t pack was the first used, later slimmed

The busy craps tables ofLas Vegas in the lastthirty vears have seenmany women encouragingthe dice with the commandto 'buy baby a new bonnet'.That dice have beenpopular in mixed companyfor hundreds of vears isshown bv these twoillustrations. The ladies inthe Elt-abc'than brothelabo ve are pro vie/ing a clien twith the subsidiary pleasureof ci dice-game, and in thelower picture it seems thathuhv himself is taking aspecial interest in hisprospects of a new bonnet.

11

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H I S T O R Y

III

down to today's standard pack, or the stan-dard pack and the Tarot triumph cards evolv-ed separately, were joined for a time, and laterseparated again.

The place of origin of the standard packhas its various claimants, the three strongestbeing Italy, where the four suits were cups,swords, money and clubs, Germany (hearts,acorns, bells and leaves) and France (hearts,pikes, tiles and trefoils). Nowadays, althoughthe names for the suits vary, all countries usethe standard symbols, known in English ashearts, spades, diamonds and clubs. Playingcards were introduced to America in 1492 withColumbus, when the modern pack (or 'deck'in America) had already established its domin-ance over others.

If the theory is accepted that cards evolvedfrom Korean divining arrows, it is possibleto trace the evolution of most games back tothe times when men first decided to makedecisions by appealing to an outside agency,which most of us now would call chance.

As soon as chance was called upon, gam-bling began, there were gambling addicts,

The game offind-the-Iady,or the three-card trick, isnot a game at a/I, hut aswindle in which themanipulator encouragea thevictim to select which ofthree face-down cards isthe queen, and by sleight-of-hand ensures that thechoice is always wrong. Ithas a long history anddescends from a .similartrick in which the victimhad to choose which ofthree cups or sea-shells hida hall or a pea. The larger-engraving, called 'TheLight of Other Days', anddating from about 1840shows a version in whichthimbles were used. Itscrookedness wasacknowledged in its name,thimble-rigging. Theglamorous props whichoften accompany simplegambling games are mostevident in modern roulette,but the Araucanian Indiansgambling in the smallerengraving used an elaboratecloth to bring aestheticpleasure to their game.

13

P A R T O N E

While gambling is thoughtby some to be a sordidpastime, many of its toolshave been beautifullydesigned, such as theseItalian tarot cards.Illustrated are the nines ofthe four suits: cups, snvoru.imoney and batons.

1

14

H I S T O R Y

and there were those who objected to gam-j bling.

Certainly since the Reformation most civi-' Used countries have placed restrictions onI gambling. In Britain, the first law againstgambling was enacted in 1661, and severalActs passed during the next 300 years sup-pressed one or another form of gambling. InI960 the trend was reversed and gambling

[became accessible to most. Nowadays oneof the strongest objections to gambling is thatit leads to the emasculation of the addict,with hardship to his dependents and incon-venience to the state. Religious objections,based on moral grounds, are more or lessvehement in different parts of the world.The ease with which criminals can use gam-

I bling as a way to financial power is a compara-tively modern objection. In old societies,based on privilege, opposition to gamblingwas based on the undesirability of the lowerclasses enjoying its pleasures, a view which

I seemed to influence British laws before 1960.Until then rich men would back horses

I easily by means of a legal credit account with a1 bookmaker, but poor men were forced to theI inconvenience of making bets by post. Illegal(street bookmakers defied the restrictions.

Even today, after thousands of years ofgaming, the attitudes towards it and its legalityvary from country to country. There is nostandard attitude in communist countries,where the Soviet Union and China do notpossess casinos, at least in theory, but Czecho-slovakia and Yugoslavia do. Many countrieswhich otherwise frown on gambling allowlotteries to raise funds for the state; some, like

The 22 trump or triumphcards of the tarot pack areknown as the major arcana.Numbered from 0 to 21,each contains anemblematic picture, andall have a title, exceptnumber 13, whichrepresents death, and isoften left untitled. Fromtop left to bottom right, thecards illustrated representdeath, the sun, the hangingman, the lovers, the moon,and the fool, which issometimes numbered 0and sometimes unnumbered.

Lord Kenyan blamedgambling for many ofsociety's ills and the 1797illustration, with thenaming 'Faro's daughtersbeware', shows hisproposed punishment forexcessive gaming.

15

P A R T O N E

the Scandinavian countries, allow footballpools for the same purpose. Many countriespermit horse-racing, but most restrict bettingto a totalisator or pari-mutuel system, whichpays a levy to the State. Some allow book-makers to take bets on the course only.

Britain at present has the most enlightenedattitude to gambling. Every citizen can con-veniently bet on almost anything he wishes,although taxes are extremely punitive onfootball pools, for many the only regularbetting activity. Also, the wish to allow thebookmakers and the tote to compete for thecustom of horse-race bettors means that lessmoney is skimmed off to improve the decliningstandard of British racing than would be thecase if the tote had a monopoly.

In America and Australia, opportunities

Closed circuit television isa luxury not found inmany British betting shops,where information onrunners, prices and results,and commentaries, areusually relayed by radio.In the betting shop abovesix screens using videotapeshow runners and resultsfrom Ascot, Haydock Parkand Ludlow race courses.

for gambling vary from state to state. InAmerica, legal casino gambling is permittedonly in Nevada. Many states now run statelotteries. Not all states yet allow pari-mutuelbetting at race-tracks, and betting on horse-racing away from the track is allowed only inNevada, which permits gambling in general,and New York. A few states allow slotmachines, but even bingo is allowed in onlyabout half the states. All Australian states runstate lotteries. The most popular betting is •on horse-racing, through the tote and licensed,on-course bookmakers. i

The size of the gambling industry is difficultto estimate, as much of it is necessarily illegal.In Britain, where figures are most available,the turnover is well over £3,000 million peryear, or over £60 per head of the population.

In America, where turnover is the biggestthe world, it has been variously estimatebetween about $300 per head and eight tinJthis amount. But turnover is not a reliabljguide to how much is spent. Gambling turtjover is estimated in various ways. For instanqthe turnover of a casino might be based on Iamount of chips bought, although each chmight be used for several bets before it isor cashed in. The turnover also includes tilmoney paid back to winners, so does nclrepresent the amount lost. In British footbalpools, for instance, where only about 28 pelcent of stakes are returned to the punters,turnover of £218 million in 1975 meant aboi£ 157 million actually spent. On the other hanabout 80 per cent of money staked on racing|returned to the punter, so a turnover of £1,91million represented less than £400 milliaspent. However it is looked at, gambling]big business, with a turnover in countriesAmerica and Britain several times bigger tthat of any of the largest companies. Survein these countries suggest that about threjquarters of the adult population gamtfregularly; probably less than ten pernever gamble at all.

Why should gambling be so popular? It|not a natural instinct, although the comptitive instinct may be: babies compete fiattention and love. Children play games, ait is natural to want to win. Adults not onlwant to win, many of them desire more thajthe winning as a reward for their skill. Aadds significance to the win. Adults with litt]skill at games can share the glory of winnflby betting on them. In this way they becofljwinners themselves by displaying acumen Imaking the right choices. Even a person wBbets on an event of pure chance displays Icompetitive spirit: he wants to show that he]favoured by luck. Gamblers rarely talklosses, often of wins, even though a win on 'event of pure chance reflects no credit onwinner. But it demonstrates that he isand a belief in luck is an instinct which all 1rationality and science in the world seefljunable to eradicate from man.

Most people who gamble would be unving to admit that they do so for any otfreason than the enjoyment of pitting thflskill against that of the bookmaker or

16

H I S T O R Y

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Fyodor Dostoevsky wasnot only a pathologicalgambler, he was also agenius who in his shortnovel 'The Gambler'conveyed the excitement ofthe addict. He was 51when the Russian artistV. G. Perov painted this

portrait in 1872, and still avictim to the mania whichcaused trips to money-lenders and pawnbrokersbetween bouts oj writing.

17

P A R T O N E

Most gamblers like tothink of their wins us thedue reward for skill andforesight, and their lossesas the cruellest had luck.Nevertheless manyparadoxically folio w luckyroutines and keep luckvcharms. Photographs oftwo Derby winners and twobig football pools winnersframe one of the mostwidespread lucky charms,a rabbit's foot.

fellow players. This is a valid reason, and nodoubt many people who play games likebridge for small stakes get as much or moresatisfaction from the exercise of their skillas from the material winnings. There areother less attractive motives. The desire forprofit is an obvious one, particularly strongin low-income groups where gambling is seenas the only hope of acquiring some of the goodthings of life. Many football pool puntershave no real interest in football, or knowledgeof form, and complete their coupon at random,with the hope of a fortune for a small outlay.

Some people gamble as a social activity.Gambling provides an opportunity to meetand discuss matters of common interest, likerace-horse form, with acquaintances. Gam-bling also buys an interest in the future: thedullness of an afternoon can be alleviated byanticipation of the racing results. Amongstricher folk, gambling might appeal for itsglamorous connotations and the opportun-ities it gives to fantasise, as well as a means ofbringing some spurious excitement to life.

The true gambling addict has a diffèreset of reasons for gambling, or if some are tsame they undergo a qualitative change. Withe addict, gambling displaces all other inteests. His mental energies are directed entireon the game to the exclusion of everythielse, even, ultimately, his family. The pathlogical gambler cannot stop gambling. Losidoes not deter him. He always believes thhe will win eventually, and regards his shepersistence as a guarantee that he will. }is deaf to all logical arguments, seeing tlirrationality of his behaviour as part ofcharm and mystique. He sees himself as somthing special, a man selected by fortune,man to whom the normal laws of chance <not apply. Attempts to dissuade him from thview merely strengthen his compulsion. Whthe addict does win, he is incapable of stoppiiwith a profit. He must go on to win morHe is confirmed in his belief that he is a winnehis optimism re-inforced, if re-inforcemeiwere necessary. He may have started withsystem of betting, perhaps even based onrational premise. But gradually his stakes wincrease beyond his means. At last a sortfever will take over, not born of desperatiobut of excitement, and he will gamble reclessly until his funds are exhausted and he museek some more.

It is when he reaches this state, that ffpathological gambler differs most from ttcasual gambler. For him, the prospect iwinning or losing becomes of secondaimportance. He needs the tension of gamblinHe is like the drug addict who must shed tmundane for a different, heightened awarness. The desperation of losing is as necessato him as the ecstasy of winning. The pibecomes a sort of orgy.

The best study of a pathological gamblis in Dostoevsky's novel The Gambler, ïdescribes the overwhelming craving for riof his hero, who having won a fortune in tcasino is impelled to risk it all on one handtrente et quarante. It is making the bet thbrings the thrill. If he wins he must do itand again until he loses, which is seentragedy only because it ends his orgy. For sortyears Dostoevsky himself was a gambhaddict, and reduced himself to beggingfunds from other writers. It is something '

18

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Questions and Answers

about the problem

of Compulsive Gambling

and theG.A. Recovery Programme

Gamblers Anonymous is amovement which began inAmerica in 1957 to helpcompulsive gamblers toovercome their addictionby means of group therapy,in which they giveencouragement to eachother. As the leaflets show,the organisation is alsoaware of the peculiarproblems of the families ofcompulsive gamblers, andGam-Anon is a fellowshipdesigned to help gambler'--families in a similar way

P A R T O N E

Dawn al Monte Carlo, andthe corpse is discovered ofanother unlucky gambler.Sarah Bernhardt was oneof many who attemptedsuicide at Monte Carloafter a particularly bad runat the tables. The officerabove might be establishinglife or death, or he mightbe putting money into thedeceased's pockets, whichwas done to prevent badpublicitv for the casino.

which the rest of us can be thankful, as hewrote some of his novels in great haste toraise money for gambling. Dostoevsky hasrecorded that he experienced orgasm on losinga large bet at roulette.

While Dostoevsky's novel gives a powerfulfirst-hand account of compulsion, andDickens' description in The Old CuriosityShop of Little Nell's grandfather losing hermoney at cards tells the other, sad side of thestory, it is not necessary to look to fiction forexamples of addiction. The case of the house-wife who lost £25 per week, or half her hus-band's earnings, at bingo for weeks on end,is just one of several similar cases. She even-tually stole from neighbours to satisfy herneed for bingo. Whereas bingo often attractsplayers because it offers social contacts,socialising disappears with compulsion. Theaddict has no time for others: the play's the

thing. A pathological gambler will sell all hepossesses for a fraction of its worth to gamble.He will steal, he may even give away his monejin a short-lived desire to starve and kill hiscraving, but he is likely to attempt to raisemore as soon as his need returns.

The compulsive gambler is not as easil)recognisable as the alcoholic, but alcoholicsmight outnumber gambling addicts by onl)[two to one. A Gamblers Anonymous move-ment, working on similar lines to AlcoholicsAnonymous, was founded in America i"1957 and spread to Britain seven years laterCompulsion cannot be cured, as compulsivegamblers are likely to relapse, but Gambler!Anonymous helps by allowing habitual garnfbiers to discuss their addictions and to helfeach other try to overcome them. Members oa group know each other only by their forenames, they confess their lapses to each othet

20

H I S T O R Y

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and members who abstain from gamblingfor a period, say two years, receive presenta-tion badges.

Objections to gambling are often based onthe undesirability of the addict, but the addictis not an exaggerated version of the casualgambler, he is a different animal altogether.Where casual gambling is concerned, there aretwo main forms of argument that are putforward in attempts to outlaw it. One isempirical: that gambling is harmful to thestructure and well-being of society. The otheris based on ethical grounds.

It is true that a vast amount of time, effortand money is spent in countries like theUnited States, Britain and Australia on apastime that is completely non-productiveand contributes nothing to the general wealthof the community. But then any pastimewhich provides amusement is not expectedto provide anything else. Smoking, drinkingor eating cream buns do nobody any good,and in excess may do harm, but they are notbanned. Gambling undoubtedly attracts thecriminal classes, and this is the most powerfulpractical objection it must face. In Americacrooks like Al Capone, Arnold Rothsteinand Dutch Schultz financed themselves partlyfrom gambling, and the vast sums they madeenabled them to buy up legitimate businesses.In 1962 Attorney General Robert Kennedycould say that corruption financed bygambling was weakening the whole nation.This, of course, could be used as an argumentthat gambling should be legalised. Nothingattracts the underworld more than a profit-able illegal operation, as prohibition proved.The repeal of the Volstead Law removed aneasy source of fortunes from a number ofhoodlums and deprived certain policemenand officials of a steady income from bribery.Where casinos are strictly controlled by thestate, as in France, not only is corruption mucheasier to control but the state can obtainrevenue from gambling. A well-run gamblingindustry should cause as little concern as any°ther large industry.

The inconvenience caused by compulsivegamblers who lose all their possessions andbecome a burden on the state can be equalled"Y casual gamblers who have a big win. Theresentment and upsetting effect poor people

sometimes cause among their neighbourswhen they win a fortune on the football poolsor a lottery, and do not act in a responsiblemanner, is a very minor inconvenience, butwhen the entire jackpot in a national lotteryis won by the townspeople of one small town,as happened in Spain in 1976, the life-style ofa region is changed. The winning town wasLugo. on the north-west coast, which sharedabout 3,000 million pesetas when the in-habitants won all 35 top prizes in 'El Gordo',the Christmas lottery which has become thebiggest in the world. Patients, doctors andnurses at the local hospital shared over 450million pesetas, soldiers at the barracks asimilar sum, and players and supporters ofthe football club over 300 million. For thoseinterested, the winning number was 49764.Lugo will never be the same again. Anti-gamblers who dislike this upheaval in the

Three American gangsters\\'ho organised gambling toincrease their fortunes andextend their power. LuckyLuciano, left, controlledthe Bugs and Merer Mob.and helped Bugsy Siegelraise the capital to startthe Las Vegas gamblingboom. He is seen at theItalian Derby in Rome afterhis deportation from theStates. AI Capone, top,went to the same school asLuciano, and regarded himas a second cousin. He wasone of the most notoriousgangsters and exercisedcontrol over many casinosand the main bookmakers 'wire service. DutchSclnilt:, horn ArthurFlegenheimer, was theking of the numbers racket.

21

P A R T O N E

The beast oj gaming. Thisengraving from a Frenchmagazine of 1845 shows afather protecting his sonfrom a dragon-like beast,representing gambling, whodevours all the possessionsof his victims.

natural order must admit that more distressingeffects on regions can happen in other ways,as when chemicals leak from factories.

The ethical objections to gambling areusually founded on religious beliefs, but theattitudes of individual churchmen vary con-siderably. The Roman Catholic Church, ingeneral, tolerates gambling as an establishedpart of human life. Indeed, in some Catholiccountries, national lottery tickets can bebought on Sunday mornings on the way toworship.

It is in the Protestant faith that Christiandislike of gambling is strongest. The churchis concerned with the wellbeing of society,and many of the evils of gambling pointedout by Christians are the practical ones: theruin of the personality of the addict, thereliance on hope rather than skill in businessaffairs, the dehumanising influence of gam-bling, the encouragement to believe in luckand superstition rather than work as a routeto success.

The religious argument against gamblingrests mainly on the element of chance. Christ-

ians deny that there is such a thing as chance.Even that which man cannot understand issaid to be subject to God's law. According toLuke (xii, 6) 'Even the very hairs of your headsare all numbered'. Blind destiny does not exist:everything in the universe is within the rule ofGod. Some Christians would say that a beliefin chance robs life of meaning, and is immoralbecause it is incompatible with a belief inGod.

Christians further believe that all propertyis owned, ultimately, by God. Therefore tostake possessions temporarily owned in anappeal to chance, is not only to deny God byappealing to a concept which cannot exist ifHe does, but is to violate the trust which Godplaces in an individual by bestowing steward-ship of property.

If the soldiers at Christ's cross had not castlots for His raiment, it might be that Christianattitudes to gaming would be less firm thanthey are. All Christians do not hold stronganti-gambling views. Raffles to raise moneyfor Church funds are common, as are games ofbingo and other forms of mild gambling forthe same purpose. A poll in the United Statessuggested that more people had taken part inchurch raffles than any other form of gam-bling. The Bishop of Durham, Dr. JohnHabgood, who later was not amused when apunter placed a bet on him to become the newArchbishop of Canterbury, said in 1974 thatit would be wrong and socially dangerous totry to remove the excitement which gamblingbrought into many otherwise dull lives. Buthe was not in favour of church-based gam-bling, believing that people should not allowthe hope of gain to influence in the slightesttheir natural desire to give to God. He wasthus expressing views contrary to the practiceof many clergymen, and confirming thatchurch opinion, while generally nearer theanti-gambling end of a scale than lay opinion,has almost as many facets.

Apart from cheats and hustlers, gamblersmight be divided into five main classes:occasional gamblers, who might bet only onbig horse races; regular gamblers, who enjoya daily or weekly flutter, but who bet hap-hazardly; serious gamblers who follow asystem; pathological gamblers, whose addic-tion is in the nature of an illness; and profes-

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sional gamblers, most of whom are proprietorsof casinos, bookmakers or gambling industryemployees.

The professional who offers the odds is notafraid of gamblers from any of these classes.He will prefer the system gambler to theoccasional gambler merely because he betsmore often - both are facing the same houseedge and the profits to the proprietor willaccrue just as surely.

However, one type of gambler sometimescauses a stir and makes a good newspaperstory: the man who dreams winners.

One of the best authenticated cases was inBritain. The gambler concerned was JohnGodley, later Lord Kilbracken, who was givena tipping job on the Daily Mirror on thestrength of his success. John Godley was atOxford University in 1946 when he dreamthe saw racing results in the following day's

paper. He could remember two 'winners', andbacked them for modest amounts : both won,at 9-2 and 10-1. A little later in Ireland,he dreamt another 'winner'. This time friendsjoined him in a nice win at 100-6. Back atOxford he dreamt he was telephoning hisbookmaker for the last race winner, and wastold its name and price, 5-4. Although nextday he found the last race field did not containa horse with the name he remembered fromhis dream, there was one of a similar name.He backed it, phoned his bookmaker afterthe race from the same telephone box of hisdream, and learned it had indeed won at6-4.

In 1947, he dreamt he was at the races, andin recalling his dream remembered that EdgarBritt had won a race in the Gaekwar ofBaroda's colours and that the crowd hadshouted home a horse called The Bogey in a

The Lone/on 'Daily Mirror 'story oj 1947 which tells ofthe strange dreams whichbrought winners to JohnGodley. Although the storyends with a possibleexplanation of Mr Godley's'supernatural'powers, thenewspaper thought itworth offering him a job.

P A R T O N E

later race. Although next day there was not ahorse called The Bogey running, Godley hadno difficulty in deciding that the two horseshe dreamt of were Baroda Squadron and TheBrogue. He tried to get this dream verified,and as attempts to find a solicitor or to get thestory date-stamped at a Post Office failed (itwas Saturday), he decided to sell the story to anewspaper. He rang a New York paper, whodeclined to pay for the story, but was just intime before the first race in question to givethe story to the Sunday Pictorial, who prom-ised to use it if both horses won. They did,the Pictorial published, and Godley receiveda small fee and won another modest bet. How-ever the small Pictorial story was taken up byits sister paper the Daily Mirror, who paidhim 25 guineas and gave him a job.

John Godley had two more winning dreams,but also a few losers, and his gift appeared tohave deserted him. It returned once more, in1958, when he was in Monte Carlo. He dreamtthat the Grand National was won by the thirdfavourite, What Man. The National was amonth or two off, and a study of the runnersrevealed no What Man, but a Mr What.Unfortunately, Mr What was not third fav-ourite, but a 66-1 outsider, so Godley decidedto do nothing. On the day of the race he wasin Paris, bought an English paper, and findingthat Mr What was now third favourite at18-1, rang his bookmaker and placed £25 onthe horse. In Paris, he could find no radioreport on the race, as everybody was listeningto a commentary on an international soccermatch. But when he checked with his book-maker, he discovered Mr What had won, andhis £450 win was his biggest in a remarkableseries.

Most stories like that of John Godley haveless disinterested corroboration, and areregarded by most with scepticism. ProfessorJ. B. Rhine and his colleagues at DukeUniversity, at about the time that John Godleywas dreaming of Mr. What, described experi-ments which suggested that some people,by mental effort, can affect physical happen-ings, i.e. they can will that a cast die will stopwith a desired face uppermost. Other peoplecan predict playing cards selected by a secondperson. Later Helmut Schmidt, an Americanpsychologist, was invited to London by the

Society for Psychical Research to demon-strate that certain people can predict which offour light bulbs, lighting separately and atrandom, will shine next. In none of theseexperiments did the subjects have a 100 percent record, but their success rate seemed tomake nonsense of the laws of probability.Gamblers do not know what to make of theseexperiments. Although they cannot refute theconclusions of such eminent scientists, instinctand, in some cases, a lifetime of experiencelead them to ignore them. Perhaps theopinions of the gambling fraternity are bestshown by the fact that in casinos, playerstrying to effect certain results by concentrationare tolerated with equanimity by the casinomanagement.

Throughout the history of gambling therehave been gamblers whose feats, winning orlosing, have captured the admiration of theirfellows. Casanova, whose name is now givento any man who enjoys spectacular amoroussuccesses, earned his livelihood by gaming.'Lucky at cards, unlucky in love' did not applyto Giovanni Jacopo Casanova, whose fav-ourite card game was faro, and whose main

reJtoi

24

H I S T O R Y

ion- source of" capital was his mistress of the:h of moment. Casanova frequently lost all he had ;

Id at although he claimed to win more than hethese lost, it is doubtful that he did. He certainly

per made a profit when he persuaded the King ofbd to France to organise a national lottery, and soldlility. tickets himself.Ithese The early eighteenth century was a notor-

the ious time for gambling in Britain, with bigItinct sums changing hands nightly in the Londonlence clubs, among them Brooks's, White's and the

the opulent Crockford's, which was founded inbest 1828 by William Crockford. Crockford began

^yers life as the son of a fishmonger, gambledition thousands of pounds a year on dice, ownedlisino the best race-horses, and died a wealthy man.

A leading light in White's was George Bryanthere Brummell, the dandy, better known as Beau|g or Brummell. Brummell inherited £30,000 fromItheir his father and once won £20,000 in one even-ïiven mg. His favourite game was macao, which has|rous similarities to blackjack and baccarat. Oneling. entry jn White's betting book read: "Lord

Jpply ^ ' innouth gives Lord Glcngal l four guineas tofav- receive 100 guineas if Mr Brummell returnslain to London before Napoleon returns to Paris'.

Having eventually lost his fortune, Brummellhad gone to France, immaculately dressed asever, after a quarrel with the Prince Regentand mounting difficulties over his gamingdebts. Before he died, penniless, in a mad-house, he claimed his bad luck came whenhe lost a coin with a hole in it - a good luckcharm given him by an old woman when hewas at school in Eton.

Another hot-bed of gambling was the fleetof steamboats operating on the Mississippiin the nineteenth century. Around 1850, about500 boats were making journeys along theriver, and about 1,000 gamblers, not allhonest, were relieving the passengers of theirmoney. Many of these gamblers were flashydressers, and their style and the romanticsetting of the palatial boats have given Holly-wood films many a big scene.

Hollywood has also profited from the legendof the Wild West, and scenes of poker playingin saloons are almost obligatory to theWestern. Wyatt Earp partly owned such asaloon and gambling den, and made morefrom his skill at cards and dice than from lawenforcement. Doc Holliday, a card-sharp,

Beau Brummell, opposite,was a dandy who inheriteda fortune and became afriend of the Prince Regent,yet he was forced to goabroad, and to die pennilessin a madhouse, after losinghis money gambling.William Crockford usedgambling to climb society'sladder. The son of a fish-monger, he won enough toopen one of London's mostexclusive gambling clubs,Crockford's, in 1828 (left).Giovanni Casanova, above,used gambling wins to helpconquer his mistresses, andthe capital of his mistressesto help pay his losses.

25

The characters aboveformed the Dodge CityPeace Commission of1883, yet at least two ofthem were dealers in WildWest gambling hells. WyattEarp, second from left inthe front row, and alsopictured right, sharedownership of a saloon andregularly won at cards anddice. Luke Short, secondfrom left in the back row,was a dandy and gun fig h 1eras well as a professionalgambler. George Devol,below, published in 1887his reminiscences, 'FortyYears a Gambler on theMississippi', which told ofhis successes on thefamous ri\'erboats.

made more killings at poker in Harp's saloonthan he made with his guns. Wyatt Earp wasthe referee of a prizefight in San Franciscobetween Bob Fitzsimmons, later championof the world, and Tom Sharkey, and had touse his revolver to discourage angry bettorswhen he disqualified the Englishman.

Tombstone and Dodge City, where Earpwas marshal and dealt at faro, were famous asgambling hells, and Cincinnati was known asPokerpolis. Poker was the favourite game,and Wild Bill Hickok, another marshal, madea poker hand famous at Deadwood in 1876.Wild Bill relaxed for once his rule of alwayssitting with his back to the wall and facing thedoor when playing poker. He had just drawncards when another gambler, Jackie McCall,came through the door and shot Wild Billin the back of the head. He had been hired tokill Hickok by other gamblers, who fearedthat Hickok would be made marshal ofDeadwood and interfere with their game.Wild Bill's hand was examinedafter his assass-ination, and was found to contain the twoblack aces and two black eights. The fifth cardis in dispute: it was either the queen or jackof diamonds. From that day, pairs of aces andeights have always been known as 'dead man'shand'.

The most famous gambler of all time isCharles Wells, whose name is less familiar

26

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than the song written about him, 'The ManWho Broke the Bank at Monte Carlo'. Wellswas a tubby Cockney, who was a small-timeconfidence trickster. He arrived in MonteCarlo in July 1891 with 10,000 francs. Hebegan playing roulette for small stakes, andappeared to be using a system, concentratingon backing the low numbers, particularly1 and 2. He increased his stakes as he hit afantastic run of luck, until he broke the bankat the table at which he was playing. In thosedays each table began with a bank of 100,000francs. Wells moved to another table andbroke the bank again. He played for 11 hourscontinuously, and next day reappeared andbroke the bank again.

During his extraordinary run, there werefrenzied scenes in the casino as other gamblerscrowded round the table and attempted tomake their fortunes by following his luck.Camille Blanc, the casino owner, played upto the excitement by draping a black cloth overthe tables which Wells broke, to reopen themlater with great ostentation, thus ensuringpublicity for Wells' feats. After three daysWells left with a million francs. In NovemberWells returned for another three days, andincredibly won another million francs.

Wells was famous. He was a celebrity where-ever he went, and when Charles Coborn sangthe song about him that winter, it swept theworld. Wells' third visit to Monte Carlo wasmade in 1892, when he arrived on a yacht,with a model for a girl-friend. This time thetheory of probability cried enough. Wells losthis money, obtained more by trickery and lostthat. He was arrested on board the yacht andsentenced to eight years in an English prison.On release he went to Paris, and after moreshady fund-raising in France was arrestedagain, and finally died in poverty.

Although hundreds had studied his playln an attempt to discover his system, beforehe died Wells confessed that he had no system,but had been betting haphazardly. The MonteCarlo casino was the main beneficiary of hisluck, becoming a household name.

The most successful gambler of all time wasNico Zographos, the youngest and mostbrilliant gambler of the Greek Syndicate,which from 1922 held the baccarat bank atsorne of Europe's biggest casinos. He played

* - f H I S T O R Y

, ALSOSUNGINTHE GAIFTVOiPf-H-?1""'"1"

for unlimited stakes against the world'srichest men. Zographos was born in Athensin 1886, and showed a mathematical aptitudeas a boy. He was trained as an engineer, butdecided that playing cards was his forte. Hemet Eli Eliopulo, the second member of theGreek Syndicate, in 1917, and married hisniece. Zographos and Eliopulo played cardsagainst the sons of Greek ship-owners, andwon. After the First World War, they wentto Paris where Zographos re-met ZaretCouyoumdjian, an Armenian whom he hadknown in Athens. Couyoumdjian had inher-ited a fortune but lost it in the war betweenGreece and Turkey, and was earning a livingas a gambler. The three men found they usuallyheld the bank at baccarat, and decided toform themselves into the Greek Syndicate.The fourth and last member of the Syndicatewas Athanese Vagliano, an extremely wealthyship-owner who loved playing cards and hadshares in the Société des Bains de Mer et

Monte Carlo inspiredmarches and dances, as theabove song sheet shows,but none achieved the fameof the song 'The Man ThatBroke the Bank at MonteCarlo', made world-famousby Charles Coborn. It toldof the exploits in 1891 ofChar/ex Wells, and helpedestablish Monte Carlo asthe world's mostfamous gambling casino.

27

P A R T O N E

Cercle des Estrangers, which owned theMonte Carlo casino. Zographos invited Vag-liano, who was not a good card player, toinvest in the Syndicate, and he accepted.

With Vagliano's capital to back them,Zographos suggested to Francois André, whowas r u n n i n g the casino at D c a u x i l l c . tha t theSyndicate should permanently take the bank atbaccarat. The bank till then went to the playerprepared to put up the largest amount:Zographos suggested that the Syndicate wouldplay without a limit. André, who later took ashare in the Syndicate, saw the value of thissuggestion and readily agreed. In 1922Zographos took the bank at Deauville,announcing 'tout va', or 'everything goes',and began an era of some of the mostspectacular gambling.

Zographos usually took the bank, withCouyoumdjian as second in command, andbetting against him were men like the AgaKhan, James Hennessey, of the brandy com-pany, André Citroen, the French car magnate,Gordon Selfridge, of the London store, andBaron Henri de Rothschild. The gaming wassuch that millions of francs changed handsevery night.

André Citroen was eventually ruined bygambling. Whether he were winning or losing,Citroen believed his gambling, reported inEurope's newspapers, was good publicityfor his company. In 1926. he continued playingbaccarat while losing heavily to Zographos,not worrying that he lost 13 million francsin a single session. His wife gate-crashedthe baccarat room, where women were notallowed, and not only tearfully persuadedZographos to end the game, but effected achange in the rule, which thenceforwardpermitted women to enter. Citroen nearly losthis factory, but continued gambling. Severalyears later he lost several million francs in tenminutes at Deauville, and did lose his factory.

Gordon Selfridge was another whose loveof gambling and his encounters withZographos led to his ruin, although in his casethey were helped by his generosity and hisaffection for Gaby Delys, an actress, and thetwo Dolly Sisters, who made up a cabaretact. He not only gave them gifts, but in thecase of Jenny and Rosie Dolly allowed themlimitless credit to gamble at Deauville andLe Touquet. Selfridge and the sisters stayed

at his villa at Deauville and over a number oyears won and lost millions of francs. Wheithey were winning, the Dolly Sisters boughjewellery, a boutique in Paris, and villaswhen they were losing they sold them allEventually Selfridge could help them no moreand Jenny, his favourite, was declared bankrupt. Selfridge himself, who was said to havspent £2 million in seven years, went bankrupt at 83, still owing money to Zographos.

Nico Zographos himself had his spectaculaups and downs, more than once almost beinout of funds. His assets were a remarkablememory for the cards played (it was said thaat the end of a shoe of six packs Zographocould state which cards were left unplayed)psychology and a knowledge of the playersagainst him. Once, on a losing streak, b£

instructed that lower value chips should btused, on the grounds that his opponentswould be reluctant to stake a large pile' an<the bets would be smaller. There are numerousstories about him. He was challenged byAmerican gambler to bet a million francsone hand of baccarat. Zographos agreedcover the stake, provided the bet could bethe best of three hands. He then lost the firs1

hand and won the following two.In 1928, after a series of unlucky shoe*

28

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H I S T O R Y

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the Syndicate was down to its last millionfrancs. The players and watchers knew it, andthe whole amount was at stake on a singlecoup. Both opponents were happy with theircards: Zographos turned up a king and queen,worth nothing. He took a third card. It wasthe best possible, a nine - to be precise the nineof diamonds. Zographos was never in troubleagain, and the nine of diamonds became hispersonal emblem, appearing on his yachtpennant, his china, his cuff-links. When hedied in 1953, he was a multi-millionaire in anycurrency. The Greek Syndicate continuedwithout him, and went on winning, some of itsmembers being relatives of the originals.

There is a tradition that Greeks are keencard-players and excellent gamblers, and overthe years names like 'Nick the Greek' orJimmy the Greek' have been applied to out-standing gamblers. The most famous of thesewas Nicholas Dandolos. The two Nicks,Zographos and Dandolos, were both pro-fessional gamblers, but whereas Zographoswas playing for the casino, Dandolos playedf°r himself. He was born in Crete in 1893,educated in Greece, and sent to Chicago bynis father, a rug merchant, when he was 18.Vears old. He moved to Montreal, quicklywon half a million dollars at horse-racing,

and returned to Chicago to play cards, anddice, at which he lost all his previous winnings.He studied gambling, and decided that studpoker was the game at which he could win,although he also enjoyed craps and faro,because of the low house edge against him.Dandolos quickly began to win. and as he betin huge amounts, he attracted crowds whereverhe played and became known everywhere asNick the Greek. He had the true gamblingaddict's trait of not caring about the amountshe won or lost: for him the game was theimportant thing. However, he did not bethaphazardly. He bet according to carefullycalculated chances. He was an intellectual,with a degree in philosophy, and was some-thing of a mystery to his fellow-players. There-fore many of the stories about him are specu-lation, such as that he lost $100,000 in asingle session.

Nick the Greek often played in the casinosof Las Vegas and more than once was askedby proprietors if he would care to play forthe casino. He preferred being a free-lance.His success came from his skill at calculatingchances and he always played honestly,although he himself was once cheated of$500,000 in a private game played by the sideof a casino swimming pool. When he died in

Gordon Sel fridge, in thepicture left, is being pulledboth ways by the actressesJulia Faye and BebeDaniels. Later in life hisgenerosity to beautifulwomen and his love ofgambling helped pull himinto bankruptcy. Thegambling losses of AndréCitroen, above, more thanonce threatened theo wnership of his famouscar-manufacturingcompany.

29

P A R T O N E

Scan Cannery in 1963proved himself a luckygambler in private life in//;a big \\'in at the casino inEstoril. No mmcler lielooks at home at the crapstableplaving James Bondin the 1971 film'Diamonds Are Forever.'

his early eighties, it was estimated that he hadwon and lost several fortunes, and that over$500 million had passed through his hands atthe tables.

An American whose gambling feats earnedhim fame and a nickname was John WarneGates, known as 'Bet-a-Million' Gates. Gateswas born in 1855 and began earning his livingas a barbed wire salesman in Texas. He even-tually owned America's largest barbed wirecompanies, expanded into other industriesand speculated successfully on the stockmarket. He became immensely wealthy andindulged his liking for making huge bets onpractically anything. A rotund, heavy man,Gates did not bet only for the excitement itgave him. He was a shrewd calculator whoalways sought the advantage of the odds.Although he bet large sums on raindropssliding down window panes and on the tossingof coins, he was aware that his huge fortunegave him an advantage in such bets. In a gameof faro at which he was losing several thousanddollars, he kept asking for the limits to beraised: when his luck changed he quicklyretrieved his losses and won $150,000. Gatesenjoyed playing poker, and used his capitalto raise heavily to frighten less wealthyopponents out of the game. He loved racingand was said to have lost $375,000 in oneafternoon. He was also said on anotheroccasion to have won $600,000 in bets on oneof his own horses. A possible explanationof his nickname lies in his being asked atone race-track to limit his bets to $10,000.Affronted, he immediately offered to bet amillion dollars on a horse. There were notakers, but his fame was assured.

John 'Bet-a-Million' Gates did not have atrue gambling addiction. He was too shrewd

to allow his betting to get out of control, andunlike Citroen and Selfridge, did not comenear to risking his entire fortune. Eventuallyhe lost interest in using his money to steam-roller lesser gamblers and in 1909 he warneda church conference against the evils ofgambling and renounced it himself.

An Italian duchess asked French casinos toban her for five years in 1972 after an extra-ordinary run of losses at Divonne-les-Bains.The limit on the trente et quarante table wasraised to allow the duchess to bet up to400,000 francs at a time. She asked for theban when her losses passed 10 million francs.

Ex-King Farouk of Egypt, in his later yearsa very fat man, was a regular large-stakegambler. While still on the throne he was afamiliar figure at Monte Carlo, where heonce lost $300,000 to Jack Warner, theHollywood film producer. Farouk was never-theless a good gambler, who frequentlyopposed the Greek Syndicate and won 30million francs from them. He liked dealingthe cards himself and enjoyed poker, andholding the bank at baccarat and chemin defer. He always appeared with a large numberof bodyguards and attendants, and was attimes an angry loser, once breaking a chemmytable. But while the game was in progress hewas impassive, even when an opponent diedof a heart attack when he'd been dealt awinning hand in a big-stake game. Faroukwas a commanding figure in the casinos ofMonte Carlo and France during the 1950s.

The lazy good-living Farouk satisfied onepopular image of a gambler. Other gamblersmentioned here, such as Wells and Gates,have been over-large tycoon-like figures.What of the other image, made popular bynumerous films, of the handsome, JamesBond type of gambler, who displays nervesof steel at the table, unerringly makes the rightdecisions and rakes in the winnings withouta flicker of surprise or triumph? Who couldsatisfy this image better than Sean Connery,the best actor to have played James Bond?At the roulette table in the St. Vincent casinoin Italy, one day in 1963, Connery backednumber 17 three times running. The oddsagainst three consecutive wins are 50,652-1.but Connery pulled it off and won over£10,000.

30

PART TWO

The mathematicsand science of gambling

31

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32

M A T H E M A T I C S

Biaise Pascal was of poorhealth, and throughout hislife his work wasinterrupted by illness. Heeventually retired to andbbev to meditate, but notbefore he had ensured hisfame by discoveries in thefield of probability. Hehad a long correspondencein the 1650s with Pierre deFermât, with whom he islinked as the founder of thetheory of probability.

• he basis of gambling is uncertainty. No-body wins money by betting on an outcomewhich is certain to occur, unless the otherparty to the wager is stupid or misinformed.When A bets B at level stakes that event Ewill occur, he is backing his judgment that Eis more likely to occur than not. He may basehis opinion on knowledge or guesswork. Thewager is only possible because B, having alsobased his opinion on knowledge or guesswork,has come to an opposite conclusion.

A bettor on a horse race might be backinghis knowledge of the form and peculiarities ofthe horses and jockeys engaged in the race.A man who wants to gamble for the sake of itmight bet, for example, that the next throw of atrue die will result in a 6 being thrown. Hisopinion is based only on guesswork, sincethere are no grounds for believing that a 6 ismore or less likely to be thrown than anyother number.

Whatever his method, each of the bettorswill have either a good or a bad bet. The firstman will have a good bet if he accepts odds of20-1 about a well-fancied horse in a field ofeight, or a bad bet if he accepts 2-1 in an openhandicap with a large field. The second manwill have a good bet if he accepts odds of morethan 5-1 and a bad bet if he accepts less. Hischances can be precisely calculated.

The ability to calculate chances is of primeimportance to the gambler. It might bethought that, since the outcome of a chanceevent by definition cannot be predicted, itmust occur in a sense accidentally, and canobey no laws. However, the theory of proba-bility and the law of large numbers giveindications of the outcome of chance events.They should not be underrated as they are thenecessary foundations for much of the mostadvanced theories of science. The theory ofprobability was first studied and defined bymathematicians in connection with problemsof gaming. It is now the basis of commercialbusinesses like insurance, and essential to allbranches of physics, chemistry, astronomyand the exploration of space.

Games upon which money is wagered fallinto three categories: games of skill, games ofchance and games where both skill and chanceplay a part. Games of skill are not necessarilymore complex than games of chance. The

child's card game called snap is a game of pureskill, as a player has nothing but his ownabil i ty to help him win. Noughts and crossesis also a game of skill. Two good players willdraw every game they play. Bridge and pokerare card games in which both skill and chanceplay a part. Poker players assert that poker isthe more skilful game as the best players winmore consistently. Most casino games aregames of chance.

Theory of probabilityAlthough casino games are in general simple,an even simpler way to begin considering thetheory of probability is to study the tossing ofcoins.

If a double-headed coin is tossed, it iscertain (barring the almost impossible even-tuality of it landing on its edge) that it will landhead uppermost. The chance of tossing a headis 100 per cent, of tossing a tail 0 per cent. Atrue coin might be defined as one which whentossed is as likely to fall head uppermost astail uppermost. In this case the chance oftossing a head would be 50 per cent and a tail50 per cent.

It is usually more convenient, as it helps inthe calculation of more complex questions ofchance, to call the 50 per cent chance of a heada probability of \. There are two possibleresults with a true coin, a head or a tail, eachwith a probability of ^. The probability of oneresult or the other is \ + \, or 1. Since theresult has to be a head or a tail, a probabilityof 1 represents a certainty.

If two coins are tossed there are four pos-sible outcomes. If we abbreviate heads to Hand tails to T, the four outcomes are HH, HT,TH, TT. They are equally probable, so theprobability of each is \. The third outcome ismerely a reversal of the second. Each is of onehead and one tail, so the probability of a headand a tail appearing is \ + \ = |. If it is notnecessary to differentiate between the coins,it might be said that there are three outcomesto the tossing of two coins, as follows:Two heads (HH) : probability \One head, one tail (HT, TH) : probability \Two tails (TT) : probability ^

To refer to the chance of tossing two tailswith two coins as a probability is to give theword a different meaning to its everyday one.

33

P A R T T W O To describe an event as probable in ordinaryusage is to say that it is more likely to happenthan not. To toss two consecutive tails is bythis definition an improbability. But in proba-bility theory both the likelihood or the un-likelihood of an event is expressed as aprobability, ranging from 0 (an impossibility)to 1 (a certainty).

The theory of probability states that:The probability of an outcome to an event(provided that all outcomes are equally likely)is the number of cases favourable to that out-

Table

Odds

1-100

1-501-40

1-331-25

1-20

1-101-8

1-7

1-6

1-5

2-9

1-4

2-7

30-100

1-3

4-11

2-5

4-9

1-2

4-7

8-13

4-6

8-11

2 : 1 Odds converted to

PercentageProbability

99-009998-039297-561097-0588

96-1538

Odds

4-5

5-6

10-11

20-21

evens95-2381 ! 21-20

90-909188-888987-500085-714383-333381-818280-000077-777876-923175-000073-333371-428669-230866-666763-636461 -904860-0000

57-8947

11-106-55-4

11-86-4

13-87-4

15-8

2-1

9-4

5-2

11-4

3-1

7-2

4-1

9-2

5-1

11-2

Percentages


55-555654-5455

52-381051-219550-000048-780547-619045-454544.4444

42-105340-0000

38-0952

36-3636

74-7826

33-333330-769228-571426-6667

25-000022-2222

20-0000

18-1818

16-6667

15-3846

Odds

6-1

13-27-1

15-2

8-1

17-2

9-1

10-1

11-1

12-1

13-114-1

15-1

16-118-1

20-1

22-1

25-1

28-1

33-1

40-1

50-1

66-1

100-1


14-2857

13-3333

12-5000

11-7647

11-1111

10-5263

10-0000

9-0909

8-3333

7-6923

7-14286-6667

6-25005-88245-2632

4-7619

4-3478

3-8462

3-4483

2-94122-43901-96081 -49250-9901

Table 2:1 shows the oddsquoted by bookmakersconverted to percentageprobabilities. I/odds of6-4, 2-1 and 11-4 areoffered in a three-horserace, the percentageprobabilities relative tothese odds add up to 100per cent, showing thatthe odds are fair.

come divided by the total number of casespossible.

This law can be expressed by the formula

P = N

Where P is the Probability, n the favourableoutcomes and N the total outcomes.

It is essential to note the phrase 'providedall outcomes are equally likely' . If told thatfive women and three men were to compete ina race, it would not be correct to say that thereis a probability of f that a woman will win. aswe cannot say all outcomes are equally likely.

;r-

t

As was mentioned earlier, probability nenot be expressed as a fraction. A probabilityof | might be expressed as 0-25 or 25 per cent.Bookmakers invite bets by offering odds,which is another way of representing a proba.bility. If an outcome has a probability of ithere are three chances of it not occurring toone chance that it will. The odds in favour ofthe outcome are 1 to 3, or, conversely, the oddsagainst the outcome are 3 to 1 (usually written3-1). For those who like formulae, the oddsO against a favourable outcome of an eventare the unfavourable outcomes N — n to thefavourable outcomes n. Thus O = (/V —/?) ton. Table 2:1 converts various odds to per-centages.

To continue the analysis of the resultstossing coins, we will imagine a coin tossed1

five times and list all the possible outcomes.Table 2:2 gives all the possible results.

The 32 results in Table 2:2 can be sum-marised as follows:5T occurs once: probability jj, or 0-03125, or3-125 percent. Odds against 31-1.4T, 1H occurs 5 times: probability ^, or0-15625, or 15-625 per cent. Odds against 27-513T, 2H occurs 10 times: probability y^, or0-3125, or 31-25 per cent. Odds against 11-5.2T, 3H occurs 10 times: probability y^, or;0-3125, or 31-25 per cent. Odds against 11-5,'IT, 4H occurs 5 times: probability ^, or0-15625, or 15-625 per cent. Odds against 27-5.5H occurs once: probability , or 0-03125, or3-125 per cent. Odds against 31-1.

It will be seen that the bottom half of thesummary repeats the top half: the probabilityof 2T, 3 H is the same as 3T, 2H.

When tossing a coin, there are two possibleoutcomes; when throwing a die, there aresix. If the die is true, the probability of throw-ing any of the numbers 1 to 6 is equal to theprobability of any other. If we want to throw,a 1, there are six equally likely outcomes, oiwhich one is favourable. Therefore, the proba-bility of throwing 1 is £, and the odds against5-1.

If we throw two dice, there are six possibleoutcomes of throwing the first die, and sixpossible outcomes of the second die, so thepossible outcomes are 36. Figure 2:1 showsthese 36 possible outcomes. In Figure 2 :1 , thetwo dice are shown in different colours toemphasize the fact that there are 36 possi-bilities. It is very easy, particularly with morecomplex and less familiar examples, to over-look some of the possibilities. For example,although there are 36 ways in which the dicemay fall, there are only 11 possible totals, allthose from 2 to 12. If the dice were identical,it could be said that there are only 21 outcomes,since, for instance, 4:3 is indistinguishablefrom 3:4. The 4 could be thrown with eitherof the two dice. This is obvious if the dice aredifferent colours; when the dice are identicalthe distinction is easily overlooked.

34

Trial

1

20

23

24

25

26

28

29

30

31

32

The probabilities can be summarised asfollows :Total 2 occurs once: probability 37,, or 0-0278,or 2-7778 per cent. Odds against 35-1.Total3 occurs twice: probability -fg, or 0-0556,or 5-5556 per cent. Odds against 17-1.Total 4 occurs 3 times: probability yj, or0-0833, or 8-3333 per cent. Odds against 11-1.Total5 occurs 4 times: probability £, or 0-1111,or 1 1 - 1 1 1 1 per cent. Odds against 8-1.Ttotal 6 occurs 5 times: probability ^, or0-1389, or 13-8889 per cent. Odds against'31 5.


Total Possible combinations

QQQQQQ

10

Total 7 occurs 6 times: probability ^, or 0-1667,or 16-6667 per cent. Odds against 5-1.Total 8 occurs 5 times: probability -j^, or0-1389, or 13-8889 per cent. Odds against 31-5.Total9 occurs 4 times: probability ^, or 0-1111,or 11 • 1111 per cent. Odds against 8-1.Total 10 occurs 3 times: probability yj, or0-0833, or 8-3333 percent. Odds against 11-1.Total 11 occurs twice: probability^, or 0-0556,or 5-5556 per cent. Odds against 17-1.Total 12 occurs once: probability jg, or 0-2778,or 2-7778 per cent. Odds against 35-1.

The decimal and percentage probabilitiesare to four places of decimals. It can be seenthat in each case a recurring decimal is in-volved. It is interesting to note that the proba-bility of throwing 7 with two dice is the sameas throwing any number with one die.

Galileo was one of the first mathematiciansto work out a problem concerning chance,when he was asked to explain why a total of 10was more likely when throwing three dice thana total of 9. It is a simple problem nowadays,and can be worked out by drawing a figuresimilar to Figure 2:1. It will be a laborioustask, as there are 6 x 6 x 6 = 216 possible

Table 2:2 (left) shows the32 possible results of tossinga coin five times, from fiveheads to five tails, and thepossible combinations ofheads and tails between.Figure 2:1 (above) showsthe 36 possible outcomesof throwing two dice,indicating that 7 is thelikeliest total, and 2and 12 the unlikeliest.

35

P A R T T W O outcomes with three dice. It will be found thatthere are 25 ways to achieve a total of 9, theprobability being ^, or 11-5741 per cent.There are 27 ways to throw 10, probabilityjfg, or 12-5000 per cent. Early gamblers mighthave been misled by the fact that there are sixways of throwing both 9 (1 :2 :6 , 1:3:5, 1:4:4,2:2:5, 2:3:4, 3:3:3) and 10 (1 :3 :6 , 1:4:5,2:2:6, 2:3:5, 2:4:4, 3:3:4). Different colour-ed dice would have shown that some of thesecombinations are more probable than others,although it must be said that gamblers, even

Early in the seventeenthcentury Galileo wrotedown some thoughts aboutdice games, in which heexplained why a total of10 is more likely whenthrowing three dice than atotal of 9, a question askedhim by a gambler, possiblyhis employer, the GrandDuke of Tuscany.

before the theory of probability was formu-lated, were astute enough to realise that 10was more probable than 9 even though thedifference was less than 1 per cent.

Independent or mutually exclusive eventsWhen considering the probability of two ormore events occurring, we must decide whetherthey are independent or mutually exclusive. Forexample the probability of throwing a double1 with two dice is the product of throwing 1with the first die and 1 with the second die,i.e. ç x g- = jg. The two events are indepen-dent, since whatever happens to the first diecannot affect the throw of the second. If we

want to throw 1 and 6, in that order,probabilities are still multiplied, and remain3g. But suppose we want to throw 1 and 6 jrany order? We do not mind if the first die jjeither 1 or 6, as we will still be in with a chanceBut with the first die, if 1 falls uppermostclearly it rules out the possibility of 6 beinouppermost, so the two outcomes, 1 and 6.mutually exclusive. In this case, the proba-bility of throwing 1 or 6 with the first die is thesum of the two probabilities, i + è = i- Theprobability of the second die being favourableis still g, as the second die can only be onespecific number, a 6 if the first die is 1. andvice versa. Therefore the probability of throw-ing 1 and 6 in any order with two dicei v i — JL3 x 6 — 1 8 •

If we draw a card from a standard pack ofplaying cards, the probability of drawing anAceisyjoryj, since there are four favourableoutcomes (four Aces) and 52 equally possibleoutcomes (52 cards). The probability of draw-ing two Aces successively, if the first Ace isreturned to the pack, which is then shuffled,is TT x T5 = T69- But if we draw two cards,hoping for two Aces, the probability is forthe first Ace, but only y\ or TV for the secondAce, since there remain in the pack three Acesamong 51 cards. So the probability of thedouble event is yj x r? = 221- In tnis case- thetwo draws of the card are not mutually exclu-sive, since drawing the first Ace does notexclude the possibility of drawing the secondAce. The two events are independent, butremoving the first Ace from the pack hasaltered the probability of drawing the second.The probability of drawing any pair of cards isTV, as whatever card is drawn first, there willremain in the reduced pack of 51 cards threeto match it.

Converse probabilitiesSometimes it is necessary when working outthe probability of an outcome involving morethan one event to use the converse probability,which is the probability of the outcome notoccurring. For example, the probability ofthrowing a 6 on a die is ç, therefore theprobability of a 'non-6' is 1 — = f.

Converse probabilities are used to work outsuch problems as: what is the probability ofthrowing exactly one 6 with three separatedice? We must imagine the dice to be separatecolours, say red, white and blue. The chanceof the red die being 6 is ^, when we wouldrequire the white and blue dice to be 'non-6s'.Each has a probability of f of being 'non-6'.Therefore the probability of the red die onlybeing 6 is £ x £ x f, or . The probabilities ofonly the white die or only the blue die being 6are the same. So the probability of one die onlybeing 6 is rfk + Tfk+ rfk = rre or 34-7222 percent. Notice that these three probabilities areadded, since the outcomes are mutually exclu-sive: i.e. the first term A5

S contains all the36

n'lbncej

post,eing

arefoba-|sthe

The-able

oneand

irow-Ice is

anJ-ablejsibleI raw-Ice is !

irds,3 fyfond^cesthe1

the>cclu-

notbond

buthas

lond.Ids is

willIhree

outlore

fl i ty,not

ofthe

|ng')nlperare

kclu-the

•hanccs of the red die being 6 and the othersn_(V. which excludes all the chances in the

•econd term y^, in which the white die showsthe 6.

Converse probabilities are used to work out,|1C well-known birthday problem. Manypeople find the answer surprising. The prob-lem is: how many people must be gathered in aroom together before it is likely that two ofthem share the same birthday? We will ignorethe complication of leap years in working thisout When the first person announces hisbirthday, the probability of the second personsharing the same birthday is ^T. Conversely,the probability of the second birthday beingdifferent is ffy. When two birthdays areknown, the probability of the third beingdifferent is f£f, as there are now two 'favour-able' outcomes among 365. The compoundprobability of birthday 2 being different frombirthday 1. and of birthday 3 being differentfrom the other two, these being independentoutcomes, is

365 x 364 x 363365x365^x365

where y|| has been added to the fractionmerely for the convenience of keeping thenumber of terms in the fraction equal to thenumber of birthdays announced. All that isnecessary now is to continue adding terms tothe fraction until it equals less than |, sinceas soon as the probability is less than \ that allbirthdays are different, the probability isclearly more than \ that any two are the same.The fraction drops to less than \ with 23 terms,so it is more likely than not that in anygathering of 23 or more persons, two of themwill share a birthday. Any directory of the'Who's Who' type will verify this fact. Only 40people need be present for the 'coincidence'of two of them having the same birthday tobecome an 8-1 on chance. In a company of100 employees the odds are more than threemillion to one on that two share a birthday.

The birthdays proposition is one where agambler who can estimate probabilities canmake money from unsuspecting punters. Thethree bags problem is one where even thosewho are practised in calculating odds can gowrong, and it shows the necessity when deal-lr>g with probabilities of taking care to countthe 'equally probable outcomes'. One bagcontains two red balls, another a red ball anda white ball, and the third two white balls.Suppose you draw a ball from a bag chosenat random and it is red. What is the probabi-'% of the other ball in the bag being red?Clearly the bag chosen was not that with twowhite balls, so it must be either the bag withtW'o red balls, in which case the remaining ball18 red, or the bag with one ball of each colour,111 W'hich case the remaining ball is white. So

the probability of the remaining ball being redis j, or it is an even chance that it is red orwhite. That sounds logical but it is quitewrong. When making the original choice, youhave three chances of picking a red ball, allequally likely. Two of those red balls are inthe first bag, in which case, the other ball isalso red. Only one red ball has a white ball asits companion. Therefore you have twochances of finding another red ball in the bag,and only one chance of a white ball, and thecorrect probability of the ball left in the bagbeing red is f. In other words it is twice aslikely that the ball you have drawn is from thebag with two reds than from the bag with a redand white. The fallacy in the earlier reasoninglay in the assumption that it was equallylikely that the ball drawn came from eitherone of the two possible bags. This exampleshows that taking short cuts when workingout probabilities can lead to disaster. It isusually best to begin at the beginning.

Periodic eventsSo far we have discussed probabilities interms of outcomes either occurring or notoccurring, but sometimes the gambler willwish to know the probability of an outcomeoccurring within a given time or during a givensequence of events. If a given event must occurexactly twice in 2 years, then if one year ischosen as a unit of time, and the occurrencesof the event are called E, and E2, there arefour possibilities:

Year A Year B1. E j , E 2 —2. E! E2

4 F F^T . -— L j , n, 2Note that these possibilities are similar to

the tossing of two coins, and that care hasbeen taken not to reduce the possibilities tothree by combining 2 and 3 as one possibility.It follows that if an event must occur twiceonly in two years, the probability of it occur-ring at least once in either year is |. Only inpossibility 4 does the event not occur in yearA. There is a formula to work out theseprobabilities.

If an event must occur exactly x times in aperiod divided equally into N smaller periods,then the probability of the event occurring atleast once in any small period is

Nx-(N-\y


Nx

Thus, if an event must occur four times inten years, the probability of it occurring in thefirst two years is

54-(5-l)4 = 625-256 = 369

54 625 625or 0-5904

or much better than 50 per cent.The Chevalier de Mere, a rich Frenchman

37

P A R T T W O who liked gambling, was responsible for invit-ing the philosopher and mathematician BiaisePascal to carry out some of the earliest workon probability theory. De Mere played agambling game in which he bet that he couldthrow a 6 in four throws of a die. De Mereprogressed from this game to betting that withtwo dice he could throw a double-6 in 24throws. It was known that the odds were inhis favour with the first game, and gamblersof the time reckoned that as four is to six (thenumber of ways a die can fall) as 24 is to 36

probability of not throwing a 6 in fouris

Pascal, right, was asked hyAntoine Gombaud, leChevalier de Mere, towork out how many timeshe must throw two dice togive himself at least aneven chance of throwingtwo 6s, and is generallycredited with discoveringthe answer, although hiscorrespondence withFermât suggests thatFermât might haveprovided the key.

(the ways two dice can fall), the second gameshould be as favourable. The Chevalier deMere was not satisfied with this assumption(legend has it he began to lose money), andasked Pascal to work out the true proba-bilities.

To work out these two problems it is neces-sary to work out converse probabilities. The

6 6 6 6625

1296Therefore the probabili ty of throwing a|

least one 6 is

As an even-money proposition, therefore,a bet to throw a 6 in four throws of a die isslightly in favour of the thrower. The proba-bility of not throwing a double-6 in 24 throwsis

35V4

36JThis is clearly a mammoth calculation with

both numerator and denominator containing0

38 digits. The answer is approximately 0-5087,making the probability of throwing a double-6 in 24 throws 0-4913. As an even-moneyproposition, therefore, a bet to throw adouble-6 in 24 throws of two dice is slightlyagainst the thrower.

Various formulae have been put forward todetermine the number of throws necessary tomake the throwing of a double-6 a better thaneven chance. The old gamblers' rule in opera-tion in de Méré's time relied on knowing theanswer to the lowest number of throwsnecessary to give a probability of throwing 6with a single die of more than \. As has beensaid, this was known to be 4, which might becalled the break-even number. According tothe rule the break-even number for the doubleevent (n2) is the probability of success on thesingle event ( P j ) , known to be ^ (the proba-bility of a 6 with one die), divided by the pro-bability of success on the double event (P2),known to be (the probability of a double-6with two dice), multiplied by the break-evennumber of the single event («J, known to be4. Thus

« =

by substitution

In this equation n2 = 24, guessed correctlyby the Chevalier de Mere to be wrong-Abraham de Moivre, in a book The Doctrineof Chances, published in 1716, set out aformula for discovering the approximatebreak-even point (n) as

n = 0-6931

For those interested, 0-6931 is the napieriaflor 'natural' logarithm of 2. The probability "of a double-6 with two dice is y^, so &Moivre's formula gives the answer as 0-6931 *

38

^6 = 24-9516. This gives an effective break-even number of 25, which is correct, althoughHe Moivre's formula gives too high a number,which is only slightly too high when theprobability js small, but may be critically toohigh when the probability is larger. Forexample de Moivre's formula for the break-even number for throwing a 6 with one diegives n = 0-6931 x6 = 4-1586, which givesan effective break-even number of 5, whichis too high, 4 being correct, as we have found,

jt is interesting that John Scarne, in hisfamous book Scarne's Complete Guide toGambling, published in 1961, states that theodds to one should be multiplied by 0-6931.Thus his approximate answer to de Méré'sproblem is n = 0-6931 x 35 = 24-2585. Thisanswer is too low, although it gives the correcteffective break-even number as 25. Scarne'sformula applied to throwing a 6 with a singledie gives the answer « = 0-6931 x5 = 3-4655,again slightly low, but giving the correctbreak-even number of 4. The third formulato find the break-even number is as follows. Ifthe probability of the outcome is , then

n =log 2

logfl-log (a-

In this case, the logarithms are the ordinarylogarithms, to base 10.

The break-even number for throwing adouble-6 thus becomes

log 2log 36-log 35

which, with the use of four figure log tables,gives n a value of 24-6721, thus giving 25 asthe effective break-even number. For throw-ing a 6 with one die, /; = 3-8005, confirming4 as the effective number.

When the Chevalier de Mere asked Pascalto help with this problem Pascal provided himwith his answer, and began a correspondenceabout probabilities with Pierre de Fermât,another French mathematician, which estab-lished probability theory as a new branch ofmathematics.

The law of large numbersThe theory of probability becomes of en-hanced value to gamblers when it is used withthe law of large numbers. The law of largenumbers states that :If the probability of a given outcome to anevent is P and the event is repeated N times,then the larger yV becomes, so the likelihoodincreases that the closer, in proportion, willbe the occurrence of the given outcome to NP.

For example, if the probability of throwinga double-6 with two dice is y^, then the moretimes we throw the dice, the closer, in propor-tion, will be the number of double-os thrown

of the total number of throws. This is,to 3ft

of course, what in everyday language is knownas the law of averages. The overlooking of thevital words 'in proportion' in the above defini-tion leads to much misunderstanding amonggamblers. The 'gambler's fallacy' lies in theidea that 'in the long run chances will evenout.' Thus if a coin has been spun 100 times,and has landed 60 times head uppermost and40 times tails, many gamblers will state thattails are now due for a run to get even. Thereare fancy names for this belief. The theory iscalled the maturity of chances, and theexpected run of tails is known as a 'corrective',which will bring the total of tails eventuallyequal to the total of heads. The belief is thatthe 'law' of averages really is a law whichstates that in the longest of long runs the totalsof both heads and tails will eventually becomeequal.

In fact, the opposite is really the case. As thenumber of tosses gets larger, the probabilityis that the percentage of heads or tails throwngets nearer to 50 per cent, but that the differ-ence between the actual number of heads ortails thrown and the number representing 50per cent gets larger. Let us return to ourexample of 60 heads and 40 tails in 100 spins,and imagine that the next 100 spins result in 56heads and 44 tails. The 'corrective' has set in,as the percentage of heads has now droppedfrom 60 per cent to 58 per cent. But there arenow 32 more heads than tails, where therewere only 20 before. The 'law of averages'follower who backed tails is 12 more tosses tothe bad. If the third hundred tosses result in50 heads and 50 tails, the 'corrective' is stillproceeding, as there are now 166 heads in 300tosses, down to 55-33 per cent, but the tailsbacker is still 32 tosses behind.

Put another way, we would not be too sur-prised if after 100 tosses there were 60 per centheads. We would be astonished if after amillion tosses there were still 60 per cent heads,as we would expect the deviation from 50 percent to be much smaller. Similarly, after 100tosses, we are not too surprised that the differ-ence between heads and tails is 20. After amillion tosses we would be very surprised tofind that the difference, was not very muchlarger than 20.

A chance event is uninfluenced by the eventswhich have gone before. If a true die has notshown 6 for 30 throws, the probability of a 6 isstill ç on the 31st throw. One wonders if thissimple idea offends some human instinct,because it is not difficult to find gamblingexperts who will agree with all the above re-marks, and will express them themselves inbooks and articles, only to advocate elsewherethe principle of 'stepping in when a correctiveis due'.

An understanding of the law of the largenumbers leads to a realisation that whatappear to be fantastic improbabilities are notremarkable at all. but merely to be expected.


39

P A R T T W O

Figure 2:3 (right) convertsthe probabilities of obtainingany total with two dice intograph form and Figure 2:2(jar right) converts theprobabilit ies of obtain inganv number of tails whentossing a coin five times intograph form. Note theregular nature ofboth of the graphs.

The chance of being dealt 13 spades in a bridgehand is one in 635,013,559,600. A man dealtsuch a hand would be staggered, and anybodyseeing the hand dealt would immediatelyexpect (probably correctly) some sort oftrickery. Yet when we consider that the num-ber of bridge hands dealt since the game wasinvented is doubtless many times the largenumber quoted, it would be surprising if ahand of 13 spades had never been dealtlegitimately.

It is frequently stated in books and articles

5 6 7 8 9

Total thrown by two dice10 11

on probability that if a succession of monkeyswere set before a typewriter with limitlesspaper, eventually the complete works ofShakespeare would be repeated by chance.If there are 50 keys on the typewriter, theprobability of the monkey getting Shakespearecorrect is JQ raised to the power of the numberofcharacters (letters and spaces)in Shakespeareplus the adjustments of the typewriter neededfor capitals and punctuation. On this basisthe chance of the monkey typing the word'Hamlet' correctly is one in 15,625,000,000,so to quote the probability of him typing thecomplete works involves a large number indeed.

Probability curvesIf we look back to Table 2:2 we see that theprobabilities of throwing various numbers oftails in five spins of a coin can be expressedas a graph, as in Figure 2:2.

This graph is regular, and always will bewhen probabilities of equally likely outcomesare considered. A graph showing the proba-bilities of the results of throwing two dice isshown in Figure 2:3. The regular nature ofthese graphs can be shown by a practicalexperiment. Imagine a set-up like a pin table,and drop 64 balls into it as shown in Figure2:4. The pins are arranged so that each time aball hits one the probability that it will goright is 4 and that it will go left is \. Imaginethe balls to behave perfectly and that of eachpair of balls to hit a pin one will go left and one

right. The figure shows the distribution of the64 balls at the end of the experiment, and thepaths they have taken. There are seven com.partments at the foot of the pin table arrange.ment and the numbers of balls in each corn-partment from the left are 1,6, 15,20, 15,61,1

Pascal's TriangleIn 1665. three years after his death. Pascal'sfamous arithmetical triangle was published.The first ten lines of Pascal's Triangle areshown in Figure 2:5.

The triangle is easily compiled. Each lineis formed by adding together each pair ofadjacent numbers in the line above. The firstthing to notice about the triangle is how neatlyline 5 summarises the five tosses of a coinshown in Table 2:2 (there are a total of 32possible results of which one contains noheads, five contain 1 head, ten contain 2 heads,ten contain 3 heads, five contain 4 heads andone contains 5 heads). Line 6 shows the num-bers of balls in each compartment in Figure2:5. The Triangle is of great interest togamblers, and provides the answer to ques-tions relating to equipartition and com-binations.

Combinations and permutationsA practical problem for gamblers is the cal-culation of combinations and permutations.A gambler frequently wants to know howmany different ways a smaller number of iternscan be taken from a larger. This occurs inhorse racing, where the number of four-horseaccumulators which can be taken from a totalof eight selections might be required, or inselecting draws for a treble-chance footballpool, where perhaps the number of com-binations of eight draws from ten selections

40

might be needed. Each of these problems is anexercise in calculating combinations, althoughBritish football pools companies and poolsjournalists always refer to the second example,vvrongly, as a permutation.

The answer to both problems is containedjn Pascal's Triangle. The question of howmany four-horse combinations are possiblefrom eight horses is the same question as howmany ways can four heads appear in eighttosses of a coin. In each case you are taking allcombinations of four from a total of eight.

0 0 0 n . O , , 0 0 0

O O , O , , O . O O

y°v« »O\/ \ /

•••A*•VA

denominator. Thus

2or = 20x 19x 18x 17 =4 4 x 3 x 2 x 1

The number 4,845 appears in Pascal's Triangleon the twentieth line.

Earlier in this chapter it was said that theprobability of receiving 13 spades in a bridgehand is one divided by 635,013,559,600. Thereis only one hand possible of containing all 13spades, so the large number is the total pos-sible number of bridge hands, i.e. 5"iC13.


Line Total in line

1024

Figure 2:4 (far left) showsthe perfect result of the pintable experiment describedin the text. Figure 2:5(left) shows the first tenlines of Pascal's Triangle.Notice that line 6, whichdeals with 64 items,corresponds to the finaldistribution of theballs in Figure 2:4.

The fraction is52C = 52 x 51 x 50 x 49 x 48 x 47 x 46 x 45 x 44 x 43 x 42 x 41 x 40

13 1 3 x 1 2 x 1 1 x 1 0 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

A glance along line 8 of Pascal's triangle showsthat there is one combination of eight heads(or one eight-horse accumulator), 8 com-binations with seven heads (or 8 seven-horseaccumulators), 28 combinations of six heads(or 28 six-horse accumulators), 56 combina-tions of five heads (or 56 five-horse accumu-lators) and, the answer required, 70 combina-tions of four heads (or 70 four-horse accumu-lators).

A similar glance along line 10 of Pascal'sTriangle shows that there are 45 combina-tions of eight draws from ten selections. It isnot necessary, however, to have Pascal'sTriangle to calculate combinations. There isa simple formula.

The number of combinations of a articlesfrom a total of n articles is usually writtenC«. The number of combinations of four

articles from 20 is written 20C4. To find thecombinations of four from 20, multiply four(the number in the combination) by everynumber smaller than itself: 4 x 3 x 2 x 1 . Thisbecomes the denominator of a fraction, thenumerator being 20 (the total number ofarticles) multiplied by each number smallerthan itself until there are an equal number of

(four) in both the numerator and

The number 13 multiplied by all the num-bers smaller than itself is known as factorial13 and is usually written 13! If the top line ofthe equation were multiplied by 39! i.e. all thenumbers from 39 downwards multiplied to-gether, the top line of the fraction would be52! If both numerator and denominator of thefraction were multiplied by 39! the fractionwould read

52!13! 39!

This can be easily solved by a table oflogarithms of factorials, although the accuracyof the answer will depend upon the tables used.Four-figure logarithm tables give an answerbeginning 634, 800 . . . , which is about 0-03 percent inaccurate. Table 2-3 gives the number ofcombinations up to eight from a total numberof up to 20.

A combination is concerned only with themake-up of the group in question, for ex-ample, if we want to know how many com-binations of two trap numbers are possiblefrom a six-trap greyhound race, there are

6 x 52 x 1

= 15.

We are not concerned with the order of the41

P A R T T W O

Table 2:3 shows thenumber of combinations ofany number of articles fromanv greater number ofarticles. It shows, forinstance, that there arc252 different iwr.v thatanv five articles canbe taken from ten.

traps in each combination. But if we wanted toforecast the first two dogs home in the correctorder, we need to calculate a permutation.In this case, there are six dogs, each of whomcould finish first, so there are six alternativetrap numbers to supply the winner. For eachof these, there are five alternative trapnumbers to supply the second dog. So thereare 6 x 5 ways, or 30, of forecasting the firstand second dog in a six-dog race in the correctorder. This can be verified from the calcula-tion of combinations. There were 15 combina-

suppose we wanted to know how manydifferent ways a pack of 52 cards could bedealt, the question would be one of permuta-tions. It is like taking a pack of cards, shuff l ingthem, and trying to guess the order of all 52cards. The number of possible orders is 52!,which is a number running to 68 digits. Thesize of this number can be grasped by imagin-ing everybody in the world being given limit-less packs of cards and each person arrangingeach pack in a different order, to a precon-ceived plan. If each person were immortal, and

Table 2 : 3 Combinations : values for "Ca

Total numberof articles

n123456789

1011121314151617181920

number in combinations (a)

2

136

10152128364555667891

105120 .136153171190

3

14

1020355684

120165220286364455560680816969

1140

4

15

153570

126210330495715

1001136518202380306038764845

5

16

2156

126252462792

128720023003436861888568

1162815504

6

17

2884

210462924

1716300350058008

12376185642713238760

7

18

36120330792

171634326435

1144019448318245038877520

8

_____ !-_9

45165495

128730036435

12870243104375875582

125970

<((

(

tions, each of which could be reversed, as thecombination of say, Trap 3 and Trap 4 hastwo orders, 3:4 and 4:3. Therefore there mustbe 1 5 x 2 permutations of the first two dogshome.

Advertisers sometimes run competions inwhich the competitor is asked to place, say,eight items in order of merit. The number ofways this can be done is a permutation ofeight articles. All eight could be first, theremaining seven second, etc., so the numberof ways is

8x7x6x5x4x3x2x1which is 8! and equals 40,320. If the adver-tiser expects 400,000 entries in his competition,he can expect, by using the law of largenumbers, that at random (i.e. discountingselection techniques) about ten competitorswill give the answer corresponding to thejudge's selection. Hence the necessity of askingfor a slogan as a tie-breaker.

Earlier the number of possible 13-cardhands from a pack of 52 playing cards wasgiven. This was a combination, since we wereunconcerned in which order the cards weredealt. Were we concerned with the order, i.e.

arranged a pack of cards a second, the num-ber of years needed to put the packs in allpossible orders would still contain over 50digits. And this inconceivable number canbe written with three characters: 52!

EquipartitionAnother glance at Pascal's Triangle willanswer the following question. When tossinga coin, what is the probability that after «events, the number of heads will equal thenumber of tails? Clearly this can happen onlywith an even number of events. Those whobelieve the 'law of averages' fallacy maintainthat the probability of equipartition, as it iscalled, increases with the number of events.Pascal's Triangle proves the opposite. Line 4shows that if we toss four times, there are 16possible outcomes, of which six contain twoheads and two tails. The probability of equi-partition is -j^. Line 6 shows that with sixtosses, the probability of equipartion is %ï-Line 10 shows that w i th ten tosses, equiparti-tion is a r^fj. chance. The probabilities arebecoming smaller as the tosses increase.

The formula to discover the probability of42

IHJpa ifthe

i

dkacliwaldie!seelon.I3x1C0l|thc|cqi

M cithaicen|apf

isdifileqi

stallofsoolequlgaianilcul

spnlblal

spulpariblaiIfbilifbee]

equ|elatofsPiistilllgoo|spirtha

One

,qUipartit ion in /; events is to divide thenumber of combinations which give equi-trirtition (in the case of coin-tossing "CJ by1 ~2the number of possible outcomes (2").

What is the probability, when tossing sixdice, of throwing each number once i.e.achieving equiparti t ion? The total number of\vays equipartition can occur is 6! The firstdie can clearly be any of the six numbers, thesecond die one of the five remaining, and soon, giving a total number of ways of 6 x 5 x 4 x3 x 2 x 1 = 720. The number of possible out-comes is 66, since there are six ways each ofthe six dice can fall. So the probability ofequiparti t ion is

- 2 ,46, 656or 0-0154, or 1-5432 per cent.

Most people would be surprised to discoverthat if you threw six dice, on about 98| percent of occasions at least one number willappear more than once.

If there are seven children in a family, whatis the probability that they were born ondifferent days of the week? This is a question ofequipartition, the answer being 7! divided by77. The answer is 0-6120 per cent.

Some gamblers might be tempted to basestaking plants on the theory that in any seriesof even-money events there must come a timesooner or later when the outcomes reachequipartition. This theory is not true, and if agambler backs black at roulette, for example,and the first winner is a red, there is a cal-culable chance that black will never catch up.

Table 2 : 4 lists the 16 possible results of fourspins of a roulette wheel in terms of red andblack, ignoring zero. In six cases there isequipartition at the end of the series of spins.It can be seen that in three cases black has ledthroughout, and in three cases red has ledthroughout. In other words, the number ofseries in which equipartition has never beenreached equals the number of series in whichequipart i t ion is the state at the end.

This equality holds true for any number ofspins. After 20 spins, the probability of equi-partition is 0-1762, which is the probability ofblack or red having been ahead throughout.If we specify a colour, say black, the proba-bi l i t y is 0 - 1 7 6 2 x 0 - 5 = 0-0881 tha t black hasbeen constantly ahead (or behind).

Thus a gambler backing black, who needseRuipartition or better before 20 spins havelapsed to save his stakes, faces a probabilityof 0-0881 that he will lose. Even after 1.000spins there is a probability of 0-0126 that he isstill behind. So even if his staking plan were sogood that he could stand being behind for 999spins, there is still a 1^ per cent probability•hat he will lose.

Fair or unfair gamesof the most valuable uses to which a

gambler can put his knowledge of proba-bilities is to decide whether a game or proposi-tion is fair, or equitable. To do this a gamblermust calculate his 'expectation'. A gambler'sexpectation is the amount he stands to winmultiplied by the probability of his winningit. A game is a fair game if the gambler'sexpectation equals his stake.

If a gambler is offered 10 units each time hetosses a head with a true coin, and pays 5units for each toss is this a fair game? Thegambler's expectation is 10 units multiplied by


10

12

13

14

15

16

the probability of throwing a head, which is j.His expectation is 10 units x^ = 5 units,which is what he stakes on the game, so thegame is fair.

Suppose a gambler stakes 2 units on thethrow of a die. On throws of 1, 2, 3 and 6 he ispaid the number of units shown on the die.If he throws 4 or 5 he loses. Is this fair? Thiscan be calculated as above. The probabilityof throwing any number is £, so his expecta-tion is | on number 6, f on number 3, f onnumber 2 and £ on number 1. His total expec-

Table 2:4 shown thepossible results, in terms ofblack /red and ignoringzero, from four spinsof a roulette wheel.

43

P A R T T W O talion per throw is therefore | + | + f + ^which equals 2, the stake for a throw, so thegame is fair.

It is usually easier in cases like this to use thelaw of large numbers to work out the gam-bler's expectation. Over a series of tosses he"expects" each number to appear an equalnumber of times. There are six possibleequally likely results from throwing a die. Heassumes a series of six throws in which eachnumber appears once. His expectation is six(for throwing 6) plus three (for 3) plus two (for2) plus one (for 1), total 12 units. His stake forthe six games is 12, so the game is fair.

Most games played in a casino are unfair,otherwise the casino would not pay for its up-keep or make a profit. Casinos do not intend(at least, not often) to mislead, so it is perhapsbetter to call the games inequitable rather thanunfair. In these cases the gambler does notwork out if the game is fair, but rather howlarge is the inequitability.

The inequitabili ty of various casino gamesand other gambles will be dealt with when thegames are discussed in their respective chapters.

Suppose, as a last example, a gambler wereasked to draw a card from a standard packand is paid 10 units when he draws an Ace.But if he does draw an Ace. he is to put it toone side and is to draw another card. If this isan Ace he is paid a further 40 units. Each drawcosts him one unit, except the draw for asecond Ace, which is free. Is this a fair game?

The probability of his drawing the first Aceis yj, and he is paid 10 units, so his expectationis yjx 10 = 0-7692 units. The probability ofdrawing two Aces is yj x = jyr, and he ispaid 40 units, so his expectation is 0-1810. Histotal expectation is 0-9502 units. As his stakeis one unit, the game is unfair.

Worked out by the other method, thegambler can expect to draw on average thetwo Aces once in 221 attempts. In theseattempts, he will draw the first Ace 17 times(as the probability is or ^). On these 17occasions he will draw the second Ace once(probability yY or \-j). His expectation on 221attempts is therefore 17 x 10 plus 1 x 40 =170 + 40 = 210. He will have paid 221 unitsto receive 210, so his expectation is 0-9502,which tallies with the previous result. In otherwords, he will receive 95-0226 per cent of hisstakes back, an advantage to the 'bank' ofnearly 5 per cent.

Five per cent is quite a large percentage tofight against. If the above game were playedin a casino, the five per cent would be referredto as the 'house edge'. The law of large num-bers states that the more the gambler playsthis game, the closer will be his losses to 5 percent of his stakes. If he plays the game 1,000times during a year, his losses will be around50 units. If a casino played the game a milliontimes during a year against various gamblers,

it could look forward to the game producinga profit of 50,000 units on the year.

Prospects of ruinationWhen we talk of fair games, there is anotheraspect to the question which experiencedgamblers know about, and which all gamblersmust remember. If a game is fair by the abovecriterion, it nevertheless is still true that if it isplayed unti l one player loses all his money,then the player who started with most moneyhas the better chance of winning. The richerman's advantage can be calculated.

The mathematics required to arrive at theformula are complex, but it can be shown thatif one player's capital is c and another player'sis C, then the probability that the player whobegan with c is ruined in a fair game played to a

conclusion is —-—, and the probability that he

will ruin his opponent is —-—;.

Suppose player X, with 10 units, plays an-other player, Y, with 1,000 units. A coin istossed and for each head player X pays playerY one unit, and for each tail player Y paysplayer X one unit. The probability of player X

10ruining player Y is 1000+10or ior100

Player Y

has a probability of j^y of ruining his op-

ponent, an advantage of over 99 per cent.This overwhelming advantage to the player

with the larger capital is based on a fair game.When a player tries to break the bank at acasino, he is fighting the house edge as well asan opponent with much larger resources.Even a small percentage in favour of thecasino reduces the probability of the playerruining the casino to such an extent that hischance is infinitesimal.

Gambling organisation's advantageWhen a professional gambling organisationlike a casino, a bookmaker or a totalisator orpari-mutuel company offers bets to the publicthere must be a percentage in its favour tomake it as near-certain as possible that it willwin over a period of time. The three main waysthis is achieved are as follows.

Pari-mutuel or totalisator systemThis system cannot lose, since it operates onthe same principle as a lottery, returning towinners a proportion of the total stakes. It isthe system used to bet on horse races in mostparts of the world. It was invented in Paris in1865 by Pierre Oiler. In France it is called thepari-mutuel, in English-speaking countriesusually the tote, short for totalisator, theequipment used to register and indicate thetotal bets and dividends.

In different countries, there are different44

ornools to accommodate daily doublestrebles and to accommodate betting on horsesto win, or to finish second or third. The per-centage taken from the pool for runningexpenses, profit and state taxes varies fromcountry to country. Examples provide thebest explanation of how the tote works.

In Britain, the tote percentage was takenfrom the win pool in the 1970s as follows. Thewin pool is the stakes placed on particularhorses to win only. If the winning stakes weremore than 50 per cent of the total pool, no

cent, the share-out for winners is only about30 per cent of the total pool, probably theworst deal offered to any punters yet wellover £1 million is staked weekly.

BookmakersThe art of making a book is to 'balance" it sothat a profit is made no matter what the out-come. If betting on an event where there areonly two outcomes, such as the Oxford andCambridge boat race, the bookmaker mightopen his book by offering odds of 2-1 on


deduction was made. If the winning stakeswere between 7 per cent and 49-99 per cent,then the deduction was 30-9 per cent of whatremains after twice the value of the winningstakes had been subtracted from the totalpool. The deduction from the total pool whenthe winning stakes represented less than 7 percent of the pool was based on a sliding scaleranging from 38 per cent when winning stakeswere less than 3 per cent of the pool to 27 percent when the winning stakes were between 6and 7 per cent.

For instance, if the total pool were £5,000and the winning stakes were £1,200, the win-ning stakes represented 24 per cent of the pool,and the deduction was 30-9 per cent of £5,000less twice £1,200. The deduction was there-for £803. Thus £4,197 was paid out to winners,a dividend of 25p to lOp staked.

In New York, the deduction is 15 per centof the total win pool, rounded down to thenearest 5 cents in the dollar. Let us assume atotal pool of $50,000 and winning stakes of$12,000, to keep the proportion the same as inthe British example. The deduction would be15 per cent of $50,000, or $7,500. If $42,500were to be shared by the holders of the winningtickets, the dividend per dollar would be$3-54. This would be rounded down to thenearest 5 cents, which would give $3-50 to $1,and the declared dividend would be $7 for a$2 win ticket. In this instance, therefore, theNew York bettor gets exactly the same returnas his London counterpart.

A British football pool works on a similar°asis to the above, but with government tax°n the total pool of 40 per cent and the poolsc°rnpany taking a further commission tocover expenses and profits of around 30 per

Cambridge and 6-4 against Oxford. By usingTable 2:1 we can see that 2-1 on representsa probability of 66-67 per cent, and 6-4against represents 40 per cent. The proba-bilities add up to 106-67. The excess of 6-67over 100 per cent is known as the 'over-round'.The bookmaker, if he can take bets in theproportion of the probabilities, say £66.67on Cambridge and £40 on Oxford, will payout £100 whichever wins on £106.67 taken, apercentage profit to him of 6-25 per cent. Inpractice, of course, the bookmaker will needto adjust his odds in accordance with supplyand demand. More money for Oxford thanthe estimated probability indicates will causehim to shorten the odds against Oxford andlengthen those for Cambridge.

His final book might look like this:For Cambridge£50 at 2-1 on£42 at 4-6 on£50 at 4-5 on

For Oxford£40 at 6-4£32 at 5-4£30 at evens

In this example, he began by seriouslyunder-estimating the fancy for Oxford, andhas been forced to reduce his odds from 6-4to evens, at the same time offering better oddsfor Cambridge. Before adjusting his odds hestood to pay out £100 on Oxford, havingtaken only £90 in stakes.

The odds offered on a horse race with manyrunners are calculated and adjusted in thesame way. The over-round usually increaseswith the size of the field. Typical odds on a16-horse race might be as follows:

7-4 Blue Lamp; 5-1 Soldier; 6-1 TurkishDelight, Ocean Breeze; 8-1 Red Scholar;10-1 Charley's Aunt; 14-1 Archie, Rhino;20-1 Deb's Fancy; 25-1 Horace, FlyingFree; 33-1 any of five others.

Two methods of hackingon the course. Far left,some of the totalisât orwindows at Cheltenham,the main meeting of theBritish National HuntSeason. Left, bookmakersat the Werribee racecourse, 25 miles west ofMelbourne in Victoria,Australia. There are somesignificant differences inthe odds offered aboutsome horses on the boards.

45

P A R T T W O

A hank of unattractive amipurelv functional slotmachines at Las Vegas,designed to collect theloose change ofthe passers-by.

If the odds were converted to percentageprobabilities, the total would be just over 142per cent, an over-round of 42-3 per cent, apercentage advantage to the bookmaker of29-7 per cent.

CasinosA casino makes a profit on games like crapsand roulette on the assumption that the proba-bility of success of every bet can be calculated,and the punter's reward for a winning bet isalways less than it would be were the game fair.

For instance, in roulette with a single zero,the gambler will be paid even money if hebacks red, whereas his probability of winningis Yfg, a casino advantage, or house edge, ofjust over 1-35 per cent. In the long run, thecasino can expect to win 1-35 per cent of allstakes bet on red. This is a very small per-centage compared to those mentioned inconnection with the bookmaker or the tote.But few go into a casino to back red once. Aman entering a casino with £10 might have 100bets at £1 a time with it, in which case he can'expect' to lose £1.35 or 13-5 per cent of hisoriginal £!().

SystemsSo much study has gone into the mathematicsconnected with probability and chance, andsome of the results of that study, like Pascal'sTriangle, seem so magical, that it is not sur-prising that thousands of gamblers haveimagined that they could so manipulate num-bers as to discover a system of betting thatwould guarantee winning. Could a formulabe arrived at that would defeat chance, ortransform the house edge into an edge for thegambler? None has yet been found, but therehave been interesting and ingenious attempts.

Martingale systemPerhaps the best known system is the doubling-up system, known as martingale. It is used oneven-money bets, such as even at roulette, orpassing at craps. The gambler bets one unit,on, say, even at roulette. If it wins he is oneunit up and begins a new series. If it loses hedoubles his stake on the next spin to two units.If it wins, he is again one unit up on the seriesof bets. If it loses, his next stake is four units.

Whenever he wins, he always wins one u n j tmore than his previous losses. Whichever \ \ j nhe decides to stop at, he is always winn ingThere are two drawbacks. The gambler musthave enough money to cover a long losing run.If 20 consecutive spins result in a win for oddthe gambler is losing 1,048,575 units and his21st bet must be this amount plus one. Thesecond drawback is that even if the gamblerwere rich enough to go on, the casino limitwould prevent him. In Nevada casinos, theminimum bet might be $5 and the maximumS300. The gambler can only double up fivetimes. After six losers he is $315 down and hisnext bet must be $320. He cannot make it.And he can expect to lose six consecutivetimes once in 64 spins on fair even-moneychances, once in 47 spins on an Americanroulette wheel with two zeros.

To increase the speed of the profits, arefinement of the martingale system, some-times called the great martingale, is to doublethe stake and add one un i t for each loser. Thestakes progression is therefore 1, 3. 7, 15, 31,etc. The wins are larger, but the house limitis reached after fewer losers.

An increasing stake system which keeps theincrease within bounds is one which requiresthe gambler to begin staking one uni t , and to Iincrease to two after, say, four losses. The [gambler keeps a record sheet on which hewrites a figure 1 for each losing bet, crossingout a figure for each win, so that when he hasa row of four uncancelled Is, he is four units /down. He now increases his stake to two units. ;If he loses, he begins a new row of figure 2s. (If he wins, he crosses out two of the figure Isand when the Is are all cancelled, he beginscrossing out the 2s for each winner. Shouldthe second row reach four uncancelled 2s, thenext stake is three, and a third row is begun,and so on. A win with a stake of three requiresa 1 and a 2 to be cancelled: should the 1 rowbe cancelled, then two 2s are crossed out and a1 added. Whenever a series is cancelledaltogether, the series has recouped its losses.and the stake becomes one unit again. A seriesis only begun with a loser, the profi t comingwith the winning stakes between each series.

If we consider the following results, we cansee how the system works:

WW*LLWLLWLLLLWWLLLWWWLWW*LLLLLLLWLLLWLLLWWLWWWLWWW*WW*LLWW

The asterisks indicate where losing seriesbegin or end.

The record sheet, which would begin withthe third trial, the first two winners havingproduced two units profit, would look like

Figure 2:6.Three times, a series has been started and

eventually cancelled. On the first two occa-sions, the series showed a profit of one uni'

46

iustfun.Md,

hisTheMer

fmittheumfivehisit.

ItiveIney|can

a|me-JbleThe31,mit

theliresi\ to 7

The (

hasInits /

its. I

IsbinsTuld

the[un,liresIrowIda11 ledIscs.IrieslingIs.:an

L'W/W

Inès

LithJ'inglike

andlea-Lit

•hen cancelled, which when added to the twounits won at the start of the sequence, and thetwo units won with a similar winning run nearthe end, make a profit on the entire sequence ofcjx units. As the sequence is a fairly ordinaryone of 25 winners and 29 losers, the value ofthe system is demonstrated. The seven suces-sjve losers in the middle of the sequence whichwould have raised the stake with the martin-gale system to 128 units, and with the greatniartingale to 255 units, has been negotiatedwithout the stake rising above four units. Thedanger of the system is again the long losingsequence which requires a bank out of pro-portion to the eventual profits, but a gamblercontent with small profits in relation to hiscapital will accumulate them if he is preparedto risk the 'impossible' sequence which willultimately occur.

D'Alembert systemThe system called the d'Alembert, also usedon even-money chances, merely requires thegambler to add one point to his stake after aloss and deduct one after a win. It is simple tooperate, and is likely to give the gambler along run for his money, since wins and losseswill accrue slowly. It is partly based, falla-ciously, on the 'law of averages', since it pre-sumes that after a loss a win is more likely thananother loss. It also contains something of themartingale principle, since after a sequence oflosers, the bet which wins will be larger thanany one of the losing bets. In a sequence ofalternate wins and losses, the winning betswill each be one stake larger than the losingbets. On an unexceptional series of spins,where the even chances win equally, a smallprofit should accrue over small periods. It will,however, lose over the long run, as the houseedge will gradually raise the stakes as morelosers than winners appear.

A system which combines principles of themartingale and the d'Alembert involves afirst stake of one unit, followed by successivestakes while losing of 2, 3, 4 . . ., etc., revertingto a stake of one unit after a winner. If thewinner comes at the start of the series, theseries shows a profit of one unit. The seriesshows a profit of one unit when the win is thesecond bet of the series. If the win is the thirdbet, the series finishes level. Thereafter, theseries is a loser, by two units on the fourth bet,and then mounting rapidly, by five units onthe fifth bet, nine of the sixth bet and fourteen°n the seventh. Many gamblers set a limit to'heir stakes by stopping after a given number°f losers, say seven, when they are 28 pointsdown on the series.

If the gambler is backing on true even-money chances, each bet has an expectation^ual to his stake, i.e. no matter what his stakehis return if he wins is twice his stake and hisProbability of winning is \. If his stake is A,"is expectation is \ x 2A = A. His expecta-

tion is the same no matter what his limit. Forexample, if he stops at seven losers, he willlose his maximum, on average, once in 128(i.e. 27) trials. Each 128 trials, he will lose 28units once, 14 un i t s once, nine un i t s twice, fiveunits four times and two uni ts eight times. On16 trials he will finish level. On 32 occasionshe will win one unit by succeeding on thesecond trial, and on 64 occasions he will winone unit by succeeding on the first trial. Over-all, he will be level. But of course in a casinoeach bet will be facing the house edge, and


over a long run the system l ike all others musteventual ly lose.

Cancellation systemThe cancellation system, called the Labouch-ère, is one of the most interesting. A series ofnumbers is written down, say 1. 2, 2, 3. Itcan be any series, of any length. The systemoperates best on even-money chances. Thefirst stake is the sum of the two numbers atopposite ends of the series, in this case1+3 = 4. If the bet wins, the two numbersare crossed out and the next stake is the sumof the numbers remaining at each end of theseries, in this case again four. If the bet wins,the two numbers are crossed out. in thiscase again four. If the bet wins, these twonumbers are crossed out, the series is can-celled entirely, the gambler is eight pointsin profit and begins again. Had the second betlost, the losing stake is added to the series ofnumbers which becomes 2, 2, 4. The nextstake is therefore six units . The beauty of thesystem is that as two numbers are deletedfrom the series after a win, while only one isadded after a loss, the series will eventuallybe crossed out altogether, and when it is theprofit will equal the sum of the series.

Figure 2:6 shows the recordsheet of the increasingstake system applying tothe sequence of resultsincluded in the descriptionof the svstem in the text.

47

P A R T T W O A sample series, say 1. 3, 3, 3, might go asfollows :

Series1,3 ,3 , 31 ,3 3 3 41 , 3 , 3 , 3 , 4 , 53 , 3 , 3 , 43, 3, 3, 4, 13 , 3 , 43, 3, 4, 13,43,4,73,4 ,7 , 104,74, 7, 1 177,7

Bet4567

107

107

101311157

14

ResultLossLossWinLossWinLossWinLossLossWinLossWinLossWin

RunningProfit/Loss

— 4-9-3

-10Level

-7+ 3-4

-14-1

-12+ 3-4

+ 10After a sequence of 14 bets, of which six

have won and eight lost, the series is cancelledfor a profit of ten points, the sum of1+3 + 3 + 3.

If there are n numbers in the series writtendown, the series will be crossed out whenever

w = n + L

W being the number of winners and L thenumber of losers. In other words, if there arefour numbers written down, the sequence winswhenever the number of winners equals orexceeds half the losers plus 2. Four winnersand six losers will win, or ten winners and six-teen losers. The only danger is a long sequencewhich never satisfies the equation. With, say,20 winners and 38 losers, the stake is likely tohave risen to a very high sum. A very longlosing sequence is unlikely, but must comesooner or later, when it is possible that it willbreak the gambler's bank or exceed the casinolimit. The most units the gambler needed inthe sequence above was 27 twice, and if agambler wishes to win ten units only and canrisk 50 units, the chances are that he will win,although if the gambler had not won the lastbet in the example, but had had two morelosers instead, he would have been 43 unitsdown, with his next stake being 32 units.

Cancellation system backwardsThe system can be played backwards, by add-ing to the series the stakes won, and crossingout the stakes lost. In this case it is necessaryfor the gambler to decide the limit of his lossesand to set a target for winnings. If the gamblercan afford to lose 21 points, he might writedown a series 1, 2, 3, 4, 5, 6. His first bet isseven units. If it wins he adds seven to hisseries, making his next stake eight units. If hebegins with three consecutive losers, he willlose his 21 points, but he knows he can lose nomore. On the sequence of results above, hewould have lost his 21 points after six spins.

Bet188

109

12151816141923283329283746

ResultWinLossWinLossWinWinWinLossLossWinWinWinWinLossLossWinWinWin

RunningProfitiL()Ss

+ 7-1+7-3+6

+ 1 8 J+ 33+ 15-1

+ 13+ 32+ 55.+ 83+ 50+ 21+ 49+ 86

+ 132

Let us suppose he is lucky, and the seqikgoes as follows:

Series1 , 2 , 3 , 4 , 5 , 61 , 2 , 3 , 4 , 5, 6, 72, 3, 4, 5, 62. 3, 4, 5, 6, 83. 4, 5, 63, 4, 5, 6, 93,4, 5, 6,9, 123,4, 5,6,9, 12, 154, 5, 6, 9, 125,6,95, 6,9, 145, 6, 9, 14, 195. 6.9. 14. 19.235. 6,9. 14, 19, 23.286.9. 14, 19, 239, 14. 199. 14, 19. 289, 14, 19, 28, 37

Had the gambler set himself a target of 100points, he could stop now 132 points in profit.

PsychologyThe most fruitful research a gambler cancarry out in an effort to gain an advantage is fin the sphere of psychology. It is known that ifa large group of people were asked to choosea number at random between 1 and 10, sevenwould probably be chosen more often thanany other number. When asked to choosebetween heads and tails, more people chooseheads than tails. More people back red atroulette than black. At craps, more peopleback the dice to pass than to lose, despite thehouse edge being slightly larger for passbettors. When picking draws on a footballtreble-chance pool, most people start at thetop, and never reach the bottom of the list.

Can these facts be of help to the gambler?Clearly if a football pool bettor picks hisdraws from the bottom (assuming draws areequally likely in all parts of the coupon, whichmight not be the case) he will expect a betterdividend when successful than if his selectionshad been nearer the top. When betting on ahorse race, a gambler who backs a horseridden by an unknown apprentice might getbetter odds relative to its actual chance thanif he'd backed the mount of the public'sfavourite jockey, say Lester Piggott in Eng-land. In 1948 a horse called My Love won theEpsom Derby, allegedly carrying the moneyof half the female population of England, wholiked its name. Did it thereby start at fais6

odds? Would a horse called Toothache, orGrey Rat, or Housefly, for opposite reasonsstart at a price longer than its ability merits'This seems a more profitable field for studythan the effort to beat a house edge, or a

bookmaker's percentage, by juggling numbers48

+7-3+6- 1 8-33

15-1- 1 3-32-55-83-50-21-49-86132

11005fit.

PART THREE

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Sports on whichgambling takes place

49

P A R T T H R E E

krimitive man no doubt began betting onsports by backing competitors in races andfights. Modern man still bets on such events,although he has trained the faithful horse todo much of his racing for him. He has alsoinvented numerous other sports as outletsfor his physical and emotional exuberance,and it is safe to say that betting takes placeon them all. A prize fighter thumping hisfists into his opponent's face in a sweaty,smoky arena and a tennis champion retrievingthe lobs in the sunshine of a strawberries-and-cream fortnight at Wimbledon are bothlikely to be helping to transfer funds from onegroup of pockets to another.

Horse RacingThe sporting activity with by far the largestgambling turnover is horse racing, whose veryexistence on an organised scale depends ongambling. Chariot races preceded races inwhich contestants were mounted on the backsof horses, and horse-drawn chariots wereknown to be used around 4000 B.C. Arabsbet on thirsty horses that were let loose to runto water, a form of persuasion not unlike theelectric hare used nowadays to get greyhoundsto race. A statuette of a mounted race horsemade in Egypt has been dated at 2000 B.C.which suggests that racing not unlike to-day'stook place four thousand years ago.

Homer describes a chariot race as part ofthe games for the funeral of Patroclus underthe walls of Troy. He also describes an argu-ment between Idomeneus and Aias aboutwho was leading, which resulted in a bet. Inthe 25th Olympic games of 680 B.C. the firstOlympic chariot race was run, and 32 yearslater came the first mounted race.

In more modern times, in 1511, it wasdecided to race for a Silver Bell on the Rood-eye at the Roman town of Chester, England.Racing still takes place on the Roodeye, andon the strength of this some writers claimthat the Chester Cup is the oldest horse racein the world. It is generally conceded thatAmerica's first race track was built at LongIsland in 1665. The first official Australianrace meeting was held in Sydney in 1810.

All the world's racehorses are thorough-bred descendants of three stallions, the ByerleyTurk, captured at Buda in 1688, the Darley50

S P O R T S

Chariots were usuallylira»'» by two or fourhorses, and occasionally byv/v , in the races held in thestadia of Rome. Thechariots turned left roundturning posts as shown inthis terracotta in theBritish Museum. At some

stadia, canals separated thespectators from the coursein case chariots failed toturn properly. Each horse'sreins were joined into asingle rein, so that thecharioteer illustrated holdsfour reins which are alsowrapped round his waist.

51

// iras not until the earlynineteenth century that thegeneral public in Britainbegan to bet on the bighorse races, the biggest ofwhich was the Derby atEpsom. James Pollard'spainting, above, shows thebetting post at Epsom in1830. In the foreground,the public are being inducedto part with even moremonev by a thimble-rigger.Cecil A/din's painting,is of the Grand National of1923, \\-on by the oldesthorse ever to win, SergeantMurphy, a 13-year-old.52

Arabian, bought in Aleppo in 1704, who isthe ancestor of most of today's thoroughbreds,and whose son, Bulle Rock, was the firstthoroughbred to go to America, and theGodolphin Arabian, foaled in the Yemen in1724.

The world's most famous horse race, theDerby, was first run at Epsom in 1780. It wasthe idea of the 12th Lord Derby and SirCharles Bunbury, who decided its name bytossing a coin. Lord Derby won, and if hehadn't one of the results might have beenthat America's greatest race, run on theChurchill Downs near Louisville ever since1875, would be called the Kentucky Bunbury.

The organisation of racing varies incountries with the most flourishing industries,particularly from the point of view of gam-1bling, as various laws have restricted oneform or another of betting.

Horse racing in BritainIn Britain, the main forms of racing are flatracing, which takes place from March tillNovember, and National Hunt racing, whichconsists of races over obstacles, either steeple-chasing, in which the horses jump fences, orhurdling, in which the horses jump less severebarriers called hurdles. The National Huntseason takes place in the winter, but consider-ably overlaps the flat season. There is a thirdpopular form of racing on which betting takesplace, called point-to-point racing. This isunder the jurisdiction of the Jockey Club, therulers of racing, but it is an amateur sport,meetings being social occasions for local [Hunts. It therefore does not command thenewspaper space or the attention of the ordin-ary gambler as flat or National Hunt racingdoes.

The highlights of the flat racing season arthe five Classic races for three-year-olds, °which the Derby, run over 1^ miles at Epsomis the most important. The other Classicare the One Thousand and Two ThousandGuineas, run over a mile at Newmarket,former for fillies only; the Oaks, run over th<Derby course at the Derby meeting, but al>°restricted to fillies; and the St. Léger.

S P O R T S

oldest, run at Doncaster over 1| miles. TheTwo Thousand Guineas, Derby and St Léger,the Classics open to colts and fillies, comprisethe Triple Crown, a much-esteemed objectivefor which there is no actual prize. Severalfamous horses have won the Triple Crown,although there were 35 years between thelast winner, Nijinsky, in 1970, and the previouswinner, Bahram. Other famous Classic winnersof recent years have been Grundy, the Derbywinner of 1976; Mill Reef, the 1971 Derbywinner who also won the Prix de l'Arc deTriomphe; Sir Ivor, Guineas and Derbywinner of 1968; Pinza, the mount of GordonRichards when he won his only Derby in 1953,beating the Queen's horse in CoronationYear; Lord Rosebery's Blue Peter, whowould have won the Triple Crown in 1939had not the war intervened; and Hyperion, asmall horse who won the Derby for LordDerby in 1933 and who became one of themost successful stallions in the world. ADerby winner who must rank with the bestls Sea Bird II, who came over from Franceto win easily in 1965. Fillies have the oppor-tunity to win more Classics than colts, as theyQan race in all five, although few attempt theDerby and the Oaks, which are run at the sameMeeting, or both Guineas races. Two of the§reatest of all fil l ies were the peerless Sceptre,who in 1902 won four Classics, being beaten°nly in the Derby, and Pretty Polly, who won[ne One Thousand Guineas, Oaks, and St.Le?er of 1904. More recently, Meld in 1955

won the same three races as Pretty Polly, asdid Sun Chariot, who won wartime sub-stitute races in 1942. Fillies have managed towin the Derby and then the Oaks a couple ofdays later, the last, apart from Fifinella in aFirst World War substitute race, being Sig-norinetta, who won the Derby of 1908 at100-1 and followed up with the Oaks at 3-1.

The best meeting in Britain is the RoyalAscot meeting, in which every race is a 'bigrace', including the Gold Cup, the principalprize for stayers, and big handicaps like theAscot Stakes and Royal Hunt Cup. Otherfamous meetings, where the best of Britishracing is staged, are at Goodwood, York andChester.

The 'Ascot' of the National Hunt seasonis the Cheltenham meeting which includes theGold Cup, for steeplechasers, and the Cham-pion Hurdle. The winners of these two races

The Grand Nationals of1973 (above) and 1974,were both won by Red Rum,the greatest of all horsesover the Aintree fences.The thirty stiff fencesspread over 4 miles 856yards make the GrandNational a law unto itself,and Red Rum could giveweight and a beating overAintree to horses whowould beat him easily overpark courses. Red Rum isthe horse with the yellowdiamond on his back justclearing the fence in the1974 race picture (left).

53

P A R T T H R E E

i.

Ark le, number 6 in thepicture above, is generallyacknowledged to be thegreatest steeplechaser of alltime. He is seen taking a

fence in the 1965 Gold Cup,which he won by 20 lengthsfrom Mill House, seenjumping with him. MillHouse was considered oneof the greatest of allsteeplechasers until Ark learrived to establishcomplete dominance overhim. Many good judgesrate Sea Bird II the bestflat race horse seen inEurope for many years. Heis shown, right, just afterpassing the post to win theEpsom Derby of 1965.

are acknowledged to be the champions forthe year. Few would argue that the greateststeeplechaser of all time is Arkle, winner ofthe Gold Cup three times in succession from1964 to 1966. There have been several goodchampion hurdlers of recent years, amongthem Bula and Persian War. The biggestbetting medium of all is the world's mostspectacular race, the Grand National, run atAintree, Liverpool, in March, over nearly4-^ miles, during which the horses must jump30 fences, some with world-famous names,like Becher's Brook. Some fences havedrops of nearly nine feet, and usually fewerthan half the runners complete the course.The greatest Aintree specialist of all is RedRum, who in 1977 became not only the firsthorse to win the race three times, but whoalso twice finished second in his five attempts.And no mention of great steeplechaserswould be complete without mentioning Gol-den Miller, the Gold Cup winner five con-secutive times in the 1930s, with a GrandNational thrown in for good measure.

Betting on the course in Britain is througheither course bookmakers or the tote. Book-makers begin by chalking on their boardsthe odds they are offering about each horse,and punters can back a horse at the price

shown, the bookmaker issuing a numberedticket and his clerk entering the transaction ina ledger. As the demand for each horse variesduring the betting, the bookmaker adjustshis odds accordingly. The bookmaker paysout at the odds obtaining when the bet wasstruck, but deducts tax, which in 1977 wasfour per cent of the payout, i.e. returned stakeplus winnings.

A bet on the tote is made at one of the manywindows at the tote building. A tote bet ismade by announcing the race-card number ofthe selected horse. Separate tickets are issuedfor win bets and place bets. A place bet is a beton a horse to finish in the first three, wherethere are eight or more runners, but in the firsttwo where there are five to seven runners. Atote indicator board shows how much hasbeen bet on each horse, and the punter cancompare the current tote odds with the priceoffered by the bookmaker, but must bear inmind that the tote odds fluctuate as bettingprogresses. The dividends paid by the tote arebased on sharing the pool of stakes by thenumber of winning tickets less tax andexpenses. The average deduction has beencalculated at 18 per cent.

There are a number of tote offices in thelarger towns of Britain, but off-course betting

54

retulB|

moc

S P O R T S

Itheing

is more likely to be either by telephone witha bookmaker with whom the punter has acredit account, or in a betting shop, many ofwhich are owned by the big bookmakingchains. Betting shops broadcast a commentaryfrom the course, which includes a frequentrun down of the current prices for each horse,which will be displayed on a board. Mostbetting shops will accept bets at the oddsdisplayed, but usually bets will be struck atthe starting price. The starting price is deter-mined on the course by a small group ofjournalists, who are representatives of theleading sporting papers, and who take theaverage of the prices being offered by thecourse bookmakers at the 'off! The startingprices of the winning and placed horses arebroadcast in the betting shops within a minuteor so of the finish.

In the betting shop bets are written out onslips of paper provided, and handed with thestake over the counter, in exchange for atime-stamped receipt which becomes the ticketby which winnings are claimed. In 1977, theta* deducted by off-course bookmakers was"i per cent of the payout, which includes the^turned stake.

Bookmakers on the course will not accom-cumulative bets like doubles, trebles,

yankees, etc. The tote, however, runs a dailytote double, usually on the third and fifth races.The punter buys a ticket on a horse in thethird race, tickets being in 50p multiples. If thehorse wins, the punter, before the fifth race,exchanges his ticket for a horse in the fifthrace, and if he is lucky again he collects thedeclared dividend. The tote also runs a treble,usually on the second, fourth and sixth races,which operates in the same way, but to 25ptickets. On selected main meetings, the totealso operates a jackpot pool, in which puntersneed to find the winners of six races. This canprovide some large wins. If the jackpot is notwon, consolation prizes are paid to punterswho find the first five winners, and the re-mainder of the pool is carried over to the nextjackpot meeting. This convention could pro-vide punters with a house edge in favour ofthemselves, as the share-out is greater thanthe pool, which is augmented by the residueof the previous pool. In practice, this is wellrealised, and the jackpot betting increasesconsiderably when a pool has been carried over.

The tote also operates a forecast pool oneach race. With from three to six runners,the punter must forecast the first and secondhorses to finish in the correct order. Withseven or more runners the forecast is known

Lester Piggott's record inhi g races all over the worldsuggests that there hasnever been a finer jockeyfor the big occasion. Herates Nijinsky as the besthorse he has ridden. Thecombination is seen beforethe Prix de l'Arc deTriomphe in 1970, a racewhich Nijinsky lost by ahead, after winning theTriple Crown in England.

55

P A R T T H R E E

as a dual forecast, and the punter is requiredonly to name the first two horses to finish, theorder not being required.

In off-course betting with bookmakers,several multiple bets are popular, and somehave been given names which most bettingshop employees will recognise. The simplestis the each-way bet, which is really two bets,one on the horse to win, and the other on thehorse to be placed. A horse is placed, forpurposes of betting, if the horse finishes in thefirst two of a field of five to seven runners, orin the first three of eight or more. When thereis a large field, bookmakers will also pay outon the fourth horse. The definition of alarge field varies from time to time, andfrom shop to shop. It might require at least17, 21 or 22 runners. The odds paid for aplace are a fifth of the win odds. Thus if £1each way is bet on a 10-1 winner (£2 staked)the payout will be £10 plus £1 returned forthe win, £2 plus £1 returned for the place,total £14, less £1.19 tax (at 8| per cent), whichis £12.81. Sometimes, in big races with bigfields, like the Grand National, bookmakerswill pay a quarter of the odds for a place.

A double is merely two horses in separateraces coupled in one bet. If the first wins, allthe return is at stake on the second. Tax isdeducted only on the final payout; it is notdeducted at both stages. Each-way doublesare also accepted. A treble is a three-horsemultiple bet on the same lines, and a multiplebet on four or more horses is known as anaccumulator. An 'any-to-come' bet is wherea second bet depends on the return from afirst. If the first loses, the second bet isn't made.For example: £1 to win Tinker - any to come£1 to win Tailor. If Tinker loses, there is nobet on Tailor. An 'up and down' bet is whentwo horses are backed singly, with an addi-tional any-to-come bet on each should theother win. A 'round-the-clock' bet is morethan two horses backed on the up-and-downprinciple, where each horse is bet singly withadditional any-to-come bets going on to theothers.

A yankee, the most popular multiple bet,is a bet on four horses backed in six doubles,four trebles and an accumulator, requiring astake of 11 units. Similar bets are the patent,which is a seven-unit bet on three horses -56

S P O R T S

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singles, doubles and treble; the Canadian,which is five horses backed in doubles, trebles,four-horse accumulators and a five-horseaccumulator, requiring a stake of 26 units;and the Heinz, which is six horses treatedsimilarly, so called because it requires 57 bets,the number of the famous varieties of tinnedfood.

A punter can invent his own exotic bets,coupling selections in any way he likes,provided that the instructions are clear andacceptable to the bookmaker.

Multiple bets are calculated at full multi-Plied odds. If a 50p treble wins at odds of

4, 3-1 and 11-2, the punter can calculatethe return which 50p earns at 9-4, and imaginethe total (£1.62£) going on to the next winnerat 3-1 and so on. But a simple calculation

that work unnecessary. If we consider

the odds of 9-4, and add the 9 and the 4together, the answer of 13 is the return we getfor a stake of 4 (9 won plus the original 4staked), so we can convert 9-4 to 13-4 andsay that the new odds represent our returnincluding stake. If that principle is under-stood, all becomes easy, because we canconvert all three sets of odds similarly (to get1 3-4, 4-1 and 13-2) and merely multiply themtogether, with the stake, thus :

il x 4 11x 50p

Cancellation makes the calculation easy:we can quickly see the answer is 4225p, so£42.25 less tax is our return.

Off-course bets at starting price carry thesafeguard that if a horse is withdrawn, and

There are less restrictionson bookmakers in Britainthan anywhere else in theworld. Bookmaking islegal both on and off thecourse, but many peoplewould prefer a totemonopoly with profitsbeing ploughed back intoracing. The main argumentsfor bookmakers are thatthey provide a choice ofbetting methods and thattheir presence brings colourand life to British courses.The illustrations showbookmakers at the EpsomDerby and at Goodwood,and a selection of ticketsissued to punters asreceipts for their bets.

57

P A R T T H R E E

The workings of a Britishbetting shop. On the righta chalker in a large shopis entering the results asthev are received. Thepunters opposite are sittingbefore a board whichadvertises the odds paidfor a forecast (i.e. thenaming of first and second).Some punters prefer toaccept fixed odds thantote odds, and somebookmakers will onlyaccept fixed odds forgreyhound forecasts. Theodds of the winner are onthe left, and of the secondabove. A 4-1 winner with a12-1 second pays 33-1.The William Hill book-making organization runs atraining school for book-makers, shown oppositebelow, through which newpersonnel must pass.

British £1 win tote tickets.A code, and the numbers ofthe race and the horse, arepunched in holes in theappropriate places when apunter buys a ticket.

doesn't come under starter's orders, the betis void. On big races, bookmakers will publishlists of prices, called ante-post prices, days orweeks in advance of the race. In the case ofthe Derby, it is not difficult to make a bet ona horse a whole season before the race. Ante-post bets are made on the 'all in run or not'principle, and no stakes are returned. Manybets are therefore lost before the race, ashorses are scratched or suffer training set-backs, but because of the uncertainty, theprices are suitably generous. Nothing is moresatisfying than backing a horse at, say, 40-1,well before the race, to find on the day that itis among the favourites. This is naturally apopular method of betting for those withknowledge of stable plans.

The ordinary punter has little to guide himto successful betting on horse races. Thenational press provides a wealth of informa-tion, but this is available to all, and a puntershould not expect to beat the bookmaker'sedge unless he has private knowledge, suchas that a horse is fit and well and is fancied byhis connections. Frequently horses run whenthey are not at their peak, or when the goingdoesn't suit them. Racing people can recog-nise these occasions, but the stay-at-homepunter cannot, and inevitably makes unwisebets on horses not expected to win.

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S P O R T S

A few guide-lines can cut down the losses.When relying on form, it is safe to assume thatin the big championship races all horses arelikely to be fit and trained to the minute,which might not be the case in minor handi-caps. Two-year-olds, perhaps because theyhaven't learned not to give their best, areknown to be more reliable than older, wiserhorses. Handicaps are notoriously tricky.Occasionally the handicapper appears tomake a mistake in allotting weights, or ahorse makes a dramatic improvement, sothat he appears to be 'thrown in' with too littleweight. Such a horse is recognised as a 'handi-cap snip', and the public plunge heavily, butall too often the good thing comes unstuckto save the handicapper's reputation. It shouldalso be recognised that a horse carrying ninestone of jockey is less handicapped than onecarrying eight stone of jockey and one stoneof lead weight. A heavy weight is harder tocarry in mud than on good going, and formany other reasons a sudden change in thegoing can turn the form upside down.

With the way the tax is calculated in Britain,it is pointless to back horses at long odds on.A winner at 3-1 on will pay £4 for £3, less taxof 34p, so the actual win is only 66p for £3,the odds altering from 3-1 on to about 9-2 on.

One decision the punter must make iswhether to back a horse on the tote or thebook. Most betting shops will accept betsmade at tote odds. Generally the tote returnsslightly more money to the punter than thebookmaker. Usually the tote return willcompare very favourably with the startingprice on outsiders and in big fields, with theadvantage diminishing as the prices and fieldsget smaller. The tote returns are usually betteron horses and jockeys which are unfashion-able. If Lester Piggott is on a favourite, heis likely to be heavily supported on the tote,and the win dividend might be less than thestarting price, but if an apprentice wins on anoutsider in a big field, the tote dividend isalmost sure to be better than the S.P.

Horse-racing in FranceRacing in France is possibly the best in theworld. Where the British pattern is to havemeetings of three or four days before the actionmoves on to the next course, the French

59

P A R T T H R

Betting in France. A parimutuel agency whichaccepts off-course bets upto 1 o 'clock on the dav 'sracing. Far right, thegreatest oj French races,the Prix de l'Arc deTriomphe, being won in1976 by Invanjica fromCrow. Invanjica also wonthe WashingtonInternational.

preference is for longer meetings. During theholiday period around August, French racingconcentrates on Deauville, where the summerseason lasts for six weeks and consists ofboth flat and jumping races. The course, withthe nearby sandy beaches, not to mention thecasino, attracts thousands of visitors annually.The racing is part of the holiday setting, andthe lushness of the grass, the spacious pad-docks and the flowers add to the festivalatmosphere.

Although racing takes place all over France,the biggest meetings and the best courses arewithin reach of Paris. Longchamp is asbeautiful as Deauville, with immaculatelykept paddocks, lawns, gardens and trees.The new grandstands are equipped with liftsand there is no shortage of bars and restau-rants to help make a day at the races a realday out. Chantilly is 30 miles from Paris and,with an expanse of first-class training gallopssituated near the course, is the home of someof the best stables.

French racing is so good because all thebetting in France is through the pari mutuel,the amount skimmed from the pool as profitbeing divided between the state and the course.About 8 per cent of the money staked onhorse-racing finds its way back to the courseauthorities. This makes a sum several timesgreater than that which British courses, forexample, receive from gambling profits and itis no wonder that Deauville and Longchampcan offer higher prize money and providebetter facilities for race-goers.

The most important race in France, andprobably the world, is the Prix de l'Arc deTriomphe, run at Longchamp over 2,400metres (1^ miles) for 3-year-olds and upwards.

Some of the greatest Freiicn noises have wonthe Arc, among them Tantieme, which wonit twice in the 1950s, Exbury, Vaguely Nobleand the great Sea Bird II, which also won theEnglish Derby. Invaders which have taken theArc include Mill Reef, the Derby winnerwhich restored English pride, and Ribot, thebrilliant Italian horse, which won in 1955 and1956. The Grand Critérium, France's toptwo-year-old race, over 1,600 metres, is alsorun at Longchamp, as is the three-year-oldrace of 3,200 metres (nearly two miles), theGrand Prix de Paris. The Grand Critériumwas won in 1976 by the outstanding BlushingGroom, which also won the Prix Morny, themost important race at Deauville, and thePrix Robert Papin, the big race at Maisons-Lafitte. The equivalent of the English Derbyand Oaks are run at Chantilly, the Prix duJockey Club and the Prix de Diane respect-ively. The Prix de Diane was won in the 1970sby two of the most delightful fillies which havegraced French racing recently, Allez Franceand Pawneese. The most important steeplechasing course is Auteuil, which stages thenearest equivalent to the Grand Nationalin the 25-jump 4-mile race, the Grand Steeple-chase de Paris.

Off-course betting in France is conductedup to 1 o'clock in agencies of the pari mutuelall over France. Cafes serve as agencies for avery small commission, and the stakes takenget back to the course to be amalgamatedwith the bets made on the course. The off-course betting is published on a board at thecourse before each race and serves as the firstindication of the approximate odds. ASbetting takes place on the course, the latestodds are circulated on tickets.

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S P O R T S

Horses can be backed to win or be placed.Horses in the same ownership are bracketedtogether for purposes of betting. Similar betsto the British tote forecast bets can be made,called couplés. Two horses are selected. Awin couplé requires that the two finish first andsecond, in either order; a place couplé winsif they are both placed in the first three. Thecouplé is an off-course bet, as is the biggestFrench bet of all, the weekly pari tiercé.

The tiercé is based on a selected Sundayafternoon race, and for French gamblersrepresents what the football pools representin Britain : a once-a-week shot at a fortune for

a small stake. Instead of filling in a coupon inmid-week, the Frenchman strolls round tothe pari mutuel agency on a Sunday morningand attempts to name in the correct order thefirst three to finish in the big race. The socialaspect and convenience of this visit to the cafeprobably accounts for the fact that the tiercéturnover is greater than British pools turnover.

Minor dividends are paid to punters whoforecast the first three in the incorrect order,and it is clear that the Frenchman has as much,or more, scope for the skilful use of permuta-tions as his British counterpart.

Racing in AmericaRacing in America is flourishing, with manynew tracks having been built in the last 20years and the overall racing attendance havingincreased considerably. There are now about30 major tracks in the United States and over100 smaller tracks, many staging harnessracing which is extremely popular.

Most American tracks are oval dirt tracksaround which the horses run anti-clockwise.The organisation and facilities for the punterare excellent. Meetings last for several weeks,during which time the racing 'circus' of

American race tracks donot provide the variety ofracing which courses inmost other countries of theworld afford. Most tracksare standard oval left-handdirt tracks, although thereare a few turf courses. TheHialeah track in Miami,Florida, was opened in1925. The tote indicatorboard states the turf isfirm, which looks anunderstatement.

P A R T T H R H E

The elegant device abovewas used on a pouteradvertising the fall meetingof the Brooklyn JockeyClub race course of 1886.The field for a KentuckyDerby of the 1890s isseen, above right, passingthe grandstand. The racebegan with the opening ofthe track in 1875. Thepicture below right showsone of the best of recentAmerican horses,Secretariat, winning theBelmont Stakes in 1973 tobecome the first horsesince Citation in 1948 towin the Triple Crown.

trainers, jockeys and horses take up residence.Some of the best tracks are operated by

the New York Racing Association, includingBelmont Park, the home of the oldest three-year-old classic race, the Belmont Stakes,run in June over 1| miles. There are threeclassic races for colts, the first, run on the FirstSaturday of May, being the Kentucky Derby.This famous race is run on the ChurchillDowns, near Louisville, over 1^ miles. Thecourse is a completely flat, dirt oval, set in themiddle of the blue grass country. The Preak-ness Stakes, which follows the KentuckyDerby in mid-May, is run over 9^ furlongs atPimlico, in Baltimore, Maryland.

The principal grass track in the UnitedStates is Laurel Park, part of the EasternAmerican racing circuit. During NovemberLaurel stages the Washington Internationalinvitation race, to which are invited leadingracehorses from all over the world. English,French, Australian and Irish invaders havelifted the race, and Russian and Japanesehorses have made the attempt.

Man O'War was the first American race-horse to become a national hero. Winner ofthe Belmont and Preakness in 1920, he wasbeaten only once on the track. There havebeen many idols in recent years, perhapsnone more esteemed than the Triple Crownwinners Citation and the tragic Secretariat.Seattle Slew was still unbeaten when he wonthe Triple Crown in 1977.

Betting in the United States is by the parimutuel system at the track. Off-track book-making is illegal except in Nevada, whichstrangely does not have a major track. Off-

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track pari mutuel betting was allowed from1970 in New York, which soon had its first100 offices operating under the control ofthe Off-Track Betting Corporation, whichdivides its revenue between the track, stateand city. Otherwise legal betting must takeplace in those states (about 30) which allowracing and pari mutuel betting.

Each race has three pools: win, place andshow. Tickets are sold at the pari mutuelwindows in various denominations, the lowestbeing $2. If a horse is backed win, place andshow, all three bets win if the horse finishesfirst, the place and show bets win if it finishessecond, the show bet wins if it finishes third.All tickets are sold independently. A bet onwin place and show is a combination oracross the board ticket (although a combina-tion on some tracks is win and place only).

There is also a daily double pool, almostalways run on the first two races. Other betswhich might be available at some tracks (butnot all) are the quiniela, which requires the

Kelso was one of the bestloved of recent Americanwinners. He is shown,garlanded, after winningthe 13th WashingtonInternational at LaurelPark, Maryland, in 1964.The race is one in whichsome of the world's besthorses take part.

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Three photographs whichillustrate some of the morepicturesque aspects ofAmerican race tracks.Above, palm trees atGulf stream Park,Hallandale, Florida. Right,sunshine, colourfulsunshades and beautifulthoroughbreds on their wayto the paddock at HialeahPark, Miami, Florida. Farright, racing at ChurchillDowns, Kentucky,Louisville. In all threescenes, the approximatetote odds indicator boardis shown.

punter to pick the first two to hmsu, in anyorder; the exacta, usually operated whenthere are less than eight runners, whichrequires the first two to be picked in the correctorder; and the triple, a pool for long-shotpunters, which requires the first three to benamed in the correct order.

American tote boards are limited to twelvehorses, so when fields are larger than twelve,the outsiders are grouped together to form'the field' for the twelfth space. Also, horsestrained at the same stable are coupled togetherfor betting purposes, and represent one'horse' for pari mutuel betting.

Although they might be illegal, it is notdifficult to find an off-course bookmaker inthe United States who will take bets on thehorses. He will pay out at the official oddsdeclared by the pari mutuel. However, thepari mutuel cannot lose, the bookmaker can,so he will limit his liability by imposing amaximum payout. For example, his maximumpayout might be 30, 10 and 5, which meansthat 30-1 is the maximum odds he will payon a win, 10-1 on a place, and 5-1 on a show.

The bookmaker is not limited to the betswhich the totalisator machinery can handle.

A parlay is a single bet that two or morehorses in separate races will win. Place parlayscan also be made. A win parlay on, say, threehorses requires all three to win before the betis a winner. To calculate the winnings on aparlay, the pari mutuel payoffs for the horsesshould be multiplied together, and dividedby two for a two-horse parlay, four for a three-horse parlay, eight for a four-horse parlayand so on. This is because payoffs are declaredto $2 stakes. However a limit will come intoforce which will make ambitious betting awaste of time. Bookmakers might not paymore than 50-1 for a parlay.

Other bets possible with the bookmaker areround robin bets, which involve making anumber of selections and backing them inall possible two-horse parlays, and 'if money'bets, which are bets that are conditional onmoney being available from a previous bet.

Racing in AustraliaAustralians are great horse bettors, with morecourses in relation to the population than anyother country. Racing is organised on a stateby state basis, with each state having a numberof major courses. Naturally the most populouscities of Melbourne and Sydney have the mostracing. Because money is ploughed back frombetting, some of the best courses in the worldare in Australia: Flemington, Caulfield andRandwick among others. The most farnou5

race is the Melbourne Cup, run over two miles

at Flemington. The Caulfield Cup, and the64

Sydrtheracedforfend

Ailof t !wontoshippAfteJwasa» A

Beltor

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and iiousailes

the

Sydney Cup and the Doncaster Handicap atthe Randwick Easter Carnival are other bigraces. All are handicaps, the most popularform of racing. There is little racing overfences.

An Australian racehorse won the affectionof the whole nation in the 1930s. Phar Lapwon the Melbourne Cup in 1930 and went onto win several other big races before beingDipped to America to take on the best there.After winning his first race in record time, he*as mysteriously found dead in his box, anda" Australia mourned.

Betting in Australia is through the Totalisa-tor Agency Boards (TAB), both on and offtoe course. Australians bet through the TAB

offices either on win or place for each race,on the daily double (two races selected by theTAB), on the quadrella (four races selectedby the TAB) and on the quinella (picking thefirst two to finish in either order, on the lastrace of the day). The quadrella is the big betof the day. The TAB restricts the choices ineach of the four races by bracketing horsestogether so that there are no more than nine'runners' in each. The quadrella still payshuge dividends when outsiders win.

At the race course, additional bets areoffered by the TAB, such as duos (backingtwo horses to be first and second, in theselected order) and triellas (backing threehorses in the same way).

Flemington race course,Melbourne, Victoria, onMelbourne Cup day, 1961.On this day, 82,000 peoplesaw Australia's major race.The river in the foregroundis the Maribyrnong River.The paddock is on the left.

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Computer Automated Real-time Betting InformationNetwork (CARBINE). In1967 the TotalizatorAgency Board of Australiacompletely computerizedthe processing of bets. Thepicture shows the maincontrol panel. Thesupervisor can tell instantlyfrom the two televisionscreens which function thecomputer is performing.

Most greyhound races inBritain concern six dogs.The dogs run often at thesame track, and are gradedaccording to their ability,so that all races are asevenly contested aspossible. Regulars get toknow the habits of the dogs,such as whether they arefast or slow from the trapsand whether they prefer tostay near the rails or torun wide. A part ofsuccessful betting is tocalculate which dogs arelikely to avoid bumping asthey round the bends.

X

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Bookmakers on the course compete withthe TAB by offering odds about each horse.The advantage that betting with the book hasover betting with the TAB is that once a betis struck the odds are determined. TAB odds,like all pari mutuel odds, fluctuate right up tothe off.

The English gambler Robert Sievier didmuch to promote bookmaking in Australia.He appeared at Flemington in 1882 with abig black bag and a great deal of show, andwon the confidence of the punters and a lotof money. On his return to England he wonand lost fortunes and court cases, once beingbanned from the turf, once being cheeredafter winning a case against a prominent

•

owner. He himself owned the peerless Sceptre,winner of four classics in 1901. He died in1939, having made his mark on the Turf atopposite ends of the world.

Other racingGreyhound racing is a modern adaption ofcoursing, which is at least 2,500 years old.About 50 years ago the perfection and use ofan electric hare, which greyhounds chaseround an oval track, brought a boom toracing dogs. Tracks were built, mostly inBritain, and betting on 'the dogs' became abig industry. Several European countries havedog racing, though none on the scale ofBritain, and in America it is restricted to nine

P A R T T H R E E

New Year athletics at theMeadowbank Stadium inScotland, in which one ofthe main attractions on theboard below is seen takingplace in the picture right -a girl sprinter racingagainst men in the 'famousSkol Sprint '. ThePowderhall Sprint, ahandicap named after theScottish village in whichit was originally run, begana tradition of betting onathletics in Scotland,particularly onNew Year's Day.

acroiPoin]Wat<andPlacd

MJtheirloddsthewillHowlmak

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or ten states, with about a third of the businessbeing done in Florida.

In Britain, races are flat or over hurdles,the usual pattern being to have eight racesto a meeting with six dogs in each race. Meet-ings are usually held in the evenings. Dogsstart from traps, and wear coloured vests foridentification. Betting is through the tote orthe bookmaker. Bookmakers usually restrictbetting to straight bets for a win, but the toteallows win and place bets (a place is second)and operates combination bets which varyfrom track to track. A popular bet is theforecast, which requires the first two dogs tobe named, in correct order.

In America, there are usually twelve racesper evening. All betting is with the pari mutuel,which provides win and place betting, dailydoubles and quinielas.

Coursing is still found in America, Britainand Australia. Hares are let loose to runacross a field and two dogs are awardedPoints by judges as they chase the hare. TheWaterloo Cup at Altcar is the British classic,and persistent, if not large gambling takesPlace.

Men do not have to rely on animals to dotheir racing for them. Betting shops will quote°dds about the winners of gold medals attne Olympic Games, although bookmakers11 not be allowed at the games themselves,

"owever one annual meeting at which book-takers flourish is the Powderhall Sprint

Handicap in Scotland. A champion sprinteremerges after winning through to the finalfrom several heats, all of which are bet on asif they were horse races. The runners arehandicapped to give all, in theory, an equalchance. Another resemblance to horse racingis that competitors train secretly and keeptheir form dark. Unlike horses, though, therunners bet on themselves.

Men have backed themselves racing inyachts, cars and aeroplanes. Bicycle racing isa popular activity in Europe, and the world's

Pan of the large field,above left, in the 1974Tour de France. Cycleracing is one of the mostfollowed sports on theContinent.The best knownriders are national heroes.That gamblers are preparedto bet on anything isshown by the mouse raceover hurdles on animprovised track at astreet party in Brixton,South London.

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greatest race, the Tour de France, is gambledupon by the French. But Japan has the biggestbicycle racing betting. There are tracks allover Japan, with programmes of races almostdaily, and spectators bet enormous sums onthe outcomes. The local government issuesthe betting tickets and some of the profits goto financing the tracks.

FightingAfter contests of speed, contests of strengthare suitably easy for betting on. Where ani-mals naturally fight, there will be bets onthe outcome. Fighting fish are bet on by theSiamese. Cock-fighting has been popular overmost of the world, and even now, althoughillegal in most places, is still very widespread.Bookmakers and bettors stand round the pitstriking bets on the spurred birds who fightto the death.

Few sports havegenerated so muchargument as bull-fighting.Aficionados revere it as asort of art-form, but theless-committed frequentlyplace bets with programmeor drinks-sellers who act asrunners for the localbookmakers. Betting is onwhich of the six bulls iskilled with the most elan,according to a previouslyappointed judge.

70

Another sport which usually ends in a deathis bull-fighting, performed in Spain andMexico. A corrida consists of six fights ateach of which the matador puts the bull todeath. Spectators bet heavily on which of thematadors will kill the bull with most grace andpanache. Official judges are appointed.

When Greek met Greek in ancient wrestlingmatches there were side bets. Nowadaysformal arts are practised in the East withgreat ceremony but little of the betting thatonce characterised them. The big money isnow bet on prize-fights, particularly on theheavyweight championship of the world.

«S..1 J - fs i -*

1

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.f"

Cock-fighting is a gorysport in which spurredcocks fight to the death. Itis illegal in most countries,and although it excites andsatisfies an aggressiveinstinct in manyspectators, it wouldprobably die without itsaccompanying betting. Thefight shown is from thefilm 'The Cincinnati Kid. '

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concontcou\mononlàsed\

blo

Boxing has notoriouslyattracted big betting. WhenDempsey, on the left,fought Willard for theheavyweight championshipof the world in 1919, it wassaid that he bet his purseat 10-1 that he wouldknock out Willard in thefirst round. Dempseythought he had won whenWillard was down andhelpless at the bell, but hadto resume and won his fight,but lost his bet, in the third.

The meeting in 1971 ofchampion Joe Frazier(left) and ex-championMuhammad Ali, who losthis title outside the ringwhen he refused to jointhe Army, inspired greatpublic interest and betting.

Jack Dempsey is said to have bet his wholepurse, when he challenged for the title, thathe would knock out Jess Willard in the firstround. Willard was down seven times but wassaved by the bell. When Ali fought Frazierin 1971 about $100,000 was wagered on theresult. So much money has been bet on boxingthat inevitably gangsters have tried to influ-ence results, and a present slump might bedue to the wariness of both bookie andbettor.

SoccerSoccer provides betting in many ways, themost popular of which is the football pool.

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o is a modern refinedversion of gladiatorialcombat. The head to headcontests of strength andcourage in the raw lead tomore betting amongonlookers than moresedate sports. As with cockfighting, the aggression andblood in the ring seem to

encourage an aggressionin the spectators whichincreases the desire to bet.The game Floyd Patterson(left) took a terrificbeating from MuhammadAll before the refereestopped their 1965fight in the twelfth round.

J*JH*~ •IE'-

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This is the momentmillions of British footballpools bettors dream of.Mr Colin Carruthers withhis cheque for £629,801-55,a world record, won on theTreble Chance in 1973.Partly because of govern-ment tax, the 'house edge 'on British football poohmake them one of thepoorest of popular bettingpropositions, but the hopeof a win like this for a fewpence make 'doing thepools' a weekly event inmillions of homes.

74

slighl

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in in

Betting with bookmakers was popular inBritain until the 1950s when heavy taxationforced the promotors to abandon it; it is nowreturning with coupons offering odds on eachmatch of a full Saturday programme. Bothteams are given a price for a win, and thereis a price for the draw. Backers can make anynumber of selections and back them in treblesand accumulators.

The football pools work on the pari mutuelsystem, where stakes are divided amongwinners after deductions. Since the 1920sfootball pools have been part of the Britishway of life. They are popular now on thecontinent of Europe and in Australia, severalcountries using the British league fixtures asa basis for the pools.

In Britain, coupons are delivered to thehomes of 50 per cent of the adult populationeach week, mostly by pools company col-Actors, but sometimes by post. Collectors willtake the completed coupon relating to thefollowing Saturday's games, and leave thec°upon for the week after. There are four|ttajor pools companies, whose coupons eachdelude around five pools and who offer as'ight variety of bet. But each of them includes

a Treble Chance pool, the pool which offersthe jackpot return, and which accounts for90 per cent of the money staked on the pools.From a list of about 55 matches, the puntermust select eight which he thinks will end in adraw. For each draw correctly forecast he isallowed three points (except for 0-0 draws, forwhich he is allowed two points), for each matchwon by the away team \\ points, and for eachmatch won by the home team, one point. Themaximum score is thus 24 points, which wins atop dividend. Three to five minor dividends arepaid, according to which pool is chosen.

Because of the heavy government tax, andthe percentage taken by the pools companyfor commission and expenses, the punterreceives only about 28-30 % of the total stakemoney back as dividends. The largest com-pany, Littlewoods, takes about £3 million perweek in stakes, paying out about £1 millionto punters. Of this 60 % or £600,000, is paidto Treble Chance first dividend winners.There is a limit of £500,000 on the first divi-dend (tax free).

The main difference between the variouscompanies' Treble Chance pools is in theminimum stake per column, which varies

When John Moores beganhis football pools operationin 1923, and took stakestotalling £4 7s. 6d. on 35coupons sold to punters atManchester United'sfootball ground, he couldhardly have visualised aheadquarters like this andan annual turnoverof over £100,000,000.

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Littlewoods is one of thefour main pools companieswhich supply coupons to thehomes of 50 % of the adultpopulation of Britain eachweek.

CHECKING CHART FOR EACH FULL PERM 8 from 10

— — — — — — — — PLEASE DETACH CAREFULLY ALONG THS DOTTED LINE

IDRAWS1 MARKX 10HOMES IAWAYS

7 MARK 2EASIER 6 Make Saturday something to celebrate with a o

CM

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from |p to jsp. Most people choose a com-bination entry (popularly called a perm), thesimplest being a selection of 10 or 11 matchesand a 'full perm' of all combinations of eightmatches from the number chosen: 45 lines isrequired for any eight from 10, and 165 linesfor any eight from 11.

There are, however, various more compli-cated permutations which will be acceptedj'y the pools companies. Sometimes they|ssue the permutation themselves, with check-'ng charts, sometimes the plans are devisedty newspaper columnists. In these caseslhe punter needs to enter only the appropriatenumber of selections, together with the Plannumber. But, if he prefers, the punter can'flvent his own elaborate permutations: allt(lat is needed is that the pools companyexPerts can understand his intentions.

The minor pools included on each com-

pany's coupon are for selecting items like10 results (usually home wins), three draws,or four away s.

When the millions of pools coupons reachthe companies each weekend, sophisticatedmachinery times their arrival and recordsthem on microfilm. Electronic reading andsorting machines help thousands of employeesto process and check the coupons. All is doneand dividends are published in the press byWednesday morning.

In Australia, football pools were launchedin 1974 by a subsidiary of one of the Britishcompanies and were immediately successful.Although using the same 55 British matches,and the same form of pool as the treble chance,the coupon was quite different to the Britishcoupon. It was collected in a pools shop. Thecoupon did not contain the names of theteams, merely a box of numbers, the punter

\ i

Computers, electronicreading and sortingmachines, the recording ofcompleted coupons onmicrofilm, are some of theequipment and processesnecessary to a company likeLittlewoods Pools, whichdistributes, receives andsettles 12 million couponsweekly during the footballseason. That it cannot bedone without personnel,too, is shown by thegeneral view of checkers onihe pools floor and the girlsoperating a couponmarking machine.

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P A R T T H R E E

being asked to cross out the numbers relatingto the matches of his choice. All he needed todo then was to complete the investmentamount and pass the coupon with stake overthe counter.

In summer, during the soccer close-season,British pools operate on Australian matches.

Other gamesA game which originated in Spain and nowis played in Latin American countries and allover the United States is jai alai, a form ofpelota which found its way to Cuba in 1900and thence to America. It is played with legalpari mutuel betting in Florida where theseason lasts for months. Crowds of three orfour thousand watch each evening and thereare a variety of bets that the pari mutuel willtake.

Betting on the popular American teamgames of baseball, basketball and Americanfootball takes the same form. The bookmaker,on enquiry, will quote a price for each of thetwo teams in a match. There are four differentprice lines and which is dealt depends on theclientele. The 40-cent line is for the poorbookie and the mug punter: the 20-cent lineis for the larger bookie and more experiencedbettor; the 10-cent, or dime, line is for bigbookies with big-money clients ; the 5-cent, ornickel, line is for big bookies attracting layoffbets from other bookies.

A 40-cent line has a differential of twopoints between the bookie's lay and take odds.For example, if Yankees are favoured in abaseball game, the bookie might quote '7-9Yankee favourites', i.e. a two-point spread.This means bettors on Yankees are offered9-5 on, and bettors on their opponents 7-5against, all prices being quoted to five. The20-cent line, for which a bet of around $50 maybe required, has a one-point differential, e.g.'7-8 Yankees favourites'. Yankees opponentsare still 7-5 against, but Yankees only 8-5 on.

Gamblers on these sports can back inparlays, round robins and all the usualcombination bets.

American football attracts more bettingthan the other sports, and bookmakers usea handicap system to bring the teams level.If Princeton are expected to beat Yale by9 points, they will be handicapped by 9^ points,78 L

S P O R T S

Pools betting is notorganized on Americanfootball like it is onBritish football, but moremoney is staked onprofessional football,shown here, and collegefootball in America thanany other sport. Sportsservices provide book-makers with the latestinformation on injuries toleading players, so that theodds offered can beadjusted to take account ofthe latest chances.

• •1

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Sports which do not existfor betting neverthelessfind that they do not escapethe gambler's attention.Golf has long been agame in which playersback themselves for smallstakes, and public bettingon professionals, longpopular in America, hasnow reached theconservative St. Andrewscourse. The picture is ofEddie Polland playing inPalm Springs. Wimbledonto tennis lovers is as sacredas St. Andrews to golfers,but nowadays a bettingtent is part of the scene atthe championships. Thepicture below, taken in1975, shows that bets canbe struck on the Salisburyraces as well as on tennis.

and the bookie will announce 'Princeton 91points over Yale'. The gambler can now backeither side at the same odds, backers ofPrinceton winning if Princeton actually winby 10 points or more, otherwise backers ofYale win. The odds might be 6-5 for bothteams with the ordinary bookmaker, ll-iofor both teams with a big bookmaker. Whenidentical odds are given against both teams,the line is known as the 'Pick em line': thebookmaker will offer 'Princeton-Yale, 6-5pick 'em'. In all cases the punter lays the odds,staking 6 to win 5, or 11 to win 10.

Tennis is a game that has attracted muchbetting lately, with interesting personalitiesplaying at top level and each having theirsupporters. Ladbrokes experimented with atent at a tennis tournament in Britain in 1975,and the sporting papers carry odds on thecontenders for Wimbledon titles before thechampionship fortnight begins.

Golf, too, an aristocratic game, has hadtrouble with gamblers. In America a wide-spread method of big-money gambling is theCalcutta pool system. Gamblers stage anauction in which they bid for each player ina tournament. It might be that to 'own' thefavourite cost $2,000, whereas an outsidercould be bought for $100. The pool is dividedin agreed percentages among the holders ofthe first three or more golfers, according toprior agreement. The holder of the outrightwinner usually tips the golfer. In the 1927British Open Championship at St. Andrews,bookies, dressed like race-course bookies andcarrying large bags, attempted to do businessby shouting the odds about the players. Theywere firmly sent on their way. However, in1972 a betting tent appeared at St. Andrews,where bets could be placed on the JohnPlayer Classic, despite disapproval.

Even cricket, the game most jealous of itsreputation for spurning the unseemly, is partof the gambler's empire. Indeed cricket hasbeen 'gambled on' for at least 250 years. I"1774 the Morning Chronicle could expostulate

This sport has too long been pervertedfrom diversion and innocent pastime toexcessive gaming and public dissipation.Well, Lord's still has its Tavern, it also no*'

has a betting office. And where is the MornMChronicle ?

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81

P A R T F O U R

"rime and fraud are often associatedwith gambling. Marked cards, loaded dice,false deals, gaffed equipment, false postmarks,tapped telephones - all are frequently found,and their users prosecuted. Gambling attractsthe petty crook, who finds large sums ofmoney depending upon events which with alittle skill and deceit he can manipulate. Theactivities of these men are simple and sordid,but occasionally gambling coups occur whichare fascinating because of the scale of theswindle, the people involved or the ingenuityof the fraud. Sometimes a swindle can be soneat that a grudging admiration for its perpe-trators seems the most natural response.

Such an operation was that in which a clevergang took a lot of money from the book-makers of London over the Easter of 1880. Itwas discovered, too late, because of a news-paper misprint. The scheme depended on thefact that Easter is a very busy time for racingmen and racing newspapers, with a largenumber of holiday meetings taking place allover England. It began when the editor of theracing paper Bell's Life, which has since beenamalgamated with The Sporting Life, Britain'sleading racing paper, received a letter pur-porting to come from the secretary of theTrodmore Hunt. It was a courteous letter,enclosing the runners and riders for theTrodmore Hunt race meeting of Easter Mon-day, and requesting the editor to publish itin his paper. The writer offered to send theresults by telegram after the meeting forpublication in the following day's paper.Glad of this relief for his overworked staff,the editor duly printed the day's racing pro-gramme, the results followed as promised,and were also published. Bookmakers inLondon found that a few punters had beenextremely lucky with their Trodmore bets,and paid out several thousand pounds. Abeautiful swindle was exposed because anotherpaper had followed Bell's Life and printedthe results, but a misprint occurred, onewinner being given the price of 7-2 in onepaper and 5-2 in the other. The TrodmoreHunt secretary had to be contacted to checkthe correct price. It proved very difficult, asenquiries showed that there was no such placein Britain as Trodmore.

An engineer called William Jaggers brought

instilandfolkworllRoycovel

82

off a coup at Monte Carlo towards the end ofthe nineteenth century. He realised that it wasvery difficult to keep a roulette wheel inperfect balance, and with the help of assistantskept a record of the numbers which won onseveral wheels. An analysis of the resultsshowed that on some wheels they were not | m R,following the pattern the law of large numbers I tewsuggested they should. Jaggers therefore I chanlbacked the numbers which seemed to ^ j °' c|favoured and won over a million francs if Ifour days. The casino, of course, then diS'lcovered the method, switched wheels an" I Sear<

F I X E S A N D S W I N D L E S

|d of instituted a system of regular examination1 was and testing of roulette wheels, which has been|1 in followed by most casinos throughout thelants world. It did not prevent Albert Hibbs and

on Roy Walford, two American students, dis-ults covering a faulty wheel at the Palace Clubnot m Reno in 1947 and running up a profit of a

Ibers few thousand dollars before the wheel wasJfore ^ Ranged. There is no suggestion of cheating,

be °f course, in logging a roulette wheel. ItIs in Would be difficult nowadays to profit from a1 dis" 'aulty one, and the application of those who

\e search for and find one can only be admired.

^ I

None of the instigators of the RunningRein scandal in the Derby of 1844 deserveadmiration. It appears that lots of skul-duggery took place in this particular race, andRunning Rein interfered with a long-standingfeud between two colourful British book-makers and gamblers. One was WilliamCrockford, who opened the original Crock-ford's Club in 1828. The other was JohnGully, who early in life was bought out ofFleet Prison to fight for the championshipof England, which he won, and later becameMember of Parliament for Pontefract. Gullyand Crockford had crossed swords over theDerby and St. Léger of 1819. Crockfordowned Sultan, and backed it heavily for theDerby with Gully, who thought, correctly,that Tiresias would win. The narrow marginof half a neck did not help Crockford's ire.It increased when Gully heard that Crock-ford's horse Sultan had broken down beforethe St. Léger, and managed to take Crock-ford's bets before Crockford himself wasaware of the break-down. In 1827 Gullysecretly bought the Derby winner Marmeluke,and backed it for the St. Léger to win a hugesum from Crockford before announcing hisownership. Marmeluke, who was known tobe a highly-strung horse, lost the race becausethere was so much trouble at the start that hegot into a lather and was left. Even so, he lostby only a length. The starter was dismissed,and there were suggestions that the botherwas not accidental.

This was the background of the dislikeCrockford and Gully felt for each otherbefore the Derby of 1844, when they ownedthe two most fancied horses, Ratan and TheUgly Buck. Each backed his own horseheavily, but neither won, due to the chicaneryof one Goodman Levy. Levy owned twohorses: Running Rein, and another a yearolder, Maccabeus. In the light of subsequentevents it seems certain that by several changesof stable, he had managed to switch theiridentities. When Running Rein, really Macca-beus, won a 2-year-old race, heavily backedby Levy, there were suspicions that he was anolder horse. Lord George Bentinck, a cham-pion of the Turf, sought evidence to prove thepoint, but could not prevent Running Reinrunning in the Derby of 1844, which he won.

John Gully, opposite, andWilliam Crockford, tworich, colourful bookmakersand gamblers of thenineteenth century whotook delight in winningfrom each other. Their lastclash was the Derby of1844, which neither won.Crockford died justafterwards, and becausethere were gambling winsto collect which would beforfeited with his death, hisbody was propped in anarmchair in his windowuntil the gains weresafely gathered in.

83

TWO COLTSMYSTERY

Both have disappearedFOR 36 HOURS SCOTLAND YARD MEN AND POLICE OF TWO

COUNTIES HAVE BEEN TRYING TO TRACK THE HORSEWHICH WAS CONCERNED IN THURSDAY'S BATH RACES

BETTING SENSATION—THE CASE OF THE CUT PHONE CABLE.A senior officer said last night that he believes that when the horse is

found the whole riddle will be solved. He was convinced that the horse i<still in this country.

Turf experts discussing the case are comparing therecords of two horses.

Both came from France a week ago in the steamerDeal. Both are bay two-year-olds.

One, Francasal, was the 10-1 winner of the Bath race—aseller. The other. Santa Amaro, has not been heard of sincei •—— - -——-.——— ne iamjerj

After his victory. Francasal] was driven away Irom the: Bat h course, and he, too.! vanished.

IMr. Percy Bailey, the Epsom

trainer who saddled Krancasal,was interviewed by the stew-1ards of the Jockey Club after

•j racing at Ascot yesterday.'j He said afterwards: " I have

i to appear again before the| stewards next week."I Bailey also said that thei owner of the horse. Mr. M.

t| Williams, and Mr. W. Rook, who).i bought the horse in, would be

! invited to attend.Santa Amaro Is entered in

Ive selling races this week. Henight turn up for one.

When they landed in Eng-land horse boxes collected thetwo colts, which are trained InFrance and owned by a Mr.

f Maurice Williams.But only one—Francasal—

was delivered to trainer Bailey,who was asked to engage *Jockey for the Bath race,

c-.f The records of the two horsesï(\ce are certainly very different.

" Santa Amaro has never run.- Francasal has run six times and

o" . been five times unplaced.

''A mistake'

,.« c. AVÀ rt'vtvfe \

»c#>x ! «W* 00°V

e tsWS' V9»vot . *v'«\4e'

On May 30 Francasal was "onoflrT " in France lor a mere £500.

Where is Francasaî now? Mr.•Bailey says: "I don't know. Ihad a phone call from a man whosaid he was Mr. Maurice Williams.

" He asked me to look afterthe horse before it ran at Bath.I did so. After the -race it was

•i driven away from Bath fay thedriver of a horse-box.

. GREYHOUND-BETTING COUP

£987 FOR 2S. TOTEWITHHELD

An attempted betting coup at Dagrn-im Greyhound Stadium, Essex, yester-

afternoon could have involved>okmakers throughout the country in'oss of more than £10m.. accordingthe estimate of one bookmaker. In

e 4.5 p.m. race the totalisator forecastvidend was declared at £987 I l s . <W.r a 2s. bet. There was only one winning:ket. payment on which has beenithheld. "A stadium official said that 10 minutes

engagements for next- by a Mr

Edward - • - -" This is a mistake," Mr. God- j

dard's wife said. " We have never j.snen or heard of the horse, nor J

Maurice Williams, the owner//!

84

Accordine to " Sportma LifeGuide," which l i s t s S a n t a ipfore the race was due to be run

—•- '-- —•* 'e telephones on the stadium switch-iard went dead, including the 'hreeess telephones. No incoming callsuld be taken or outgoing calls m.tder half an hour.The method used at Dagenham toick Buckwheat, a 2-1 chance wi th the>okmakers and Handsome Lass, a ^-2

chance, for the first two places. vvas toflood the tote windows wi th peoplebacking unl ikely combinations. In th isway few outsiders could place bets.

ONE TICKETAs only one w i n n i n g ticket was sold,

the totalisator declared a dispropor-tionalely high dividend. But Ihe combi-nation of Buckwheat and HandsomeI av. was backed in outside oflicex a!tote odds. In all there were 11.757 tore-c:i,t bets on the race placed on thecourse.

The w i n n i n g forecast had been widely,backed in hel l ing shop., throughout thecoun t ry . Coral'., say tha t most of the i rshops in Ihe London a i e u are affected

Mr. Ron Pollard, general manager olladbroke's. said: "We alone stand tolose £25().(HKI on the i.ice."

Mr. Mark I ane, biggest nookmakei in

CO'*

Levy had divested himself of ownership bygiving the horse to Alexander Wood, a pawnin the game, and had backed Running Reinto win £50,000. The result caused a scandal,bookmakers refused to pay on the winner andthe prize money was withheld. Wood wasforced to go to law in an attempt to get hismoney, and after Lord George Bentinck'sevidence of dye being sold to Levy, the judgeasked for both Levy and the horse to attend.Both had disappeared, and the Jockey Clubhad no difficulty in awarding the race toOrlando, who had finished second. It latercame to light that at least one other horse inthe race had been over age.

As for Crockford, he discovered that histrainer's son had backed Gully's horse, andsuspected his own horse, who finished seventh,of being doped. He claimed he was robbed,and died three days after the most famouscase of a ringer in racing history.

A more recent ringer was Francascal in arace at Bath in 1953. Over £5,000 was bet onthe horse with London bookmakers and itduly won comfortably at 10-1. The book-makers were rather annoyed at their liabilitiesbecause they had been unable to transfer thebets via the blower service to the course.Had they been able to do so, the starting pricewould have been considerably shorter. Theirannoyance turned to anger when it wasdiscovered that the telephone lines to Bathhad been cut, and that two men with a ladderhad been seen acting suspiciously in a lanenear the city. Police investigations discoveredthe men who had cut the wire and a complexplot was revealed. The horse which had runas Francascal was really a much better horsecalled Santa Amaro. The gang went to prison.

Another swindle of cut wires happened inAustralia in 1939. Before the last race of ameeting at Ascot, Melbourne, crooks cutthe cables of all the radio stations except one,which then proceeded to give a fake broad-cast of the race a few minutes after it had beenrun. In the few minutes between the race andthe fake broadcast, the name of the winnerhad been telephoned to accomplices whobacked the horse with bookmakers waitingfor the broadcast. The fake broadcaster wassoon apprehended and sentenced, but manybookmakers paid out and lost money.

F I X E S A N D S W I N D L E S

A casino gambling racket which swindled20,000 Britons of over £100,000 began in 1962.Leaflets carrying the name of the FrancoBritish Casino Syndicate, with a Mayfair,London, address and telephone number, wereposted in empty shop windows and on tele-graph poles in many large cities of England,inviting punters to invest in units of up to£100 in the Syndicate. The Syndicate promiseddividends from its casino operations of at least£6 per week, tax free, on £100 invested. Thedividends, according to the Syndicate litera-ture, came from an infallible system at roul-ette. While the Syndicate was collecting moneyfrom investors, the promised dividends werepaid, but one day the cheques stopped andenquiring investors found the offices deserted.The swindle was not very ingenious, but it wasclever enough to catch thousands of suckers.

No ingenuity was needed to cover up a plotat the Dagenham greyhound racing track in1964, because no attempt at concealment wasmade. It was not the first or last time thatefforts have been made to tamper with thetote odds, but it was the most spectacular.When betting began on the 4-05 race one Juneafternoon a number of men with bags of silvercoins began to bet at every one of the few totewindows taking forecast bets. They occupiedthe windows right up to the time of the race,buying a few hundred tickets on the forecastpool. An ordinary race-goer found he couldn'tmake a forecast bet. Remonstrances with anyof the gang, for that is what they were, pro-voked the necessary amount of physicalintimidation to persuade him to go away.When the race was run, it was found that onlyone ticket had been sold correctly forecastingthe first and second dogs to finish. The divi-dend was a staggering £987 11s 6d for a 2sticket. All over the country it was found that"etting shops and bookmakers had taken bets°n the winning forecast. The amount wageredwas estimated to be about £1,000 and since the°dds represented around 10,000 to 1, book-Wakers were being asked to pay out about110 million.

Ihe swindle was so obvious and its scales° ludicrous that it is surprising that the gangc°uld expect to get away with it. BookmakersRurally withheld payment while enquiries

made, and finally declared the race void.

Presumably the gang reckoned that it wouldbe practically impossible to prove conspiracy,and decided that since it was too much to hopethat the coup would be undetected, they mightas well be in for a pound as a penny. Theyconsiderably overdid it and failed to collectthe hoped for ill-gotten gains.

A scandal of a very different nature, since itinvolved the Prince of Wales and certainly didnot amuse Queen Victoria, began during theDoncaster St. Léger meeting of 1890. ThePrince, who was a member of a house partyat Tranby Croft, was very fond of baccarat,

Edward VII when Prince ofWales loved gambling, andwas frequently to be seenat Monte Carlo. Heintroduced baccarat toEngland and eventually wasinvolved in a scandal whenone of his fellow-playerswas accused oj cheating.

85

P A R T F O U R

The famous house parly atTranbv Croft on September11, 1890. His RoyalHighness the Prince ofWales is seated in the frontrow. On his right isLieutenant Colonel SirWilliam Gordon-dimming,who was accused ofcheating at baccarat, andsued his accusers forslander, thus forcing thePrince to give evidence incourt, causing a societyscandal. General Williamsand Lord Coventry arestanding on the left.

which he introduced to England. Betting oncards was illegal, but the Prince had his owncards and counters, and he took them with himto Tranby Croft, where the game was playedin the evenings. One of the players was thePrince of Wales' friend, the Scottish land-owner Sir William Gordon-Gumming, a sol-dier, and a man for whom the phrase 'an officerand a gentleman' might have been invented.

On the first night, the son of the housesuspected Gordon-Gumming of cheating, byadding or subtracting from his stake accordingto whether or not he won, a manipulationknown as la pousette. He conveyed his sus-picions to others of the party, Gordon-Gumming was watched on the second night,and the others agreed that he appeared tocheat. When Lord Coventry and GeneralOwen Williams were informed, they told thePrince of Wales and Gordon-Gumming wasconfronted with the accusation. He indig-nantly denied the charge, but because thePrince was involved he agreed to sign a paperthat he would never play cards again. Inreturn, the matter was to be hushed up so thatno public scandal would attach to the Prince

of Wales or Sir William Gordon-GummingHowever, scandal being what it is, the storygot out and eventually reached Gordon-Gumming, who regretted signing the paper.He then re-affirmed his denials of guilt, andtried to get those who had accused him otcheating to withdraw the charge. Final!}. uiorder to clear his name, he sued them lorslander.

Although Gordon-Gumming cut an impres-sive figure in the witness box, he could nothope to win the case with five claiming to have >seen him cheat. The Prince of Wales wasjforced to give evidence, and the disclosure of;his private gambling upset the Queen an<|caused consternation in the country.William Gordon-Gumming was banishefrom society and retired to his estates at!Gordonstoun, where, ironically, the present]Prince of Wales went to school.

In Scott Fitzgerald's novel TheGatsby, the narrator asks Gatsby who another|character called Meyer Wolfsheim is.

'Meyer Wolfsheim? He's a gambledGatsby hesitated, then added coolly: 'He'1the man who fixed the World Series in 19l

Finger Ring forpricking cards.

Refleetor fixed underneath table for reflecting cards whendealing (open and shut).

Dye Box, sewn on towaistcoat, for stainingthe bucks of cards.

Ace. King. Knave. Ten.Method of marking card-backs. The darkening of various parts of the figure indicates the

value of the card.

" Stripper-plate "for curving the edges of cards.

Apparatus for shaving off the edges of certain cards forpurposes of dealing.

" Electric" DiceUsed in conjunction with a special

table, through which an electric cur-rent is turned on and off at will. Thecurrent, when operating, attracts theside of the dice opposite the " six,"which thus turns uppermost.

at cards and dice. The ringis used to prick certaincards during a game sothat they becomerecognisable later. Thestripper plate can be usedto trim high cards on thelong side and low cards onthe short side, enabling thecheat when cutting to cutto a low card or a highcard depending uponwhether he holds the cardsby the long or short sides.These and other deviceshave been manufacturedand sold in America.

Mirror in pipe lying on card-table, reflecting cards when dealing

P A R T F O U R

Arnold Rothstein was amoney-lender, rum runnerand drug trafficker. He wassuspected of organising thefamous Liberty Bonds theftracket of 1918. He ownedproperty and race horses.He was one of the mostpowerful of all Americangangsters. Called 'TheKing of Gamblers', he isbest known for theallegation that he fixed theWorld Series of 1919.

Later, Gatsby is asked why Wolfsheim isn't injail.

They can't get him, old sport. He's a smartman'.Meyer Wolfsheim was based on a real

character, Arnold Rothstein, and althoughhe was declared innocent, it has not preventedwriters suggesting that he really did fix theWorld Series. When it is realised that tomillions of Americans the World Series wasthe sporting event of the year, if Rothsteindid arrange the result it must rank as justabout the biggest fix of all time.

What is not disputed in the story is that someof the Chicago White Sox baseball team, inorder to avenge themselves on their employerwho, they considered, underpaid them, and toearn some cash, decided to look for a gambler

who would pay them $10,000 per man tolose the championship match with CincinnatiArnold Rothstein, an immensely rich andcorrupt gambler, who at one time seemed tohave judges, policemen and city officials inhis employ, as well as crooks of all kinds, wasapproached to put up the money. The crackWhite Sox team, the 4-1 on favourites, lostthe series, to the surprise of America, althoughsome thought the mystery explained wheneight of the players and Rothstein werebrought to trial. Some of the team confessedto throwing the series, but Rothstein main-tained that although he had been approached,he had declined to have anything to do withthe plot. At the trial, it was not proved that afix had taken place, and Rothstein wasacquitted.

Despite this, it was shown that Rothsteinand his friends had bet large sums of money onCincinnati, and had won $350,000 on theseries. There is no doubt that Rothstein had avery strong conviction that Chicago WhiteSox (after the trial popularly known as theBlack Sox) would lose.

Arnold Rothstein escaped the punishmentof the law on several occasions. More thanonce he won hundreds of thousands of dollarsbacking his own horses, and on more than oneoccasion their victories were not above suspicion. He was once charged with shootingat policemen raiding an illegal craps gameHe was acquitted.

But although he was the most powerful ofAmerica's gangsters, known as 'The Brain'and The King of Gamblers', Rothstein couldnot defy underworld justice as easily as heseemed to defy the law. He finished a pokergame in 1928 owing over a quarter of a milliondollars to fellow crooks, and took too long topay up. He suggested the game was rigged'On November 6, 1928, Rothstein should havewon over half a million dollars on bets he hadput on Herbert Hoover winning the Presi-dency and Franklin D. Roosevelt the gov-ernorship of New York, but on that day hedied from a bullet wound. Two days earlier)the man of many nicknames, one of which was

'the man who dwells in doorways', had bée"found in the servants' entrance of New Yorks

Park Central Hotel with a fellow-gambler'sbullet in his stomach.

88

MRT FIVE

LOTERIft NATIONALE

Games of chance

89

P A R T F I V E

"hance, according to Voltaire, is a wordvoid of sense; nothing can exist without acause. For the gambler, a chance event is oneungoverned by any influences, such as thetossing of a coin, where the result, heads ortails, appears to be accidental and unpredict-able. Chance is said to be blind. A 'pure1

gambler is one who puts his whole trust inchance, taking risks on events over whichnothing and nobody, let alone he himself, canexercise any control. Games of chance arethose in which skill cannot affect the resultor outcome.RafflesAt first thought, thebuyer of a raffle ticketmight not consider himself to be a gambler.Raffles are often seen simply as a way of rais-ing money for a good cause, like a charity or aworks sports club, or to finance local ameni-ties, or even to repair the church roof. None-theless, to enter a raffle is to take part in achance event. This is recognised in those partsof the world where raffles have to be registered,and in those North American states whereraffles are illegal. Raffle prizes can be moreexpensive than an automobile . . . or less ex-pensive than a bottle of whisky. The annualamount speculated in raffles is enormous, andfew adults have not bought a raffle ticket atone time or another. That a ticket is bought asa donation to a good cause, and the prospectof winning not of importance to the buyer,cannot disguise the fact that gambling is tak-ing place. The operation of a raffle is simple:the organizers merely have to ensure that theprizes offered cost them less than the ticketmoney collected minus their expenses. Thedifference is the profit.LotteriesBig raffle-type operations such as those run bythe state in various parts of the world areusually described as lotteries. The top prizesare often large enough to change the wholeway of life of the winners. The chances ofwinning are correspondingly small and,though lotteries are pure gambles, it is unlikelythat they will cause serious addiction inparticipants.

The Puerto Rican lottery sells 135,000tickets, in three series of 45,000 each. Eachticket costs $20, so the pool is $2,700,000.90

FROM A RARE CO1"•KG

G A M E S O F C H A N C E

' • • '' "——;——-———————'^r^KStnaiai*^

-A- LOTTE:LOHDOJst, 1739-

PRESER3/ED INL THE BRITISH MUSEUM.

When local authorities inBritain were allowed to runlotteries in 1977, aftermuch opposition, thev wererestricted in the prizemoney and number oftickets sold. So manvpeople wished to take panthat it was reported that inPlymouth tickets werebeing exchanged on theblack market at inflatedprices. The engravingshows a scene at the drawingof a lottery in Guildhall,London, in 1739.

:.y-. ;•.:-*-„.»:

91

P A R T F I V E

Diee play in literature andpainting. In the seventeenthcentury book the text is inEnglish and Latin and thenumbers relate to the itemsof equipment in the drawing.Notice that dice were usedin casting lots by throwingthem through a casting boxonto a numbered board. Abackgammon boardillustrated is called a pairof tables. The painting byGeorges de la Tour iscalled The Dice Plovers.They are using three diceand may be playing a formof a game called buck dice,in which case the three Iswould be a winning throw.

CXXXIV.

Ludttt Alt*.

Dice-Play.

Git

•f

( « 7 9 ;

ttismott take up all

c a f t i n f i - B O K 2.upon a Boara 3.

ono tljtB 1»Dice-pliycr»at calling Lots.

SBtnplavb?L u c k a n o Skill8t Tahi t iin a pair of Tables, 4,a n D a t Cards, j.

S8H» plat »' Chclfeon a ChclTe-board, 6.Uiljtrc on lpa r tbearetb t(n flusf.

Ctie mott(ngcntona Came,

toi jc i t iu as it tociettoo f lrmitsf igt l tto2ctU« In JSjttcl-

Ttfcrii (tain) I.ludimm,

vel immit-nrrius i l lasper Fritillrirt* 2.wTtMUm 3.nuracris noca tam,idque eflLudus Scrtiltfn

Sorte & Aneludi turCalculain dlvcv tdiMarit^ 4.& Chartir Iffinii, J,

Aluculi:Indiraut ifiAinci, <5.'uM folasrsrégnât .

Jngeniofl î rau»l u d u s eft ,L. Js<rtrHx(ttlarnmt 7.<juo ve lu t iduoexercicti»pr^cl io con^ igunt .

Curfil

92

P A R T F I V E

21! «3

IBS^

National lotteries have beenpopular on the Continentfor 400 years. Theengraving shows a FrenchNational Lottery draw in1835. Two soldiers keepguard while a blindfoldedman draws five numbersfrom a barrel. Thewinning numbers on thisoccasion were 60, 12, 1, 2and 71. The photographshows tickets being sold inthe weekly ItalianState Lottery.

Each ticket is divided into eighty parts, so thecheapest stake in the lottery is one-eightieth ofa ticket, costing 25 cents. A draw is madeweekly, and thousands of prizes distributed.The top weekly prize is $100,000, won bythree $20 tickets, one in each series. Thesecond, third and fourth prizes are $36,000,$16,000 and $10,000, drawn separately. Thesmallest prizes, paid to one-tenth of all en-trants, are of $20 (i.e. the winners get theirmoney back) for tickets whose last digit cor-responds with the last digit of the top prize-winning number. Twice a year, at Christmasand in mid-summer, there are bigger lotteries,in which the tickets cost four times as much,and the top prize, known as El Gordo, is$480,000. The payout on the top prize, there-fore, equals 6,000 for one, iax free.

In 1970, the New Jersey State Lottery beganoperations. Prizes have varied, but the follow-ing shows how the lottery worked. There wasa weekly draw, tickets costing 50 cents each.All tickets contained a number of S'K digits:when the number of tickets sold exceeded onemillion, the numbers were repeated. As in thePuerto Rican lottery, the top prize ($50,000)was won by the tickets showing the winningnumber, but minor prizes in this lottery werealso based on the winning number. Ticketswith the last five digits correct won secondprize of $4,000. Third and fourth prizes,decided on the same principle, were $400 and

94

1 G A M E S O F C H A N C E

$40. Tickets with the last two digits correctplus those with the first two digits correct wereplaced in a special draw which took placeevery few weeks, according to the number oftickets sold. A three-digit winning numberdecided this draw, the winners entering a thirddraw. Again there were consolation prizes of$ 100 for holders of tickets with the last twodigits corresponding to the winning number.All tickets in the third draw won $500, thewinner taking $1,000,000, with second andthird prizes of $200,000 and $100,000. Therewere seven fourth prizes of $10,000.

Other American states run lotteries whichoperate on similar lines. About 40 per cent ofthe pool is returned to winners, the remaindergoing to the state funds after the deduction ofexpenses.

One of the oldest lotteries in the world is theItalian State Lottery, which began in Florencein the sixteenth century. The lottery is run bythe Ministry of Finance, and tickets are sold bythousands of offices throughout Italy. Ticketsare numbered from one to 90, and there areten separate draws made each Saturday fromten wheels, each named after an Italian city.Five numbers are drawn from each wheel. Thebuyer of a ticket may back a single number tobe drawn from a specific wheel, or he mayback any selection of numbers up to five to bedrawn from a specific wheel. Stakes can vary,and odds of a million for one are paid to anyticket holder who has specified all five num-bers to be drawn from a wheel. The proba-bility of picking all five numbers is one in thenumber of combinations of five from 90,90C5, which is 43,949,268. The Italian lotteryis not strictly a lottery, as there is not a per-centage take from an overall pool, and thepayout varies with the number of winners.

In 1977, after much opposition, localauthorities were allowed to run lotteries inBritain, although restrictions on the size ofprizes and price of tickets caused few of themto enthuse over the legislation. However, thereis a long history of lotteries in Britain, datingback to 1569, and since 1956 there has been anational lottery, the Premium Bonds scheme.Bonds can be bought at most Post Offices,banks and Trustee Savings Banks in units of£1, although two units is the minimum hold-ing. The bond has two functions. The first is

95

P A R T F I V E

Ticket sellers for the Greet.National Lottery sellingtickets on the street inCrete. The Irish HospitalsSweepstake is based on afew of the years biggesthorse races. Below isshown the cover used forthe books of tickets for the1977 Irish Sweeps Derby.The draw is made by Irishnurses, and all ticketsdrawing a horse win aprize. Each draw is amulti-million poundexercise, benefiting Irishhospitals by nearly £10million per year.

B, ._„__

,£ 86 DhB 63517

96

SweepIn a s\|generaresult fbestSweepfunds |side IrallotherU.S.netwolbute tor fou|racesracesDerby!

In tit hasSweeplnurses!and trianothea tickdallocat)vised

EveilPrize, Ithe 19of molwouldc«nt'ntowinnercash£l20.oreceivethird


to provide a method of saving, since bondscan be cashed at their face value at any time.However, no interest is paid, and it is theinterest on the bond which goes into a pool tobe shared by the winners. The winning num-bers are generated by Electronic RandomNumber Indicator Equipment, known popu-larly as ERNIE. A top prize of £25,000 is paidweekly, with numerous smaller prizes rangingfrom £5,000 to £25, and there is a specialmonthly prize of £50,000. Several millionpounds are currently invested in Britishpremium bonds.

SweepstakesIn a sweepstake, the winning numbers are notgenerated at random, but are based on theresult of an event, usually a horse race. Thebest known example is the Irish HospitalsSweepstake, set up in Dublin in 1930 to raisefunds for hospitals. The Sweep was illegal out-side Ireland, but it quickly gained popularityall over the world. It had to overcome, amongother obstacles, the refusal of the British andU.S. Post Offices to handle its mail. A vastnetwork of agents was quickly set up to distri-bute the illegal tickets. The Sweep is run threeor four times a year, based on major horseraces in Ireland and Britain. Some of theseraces are sponsored by the Sweep. The IrishDerby has been sponsored since 1962.

In the past, the lottery has been so large thatit has been divided into uni ts , or separateSweeps. The draw for horses is made by Irishnurses, who draw a ticket stub from one drum,and the name of a horse in the race fromanother drum, until all horses are allocated toa ticket. If there are 20 units, each horse isallocated to 20 tickets. The draw is super-vised by the Irish Police.

Every ticket which draws a horse wins aPrize, and there are also consolation prizes. In

1960s, the tickets stated that 25 per centmoney received from the sale of tickets

w°uld be paid to Irish hospitals. The 75 perCent left, minus expenses, would be dividedmto units of £120,000 for distribution toWlnners, any remainder being divided into 50cash prizes of equal amount. Of each unit of

20,000, the holder of the winning horseReived £50,000; the second £20,000 and thehlrd £10,000. The drawers of also-rans shared

°'

£30,000, the last £10,000 being shared outamong consolation prize winners.

It is probable that at least half of the IrishHospitals Sweepstakes tickets were sold in theUnited States until the early 1970s, when thelegalization of State-run lotteries in variousStates caused a big drop in sales.

The numbers gameThis gambling operation, sometimes called thepolicy game, has been operating in the UnitedStates for hundreds of years and became bigbusiness in the 1920s. Because it is illegal, theturnover is unknown, but it is likely that it islarger than that of any lottery in the world.

Tickets for the numbers game are sold byagents who might be cafe owners or news-paper sellers, or who might even run an officefronting as a legitimate business.

To place a bet the gambler selects a three-

The numbers game beganin Harlem in the early1900s and by the 1920s hadbecome big business,particularly among theBlack population. Whenprohibition ended in the1930s bootleggers turned tothe numbers game forquick profits. DutchSchultz, seen awaiting a'not guilty ' verdict in a taxevasion trial, became kingof the numbers racket,making huge profits andnot being particular aboutpaying winners.

97

P A R T F I V E

Bingo is one of to-day'smost widespread gamblingpastimes, attracting playerswho gamble on nothingelse. Bingo is believed toderive from the Italiangame Lotto, which itselfwas inspired by the ItalianNational Lottery. Thegame in the engraving wasbeing played in Trastevere,Rome, in 1875.

digit number from 000 to 999 and writes it on apad with his stake, for instance 661-$1. Thepad contains two carbons of the bet: thegambler is given the top sheet, one carbon iskept by the agent, and the other taken by arunner to the bank.

An example of one bet has been given. Somebanks will allow bets of other than a three-digit number. Bets that a selected digit willappear in a specified place in the winningnumber might be allowed. Or bets might beaccepted on the first two or last two digits. Thewinning number used to be based on the lastthree digits of the Federal Reserve ClearingHouse report, but nowadays the last threedigits of the daily take at a racetrack are used.

The bank for a correct three-digit numbermight pay 500 for one or 400 for one. Of this,10 per cent will be deducted as commissionfor the runner. At worst, therefore, the lucky

gambler might get $360 instead of the $1,000he deserves, a bank edge of 64 per cent. Singlenumbers might pay as little as six for one, anedge of 40 per cent.

The bank takes an even bigger advantagethan this, because on certain numbers the bankwill either refuse to accept bets or offer smalle'odds. These numbers are known as cut num-bers, and are the numbers on which the bankcould otherwise expect more than normal jbusiness. There might be 100 or more suchnumbers: 777, for instance, or 123, or thenumbers ending with two noughts such as 700-

There is little room for systems of bettingon the numbers game. Most banks will accepa boxed number. If a box is drawn round ti [number 468, the gambler is backing all cofl'binations of these numbers: 468, 486, 64»684, 846, 864. This represents six bets, and »$1 a bet the total cost is $6.

98

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BingoWhen bingo was legalized in Britain in 1960,the amount of business which took place sur-prised everybody. In no time, cinemas wereceasing to show films and beginning to holdbingo sessions. Conversely, in America, asmany States have legalized bingo, the turnoverhas dropped because the prizes allowed by theState have been lower than the prizes whichcould be won in the illegal games. Big businesshas given the name bingo to a game which hasbeen played for centuries under other names:lotto, housey-housey or tombola.

Basically, each player has a card containingcertain numbers. Many current kits for chil-dren's recreational games contain 15 of thenumbers between one and 90, which was thecommonest form of card for many years. Mostmodern cards contain 24 of the numbers be-tween one and 75, arranged in five rows of fivenumbers printed in columns below the lettersof the word 'bingo'. The central space on thecard is not given a number: it is a 'free' space,usually called a 'free play' or a 'free number'.

By a system of random selection, numbersbetween one and 75 are called by an operator.and as each number is called, holders of cardscontaining that number cover it on their cards.The holder of the first card to have all itsnumbers covered is the winner. He or she(usually she as the game is most popular withwomen) calls out 'bingo'.

There are, of course, variations. The mostpopular is to have a minor prize for the firstplayer to cover one row of numbers. There areas many ways of deciding minor prizes as thepromoters like to devise. A prize is sometimespaid to the first player to cover a line in anydirection, or to cover the numbers in the fourcorners of the card. Some big games might paythree or four prizes per game.

The numbers to be called are usuallychosen' by a machine which is loaded withlumbered balls. They are rather like table-tennis balls, and they are held in a wire or clearPlastic cage, where they are agitated bymechanical means or by a jet of air. One ballat a time falls or is blown out of the cage into aPocket, when its number is called by the caller.

lngo is not a game of skill, though mental andmanual dexterity is demonstrated by those

tlcipants who play several cards simul-

taneously. Sometimes, the players are giventhe help of an electric scoreboard which lightsup the numbers which have been called.

Usually, bingo halls charge for admissionto a session, and a fee is charged per card pergame. This way of paying for the entertainmentis obligatory in Britain, where the entrance feeis used for the operator's expenses and profits,while the fees paid for cards are used as prizemoney. In Britain, large prizes are sometimesgenerated by the linking of several simul-taneous games under the same proprietorshipbut at different venues.

It has become clear that bingo can easilycause addiction. A typical bingo addict hasbeen postulated: a bored housewife whoattends a session, perhaps in the afternoon,finds friends and a social atmosphere, and getsso hooked on the game that more and morehousekeeping money is spent on the diversion.

Bingomania overtookBritish housewives in the1960s, when many cinemaowners found it moreprofitable to stop showingfilms and switch to bingo.The queue entering the TopRank Bingo and SocialClub at Peckham, London,

for an afternoon session,are entering what wasrecently the Odeon Cinema.

99

Keno is a form of bingo inwhich the players choosetheir own numbers. Modernkeno, as played in mostLas Vegas casinos, differsfrom the original version ofthe game played in NewOrleans from the middle ofthe nineteenth century.This game more resembledmodern bingo, as is shownby the engraving of a gamein America in 1870.

100

I


The Gaming Board of Great Britain hasexpressed concern at the growth of a relativelyharmless and cheap method of recreation intoa large-scale gambling activity.

The assessment of chances does not norm-ally enter into bingo, as each player, or rathereach card, has an equal chance of winning.However, in America, where the popularityof bingo has forced some casinos in Las Vegasto operate games, large prizes are sometimespaid to winners who can cover a card in acertain time, say within the first 50 numberscalled. It is possible to calculate the proba-bility of covering a 24-number card in 50random numbers. To do so, it is necessary todivide the number of combinations of 24numbers in 50, 50C24, with 75C24, the numberof combinations of 24 numbers in 75. This is amammoth calculation, but by using logarithmsof factorials it can be calculated as being aboutone in 212,000. So the chance of covering acard with 50 or less numbers called is verysmall.

German lottoThis is a national game which has more simi-larities to the Italian lottery than to bingo.Customers complete coupons in agents' offices,often shops as in the style of the Americannumbers game. They choose six numbers be-tween one and 49. Each week six winningnumbers plus a reserve number are drawnby the bingo method of numbered balls. Thetotal pool, less the usual deductions, is distri-buted among the classes of winners. All sixnumbers right takes top prize, and five rightplus the reserve takes second prize. There arealso consolation prizes for those with three,four or five numbers correct of the winningsix. The top prize is limited to 1^ million DM,a little less than the limit placed on a Britishfootball pool first dividend. The chance ofselecting the six winning numbers is one in

C6, or nearly 14 million to one, and of get-ting a prize at all nearly 700,000 to one.

KenoThis game, not unlike German lotto, is veryPopular in the casinos of Las Vegas. Electronic"°ards in various parts of the casino list the"umbers from one to 80. Twenty winning"Umbers are selected in the manner described

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for bingo, and the winning numbers are lit onthe boards. Gamblers can select any quantityof numbers from one to 15 to appear aswinning numbers. They indicate their choiceby crossing out their selections on standardkeno tickets. Tickets are presented at the kenocounter, with the total stakes, where a kenowriter makes two copies by punching out thenumbers on an 'inside' ticket. The keno writergives one copy to the gambler, and keeps theother together with the gambler's originalticket. Tickets are marked with the numberof the appropriate keno game. Games takeplace every few minutes. Keno runners carry-ing blank tickets and crayons enable gamblersnot in the keno lounge to bet by taking ticketsand stakes to the counter, and later deliveringany winnings. There will be a minimum stakeon a keno bet, usually 50 or 60 cents, and allstakes must be in multiples of it, althoughlower stakes might be accepted on way-tickets, to be explained later.

The ticket of a gambler who bets one num-ber only to be in the winning 20 is known as a1-spot ticket, and other tickets are known as4-spot, 8-spot etc. A simple 8-spot ticket isshown in Figure 5:1. The figure 8 written onthe right indicates an 8-spot ticket, the 60 in

Figure 5:1, a simple keno8-spot ticket. The plaverhas marked eight numbers.The 8 indicates an 8-spotticket. The 60 indicates astake of 60 cents. Theprinted 16 is the number ofthe game.

101

P A R T F I V E

Figure 5:2, a keno wayticket. The instructionsmean 21 6-spot bets at$7.20 each way, and 3512-spot bets at 60 centseach way. The total sumbet is $46.20.

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the box at the top indicates the stake of 60cents. The signs for dollars and cents are neverused. When the total stakes on a ticket exceed$1, the cents are written over a line, thus l1-indicates stakes of one dollar 20 cents.

Where three or more numbers are selected,consolation prizes are paid. On a 4-spot ticket,a prize will be won if two, three, or four win-ning numbers are selected. A 10-spot ticket,the most popular, will win when five or morenumbers selected are winners. This enablescombinations to be backed. A combinationticket (or way-ticket) is shown in Figure 5:2.On this ticket seven groups of three numbersare selected. The gambler has taken each pairof groups to bet a 6-spot ticket 21 ways at$1.20 each way, and has taken each foursometo bet a 12-spot ticket 35 ways at 60 cents each,his total stake on the ticket being $46.20. Onway-tickets a minimum stake of half the usualminimum is accepted in most casinos.

As an example of payouts, the most popularticket, the 10-spot, might pay, per 60-centstake: for 5 spots $1.20; six spots $12; sevenspots $90; eight spots $660; nine spots $2,400;ten spots $12,500, but these payouts will varyfrom one casino to another.

High-low tickets are special tickets which

figu\lowinstrt

carry special payoffs. With a high-low 12-spotticket, three groups of four connecting num-bers are circled as in Figure 5:3. A gamblergetting five or more spots correct will win, butthe win will vary according to how the winner'snumbers fall within the three groups, e.g. sixcorrect numbers, two from each group, willwin less than six correct including one wholegroup of four. Payouts, which vary consider-ably between casinos, might be as follows on a30-cent ticket:

5 spots: 2-2-1 pays $0.153-1-1 pays $0.203-2 pays $0.254-1 pays $0.30

6 spots: 2-2-2 pays $1.303-2-1 pays $1.653-3 pays $2-054-1-1 pays $2.054-2 pays $2.25

7 spots: 3-2-2 pays $9.703-3-1 pays $12.204-2-1 pays $14.704-3 pays $19.70

8 spots: 3-3-2 pays $65.604-2-2 pays $75.204-3-1 pays $84.754-4 pays $113.40

9 spots: 3-3-3 pays $166.654-3-2 pays $169.704-4-1 pays $175.90

10 spots: 4-3-3 pays $3704-4-2 pays $385

11 spots: 4-4-3 pays $64812 spots: 4-4-4 pays $1,110

The maximum payout in Las Vegas is$25,000 per game, and if the total winnings ona game exceed this amount, the winnings mustbe scaled down in proportion to each other sothat the total is $25,000.

The house edge at keno varies slightly fromthe 1-spot to the 15-spot ticket. On a 1-spotticket, the usual payout is $3.20 for a dollarstake. As the probability of a selected numberfrom 80 being one of the 20 winners is f$ or f,the payout, were the game fair, would be $4-The house edge on the 1-spot is therefore 20per cent. The house edge on the other tickets [is usually a little more than this. Keno 'stherefore a very unfair game for the gambler-particularly for gamblers looking for a bigpayout. The odds against winning the $12,500

102

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figure 5:3, a 12-spot high-low ticket, indicated by theinstructions HL.

23

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for 60c mentioned above on a I0-spot ticketare nearly nine million to one.

Slot machinesSometimes they are called fruit machines,because of the symbols which determine wins;sometimes one-armed bandits, because of thesingle handle to rob gamblers. Either way, theyare forms of mechanical lotteries. They wereinvented by Charles Fey, an American mech-anic, in the late nineteenth century. The firstmachine, Liberty Bell, used playing card suits,bells, stars and horseshoes as its symbols.

The basic slot machine, until refinementsappeared after the Second World War, con-sisted of three reels each containing 20 sym-bols (not all different). When a coin is insertedin the machine, and a handle pulled, the reels•"Pin, and when they stop a line of three sym-°°'s is shown through a window. Depending°n the composition of the line of three symbols,tne machine either pays out an amount ofc°ins according to a schedule stated on theMachine, or it does not pay at all. The payoutls unfair, as it is less than it should be accordingto the laws of probability.

A hypothetical slot machine might containhe following symbols on its three reels :

BarBellHorseshoeCherryOrangePlum

Drum 1231428

Drum 2113843

Drum 3223247

Suppose the payouts were (X means anysymbol): three bars 20; three bells 20, threehorseshoes 20; three oranges 10; three cherries5; three plums 5; bar bar X 10; bell bell X 10;horseshoe horseshoe X 10; cherry cherry bar5; orange orange bar 5; plum plum bar 5;plum cherry X 2.

The number of ways the reels can stop is203 = 8,000. The winning lines, on average,will pay out as follows each 8,000 spins:

Three barsThree bellsThree horseshoesThree orangesThree cherriesThree plumsBar bar XBell bell XHorseshoe horseshoe XCherry cherry barOrange orange barPlum plum barPlum cherry X

1,832

The machine pays out on average onceevery 4-37 spins, and makes a profit of justunder 20 per cent. Machines can be set to paywhatever percentage the operator requires.Many machines since the 1920s have incor-porated a jackpot mechanism. The machineis geared to feed coins into the jackpot whichopens when a certain combination shows (itmight be three bars in the example above) andadds its coins to the normal payout.

In the 1950s, various innovations speededup the slot machine action. Machines weremade with four reels, with very large payoutsfor the jackpot lines. Then came the holdbutton, which allows a player to hold anysymbols for a second spin of the reels. Laterstill came the three-line-pay machine. In mostslot machines three lines are visible - the

Number of ways Payout2x1 x 2 =3x1 x 2 =1 x3x 3 =2 x 4 x 4 =4 x 8 x 2 =8 x 3 x 7 =2x1 x!8 =3x1 x!8 =1 x 3 x 1 7 =4 x 8 x 2 =2 x 4 x 2 =8 x 3 x 2 =8 x 8 x 20 =

469

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The modern slot machinewas invented by CharlesFey in San Francisco, andthe first one was installedand collecting nickels fromthe customers in 1887. Thenumber of slot machines inNevada alone is now in theorder of 50,000. Even aluxury casino might have1,000 slot machinesarranged in banks so thatreal addicts can play morethan one at a time. Theplayer in the pictureappears to be pulling thehandle of one machinewhile watching the resultson a neighbouring machine.

105

P A R T F I V E

1500 t500 1500$150-I50'-I50

Women find slot machinesparticularly attractive, andsome become addicts.There is an obvioussimilarity to bingo, as it iseasy to begin by spendingthe loose change from thehouse-keeping money andto remain to try to retrievelosses. It is not uncommonto see women in theFremont Street casinos ofLas Vegas wearing a gloveto facilitate the operationof four machines at once.

winning line and those immediately above andbelow it. The player could put two coins in theslot, in which case the line above the winningline also became a winning line. Three coinswould qualify all three lines as a possiblewinner. The latest machines in Nevada aremultiple coin machines, in which gamblerscan bet up to eight coins at a time. The extracoins increase the jackpot payoffs. A refine-ment of these are progressive jackpot machineswhich indicate the top jackpot payoff. Thisincreases with the number of coins fed intothe machine. The progressive jackpot canonly be won by feeding the machine a statednumber of coins.

Ingenious ways have been found to cheatslot machines in the past, with wire, spoonsand even drills, and there was a much-

advertised rhythm method. Slot machinemanufacturers now seem to have cheatsbeaten, and for the honest player, the morethe slot machines are played, the more certainit is that the large house edge will reduce hiscapital.

Craps/)ÔÏMiasino games of chance, craps probablyhas the biggest turnover. A fast moving game,it is the most popular casino game in Nevada,and has been introduced into Monte Carloand other casinos round the world.

Craps is a simple game, but difficult for thebeginner to grasp. There is no standardizationin the layout of casino tables, which lookcomplicated. Craps is extensively played as aprivate gamble in America, as in Damofl

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Runyon's Guys and Dolls, where NathanDetroit runs a floating crap game. The casinogame in Nevada is more sophisticated, and thegame allowed in Britain is different again.

The private game requires only two dice,Preferably identical. Participants enclose thePlaying area, called the centre, which might bea carpet. The use of a soft surface will ensurethat the dice are not damaged. Ideally, thereshould be a wall for the dice to hit and bounce"ack from, as this eliminates most suspicions°f cheating. The first player to take the dice is'he shooter, and he places a sum of money intr°nt of him as his bet. He is betting he will^'n, and the other players are invited to fade

15 bet; in other words they collectively put|JP an equal amount as a bet that he will lose.

he bets can be won or lost on the first roll.

If the shooter throws 7 or 11 (i.e. the numbersshown on the top faces of the dice make eitherof these totals) he wins. Each of these numbersis known as a natural. If the shooter throws2, 3 or 12, he loses, these numbers being knownas craps. Any other number, i.e. 4, 5, 6, 8, 9 or10, becomes the shooter's point. He continuesto throw the dice until he throws either hispoint, i.e. the same number again, when hewins, or a 7, when he loses. Therefore a 7 is awinner for the shooter on his first roll, a loserthereafter. A throw of 7 settles all bets eitherway. When the shooter wins, it is said that hepasses, and he retains the dice and is theshooter on the next roll. When he loses, it issaid that he misses, and the dice pass in rota-tion clockwise, so that the player on his leftbecomes the shooter on the next game.

The tendency of slotmachines to rob thecustomer when he pulls thearm led to them beingcalled 'one-armedbandits'.Not slow to cash in on agimmick, manufacturersbegan to make machines inthe form of actual bandits.This player is trying to beatDavy Crockett.

107

P A R T F I V E

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Figure 5:4, a Nevada-style craps layout. Thetext explains the variousbets that can be made.

Players also bet amongst themselves. Theymight bet that the shooter passes or misses.A bet that the shooter will win is called a rightbet, that he loses a wrong bet. At any stage inthe shooter's series of rolls players may betthat the player comes or don't come (does notor doesn't come are terms never, it seems, usedin craps). A come bet is a bet that the shooterwins, taking his next roll as if it were his first.The first roll is usually called the come-outroll. A don't come bet is one that the shooterloses. Again, the bet must be settled on thenext 7 or earlier. Further side bets are madeafter the shooter has made his point, whenplayers can bet either that he makes it or thathe does not. If the point is 6 or 8, the odds are6-5 against the shooter making it. If the pointis 5 or 9, the odds are 3-2 against. If the pointis 4 or 10, the odds are 2-1 against. Sometimesthe true odds are offered and accepted, butsometimes incorrect odds are offered, such aseven-money for 6 or 8, and these bets shouldbe declined.

Many other side bets can be made, but themost popular are the hard-way bets. Pointsof 4, 6, 8 or 10 can be made with a double (i.e.double-2 makes 4). A bettor may bet that theshooter makes his point with a double, i.e.the hard way. The true odds are 8-1 againsthard-way 4s and 10s and 10-1 against hard-way 6s and 8s. Clearly there is only one way toshoot 10 the hard way (5-5) where there aretwo other ways (4-6 and 6-4) to shoot 10,

plus six ways to score 7. In private crapsgames, the wrong bettor has an advantageover the right bettor of 1-4141 per cent.

In a casino, all bets will be made against thebank. Craps layouts vary, but that in Figure5:4 will serve to demonstrate the availablebets. It is typical of Nevada.

Four operators look after the administra-tion of the table: the boxman, the stickmanand two dealers. The boxman directs the gameand oversees all the action. The stickmanhandles the dice and looks after the bets in thecentre of the table. The dealers settle the betson their own side of the table. A player changescurrency into chips by placing it in front of thedealer, who will pass it to the boxman forchanging. A player's chips should be kept inthe grooves directly in front of him in the tablerailing, not on the table itself.

As in the private game, the first roll of theshooter is the come-out roll, and all playersmay bet that the shooter passes or misses.When throwing, the shooter must throw hardenough for the dice to rebound from theopposite end of the table. If a dice bouncesoff the table, or lands on a pile of chips, theroll is void.

The shooter's probability of passing can beestimated by considering 1,980 rolls of thedice, and considering what would happen it alloutcomes occurred in the proportions that thelaw of large numbers suggests they wouWapproximate in the long run.

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108


fable 5:1. Shooter's Probability of Passing

Number of Number of Number ofCome-outroll2 crap3 crap4 point5 point6 point7 natural8 point9 point10 point11 natural

i 12 crap

Totals

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976

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The table is worked out in the followingmanner. If the shooter throws 2, 3 or 12, heloses immediately. This occurs 55, 110 and 55times respectively in 1,980 throws. A 7 or 11wins immediately, on a total of 440 throws.If the shooter throws a point of 4, whichoccurs 165 times, on 55 occasions he will throwanother 4 before a 7 and win, on 110 occa-sions he will throw 7 before 4 and lose. Theshooter passes 976 times in 1,980, an advan-tage to the bank, since it pays out at evenmoney, of 1-4141 per cent. A don't pass betwould enjoy the same advantage in thegambler's favour, but the bank adjusts the bet,as we shall see. The following bets are allowed :

Pass: This bet is also called the 'win', 'do',or 'front-line' bet, the last because the pass'ine is usually the front line on the craps tablelayout. Chips arc placed on the pass l ine on thelayout. If the shooter throws a point, a pointmarker is placed in the appropriate numberedbox near the top of the layout. Once a pointhas been established, the casino has an advan-tage over the pass line bettor, as it is likely thata ~l will be thrown before the point, so a beton the pass line cannot be removed once ashooter has made his point. As calculatedabove, the house edge on a pass line bet is'•4141 percent.

Don't Pass: This is a bet that the shooterWl" lose, and stakes are placed in the don'tPass space on the layout. As this bet wouldl ; ivour the gambler, it must be adjusted, and

the adjustment is shown on the layout, whichstates 'don't pass bar 6-6'. This means thatif the come-out roll is double-6, which losesfor the shooter, the bet on the don't pass lineis a stand-off, and does not win. A gamblermay remove his bet if 6-6 is thrown. Once apoint is established, the don' t pass bettor hasan advantage over the casino, so the casinowill allow him to remove his stake, but notadd to it. It will be seen from Table 5:1 thatif 6 6 is barred, the shooter has 949 ways topass against 976 ways of not passing, so thebank has an advantage over the don't passbettor of 1-4026 per cent, slightly less than onpass bets. Some casinos, particularly in Reno,bar 1-1 instead of 6-6, and the odds remainthe same. There are a few casinos which barcrap 3, and this gives them a house edge of4-3850 percent.

Come: This bet is made after the shooterhas established a point, and the stakes areplaced in the come space on the layout. Theshooter's next roll is regarded as his come-outroll for come bettors, and bettors win if theshooter throws a natural, and lose if he throwsa crap. Otherwise the shooter will establish anew point for the come bettor. When thishappens, the dealer moves the player's staketo the new point box, and the player wins ifthe new point appears before 7. The houseedge on come bets is therefore the same as forpass bets, 1-4141 per cent. The come bettorand the shooter might therefore have differentpoints, and will win on different throws,though both will lose if a 7 is thrown.

Don't come: This is the opposite of a comebet. and stakes are placed in the don't comespace on the layout. Notice that this also bars6-6, to adjust the odds in the casino's favour.The don't come bet wins if the shooter's nextthrow is crap 2 or 3, and loses if the nextthrow is a natural. If the shooter throws 6-6,the bet is a stand-off and may be removed orleft for the next throw. If the shooter estab-lishes a point for the don't come bettor, thedealer moves the stake into the empty boxabove the appropriate point number box.Thereafter the don't come bettor wins if a 7is thrown and loses if his point is thrown. Thehouse edge, as for don't pass bets, is 1-4026per cent, but increases to 4-3850 per cent ifcrap 3 is barred instead of crap 12.

109

P A R T F I V E

Field bet: The stakes for this bet are placedin the space above the don't pass line. Somelayouts mark this 'the field', as well as markingthe numbers which win (in this case 2, 3, 4, 9,10, 11, 12). This is a bet that any of thesenumbers appear on the next roll. A glance atFigure 2:1 in Part Two shows that one ofthese numbers will appear only 16 times in 36throws. However, as the layout shows, 2 and12 are paid double, i.e. at odds of 2-1. Thebettor can therefore expect a return of 34chips for each 36 staked, a house edge of5-5556 per cent. Some casinos include 5instead of 4 in the field, but do not pay doubleon 2 or 12. The house edge remains the same.

Big Six and Big Eight: The stakes for thesebets are placed in the spaces so marked in thelower corners of the table. A bet on big six is abet that 6 will be thrown before 7. The houseedge on this bet, and on big eight, is 9-0909per cent. It is a bad bet, as a better way ofbacking 6 or 8 is available, as will be shown.

Hardway: The stakes for these bets areplaced in the centre of the layout marked'3-3, 10 for 1' '5-5, 8 for 1' etc. They are betsthat the appropriate point, 4, 6, 8 or 10, ismade the hard way (i.e. by means of a double)before it is made the easy way or before a 7is thrown. As, for example, 10 or 7 can bethrown nine ways, only one of which is 5-5,the correct odds against hardway 10 are 8-1.The bank pays 8 for 1, a house edge of 11 • 1111per cent. The bank enjoys the same largeadvantage on hardway 4, and an advantage of9-0909 per cent on hardway 6s and 8s.

Place number to win: This is a bet that aparticular point number (4, 5, 6, 8, 9 or 10)will appear before a 7. The payoff on points 4and 10 are 9-5, so bets must be made in unitsof five times the table minimum or multiplesthereof. Points 5 and 9 pay 7-5, and points6 and 8 pay 7-6, so bets on 6 and 8 must bemade in multiples of six times the table mini-mum. The correct odds respectively are 8-4,6-4 and 6-5. In effect, when betting five chipson 4, the gambler gets the true odds of 8-4 forfour chips, and even money on the last. Thesame is true for the other bets, and is the reasonwhy big six and big eight bets are misguided,as the gambler can accept 7-6 on place sixand place eight against even money on bigsix and big eight.

10


^ craps diversion tried inHarold's Club in Reno.Instead of the shooterrolling dice, the dealerreleases a pair of whitemice which run throughnumbered sections of acircle to determine thevalue of the 'throw'.

The stakes on place bets are placed on theline above and below the appropriate pointbox on the table layout. The house edge on4 and 10 is 6-6667 per cent. On 5 and 9 it is4-000 per cent. On 6 and 8 it is 1-5152 per cent.

Some casinos offer 11-10 instead of 7-6on 6 and 8, when their edge becomes 4-5455per cent. Others offer even money, whentheir edge becomes 9-0909 per cent, as for bigsix and big eight bets.

Place number to lose: This is the oppositebet to the previous one, where a player maybet that 7 is thrown before his choice of pointnumber. The player must lay odds of 11 -5 on 4or 10, 8-5 on 5 or 9 and 5-4 on 6 or 8, so hisstake must be in multiples of 11, eight and fiveof the table minimum respectively. These betsare not popular. The house edges on the threevariations are 3-0303 per cent, 2-5000 per centand 1-8182 per cent. Some casinos ask 7-5to be laid on 6 or 8, their edge increasing to6-4935 per cent.

Buy bet: A buy bet is similar to a placenumber to win. The player bets that a pointnumber will appear before a 7. The differenceis that instead of the casino's edge comingfrom odds offered, the casino pays at thecorrect odds but exacts a 5 per cent com-mission on the stake. The player sets his stakeon the layout and announces the point herequires. The dealer takes the casino com-mission from the stake and places the stakein the appropriate point box, as for a comewager, but with a 'buy' button on the staketo indicate that it is to be paid at correct oddsand not as a place bet. On points 4 or 10, theodds are 2-1, and the player must stake inmultiples of 21 of the table minimum to getfull value for his bet. For example, if theminimum stake is $1, the player must stake$21, to allow the dealer to take $1 as com-mission. If the player stakes only $11, thecasino will still take $1 commission, and theplayer will thus pay 10 per cent commissionon his stake. On points 5 or 9, the odds are 3-2,or 30-20. On points 6 or 8, the odds are 6-5,or 24-20. As the casino wins 1 unit in 21, thehouse edge is 4-7619 per cent.

A comparison with betting place numbersto win shows that the player does best to placepoints 5, 6, 8 and 9 and to buy 4 and 10.

Lay bet: A lay bet is the opposite to a buy111

P A R T F I V E

Figure 5:5, a crapslayout as found in GreatBritain. Notice theelimination of certain betsavailable on the Las Vegaslayout and the adjustmentto the odds on other bets.

bet. The player bets that 7 appears before hisselected point. He is paid at the correct oddsof 1-2 on points 4 or 10, 2-3 on points 5 or 9and 5-6 on points 6 or 8. The commission of5 per cent on the lay bet is deducted from thehypothetical winnings, not the stake. Thus toget the maximum value for his bet, the playermust stake 40 units on 4 or 10, 30 on 5 or 9 and24 on 6 or 8, plus one unit commission, sinceall of these bets will win 20 units, qualifyingthe dealer to deduct one unit as the casinocommission. The player places his stake on thetable and the dealer removes the commissionand puts the stake in the don't box above theappropriate point, with a 'buy1 button aboveit. As the commission is deducted on each bet,not just winners, the house edge is 2-439 percent on 4 or 10, 3-2258 per cent on 5 or 9 and4-000 per cent on 6 or 8.

Proposition bets: One-roll proposition betsare made on the centre layout of the table. Theplayer places his stake on the table and callshis bet, and the stickman positions it on thetable. From top to bottom of the centre lay-out, the player can back 7 to appear on thenext roll (payout 5 for 1, house edge 16-6667per cent) ; the high bet is a five unit bet, a singleunit on three of the four numbers 11, 3, 2 and12, and two units on the fourth. The payoff isat the odds of 15 for 1 on 11 and 3, 30 for 1 on2 and 12, the three or four units on the num-bers which do not appear being lost. Thehouse edge is 16-6667 per cent. The four centreboxes are for hardway bets already discussed.The next five boxes are for bets on 3 or 11(each 15 for 1) and 2 or 12 (each 30 for 1). Thehouse edge is 16-6667 per cent. The bottomline, any craps, is a bet that any of 2, 3 and 12will appear. The payoff is 8 for 1, and thehouse edge is 1 1 - 1 1 1 1 per cent. A popular betis on craps or 11, in which case the stickman

might place the stakes between a pair ofcircles marked 'C and '£', choosing the pairpointing to the player's position round thetable. It is also popular to make a four-unitbet, one unit on each of the craps 2, 3 and 12,and one unit on 11. This is known as the hornbet, and some casinos include a space for iton the layout marked horn bet. Three unitsmust be losers, and if one is a winner thepayoff is at the odds stated for the single bet,the house edge being 16-6667 per cent.

Odds or free bets: The odds bet is a betallowed by the casino to encourage betting onthe pass, come, don't pass and don't comebets. The casino does not take a commission,and the payoff is at true odds, but an odds betcan only be made on point rolls in conjunctionwith a pass, come, don't pass or don't comebet on which there is already a house edge.

For example, if a player places a bet of oneunit on the pass line and the shooter establishesa point of 4, the casino will allow him to add anodds bet of one unit (in most casinos it mustbe equal to the original stake) to his stake.Should the shooter make his point, the passline bet will be paid at 1-1 (usually called aflat bet), but his odds bet will be paid at 2-1,the true odds of a 4 appearing before a 7. Acomplication arises should the point be 6 or 8,where the true odds are 6-5. Since a casinowill not pay out fractions of a chip, the stakefor the odds bet must be five units. A pass linebettor will not be allowed an odds bet if hispass line bet is of one or two units, unless heincreases the stake on the pass line. This wouldbe bad business for the player, as he is takingbad odds if he increases his pass line stakeonce a point is established. However, if thepass line stake was three or four units, theplayer is allowed an odds bet of five units-A player wishing to get the maximum benefit

112

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BEAT THE DEALERDEALER TAKES ALL TIES

Figure 5:8, the layout forbeat the dealer. Playerssit at the spaces round thetable, placing their stakesin the boxes before them.

Under and over sevenAnother dice game found in American casinosfor which two dice are used, and the layout isshown in Figure 5:9. The player can bet thatthe total will be under 7, exactly 7 or over 7.The under and over bets pay even money and 7pays 4 for 1. The correct odds are 21-15 and5-1 respectively, and the house edge on all betsis 16-6667 per cent.

BaccaratThe game as played by the Greek Syndicatem Deauville and elsewhere between the warsis sometifnes called baccarat à deux tableaux,though it is more often known simply asbaccarat. A later version of the game is some-times called baccarat à un tableau or baccarat-chemin de fer. This version is commonlyknown just as chemin de fer. A combination°f the two games, popular in some Britishatld American casinos, is most often knownas punto banco, although in Nevada it iscalled baccarat-chemin de fer. Even in thebasic game of baccarat, procedures vary.

In Britain, the bank is held by the casino,and does not have a limit, although minimumar|d maximum stakes will be imposed on thelayers. In France, the bank will have a mini-murn and maximum amount, and is in theory

UNDER

EVEN 4FOR1

OVER

EVEN

Figure 5:9, the layout forunder and over seven. Theplayer can choose fromthree possible bets, andone throw of two decidesthe outcome.

put up for auction among the players. Thegame is therefore known as baccarat banquelimitée and the casino will deduct 2 per cent ofthe banker's winnings per coup as commission.In 1922 Nico Zographos took the bank atDeauville and made the famous announce-ment 'tout va\ meaning everything goes:there was no limit to the stakes. This form ofthe game is known as baccarat banqueouverte.

The table for baccarat is shown in Figure5:10. Twelve players can be seated at thespaces shown. The table is in two halves, thehalf to the right of the banker being tableau un,and that to the left tableau deux. The portionsmarked 1 and 2 in the centre of the table arethe staking areas. A stake in the area marked1 is a bet that tableau un will beat the banker,a stake in area 2 a bet that tableau deux will

115

P A R T F I V E

The opulence of theBaden-Baden casino. Thecroupier is seated at achemin defer table and ispractising handling theequipment, which includessix packs of cards, thesabot and the spatula. Mostcasinos providecomprehensive training forcroupiers, who alsopractise between sessions.

16


beat the banker. A stake placed on the linebetween areas 1 and 2 is a bet à cheval thatboth sides of the table will beat the banker.This wins if both sides win and loses if bothsides lose; if one side wins and the other loses,or if both sides tie, the bet is a stand-off andthe stake removed.

In baccarat, all cards have their pip value,with court cards having a value of 10. Allbaccarat hands consist of two or three cards,and the point count of the hand is the sum ofthe cards held, except that only the last digitcounts, for instance a 6 and a 5 equals 11, andthe point count is 1, two court cards and a 4has a point value of 4. The object of the gameis to draw an initial two-card hand with apoint value higher than that of the banker,with the option under certain circumstancesof drawing a third card in an attempt to im-prove the hand.

Six packs of cards (sometimes three packsin France) are shuffled and cut and placed ina sabot or shoe, with an indicator between thetenth and eleventh cards, to mark the end ofthe shoe, the last few cards not being used.Players place their stakes on the table.

The banker then deals three hands of twocards, face down, one to each side of the table,and one to himself. The players immediatelyto the banker's right and left play the handsfor their sides of the table until either loses acoup, when the player in the next seat playsthe hand. Any player may decline to play.

When the cards are dealt the three handsare examined, and any with a point of 8 or 9are exposed immediately face up on the table.The point of 9 is shown as le grand and 8 as lePetit. A point of 8 or 9 wins immediately, un-less both player and banker have 8 or 9, in*hich case a point of 9 beats a point of 8. Ifthe hands are equal, the bet is a stand-off andthe stake withdrawn.

The banker deals first with tableau un. If"either the player nor the banker has declared8 or 9, the player must stand or draw a thirdCard. As he is playing for all the players on hisS'de, he has no choice but must obey the'^lowing rules, which are the optimum play,1 e. they give him the best chance. With a pointof °, 1, 2, 3 or 4 he must draw. With 6 or 7 hemust stand. Only with 5 has he the option ofe'ther standing or drawing. If he draws, the

third card is dealt to him face up. The bankerthen deals similarly with the player holdingthe cards for tableau deux.

The rules for the player are called the Tableof Play, and there is a Table for Play for thebanker. It is advised that he should draw on0, 1 or 2 and stand on 7. His play on 3, 4, 5 or 6is listed in Table 5:2.Table 5:2. Banker's Table of Play at Baccarat and Chemin de Fer

Figure 5:10, a baccarattable. This is forbaccarat à deux tableaux,the game played by theGreek Syndicate atDeauville and elsewhere.

Banker's point3456

Banker drawsif playerdraws0, 1 ,2 ,3 ,4 , 5,6, 72, 3, 4, 5, 6, 75,6, 76,7

Banker standsif player

draws8

0 , 1 , 8 , 90, 1,2, 3 ,8 ,9

Banker hasoption if

plaver draws9

40, 1 ,2 ,3 ,4 , 5, 8, 9 —

Note: If the player does not draw, the banker is advised to stand on 6 anddraw on 3, 4 or 5.

As the banker is playing against both sidesof the table, his situation vis-a-vis each will notalways allow him to make the optimum playagainst both, so the Table of Play can only beadvisory. The banker therefore may use hisskill to decide whether or not to draw, and ifthe optimum play is different against bothsides, will usually attempt to win against thetableau showing the higher stakes.

When players and banker have exposed 8or 9, stood, or drawn, the hands are declaredand the bets settled according to whether theplayers or the dealer have the higher point.Equal hands are stand-offs and bets void.

The player's only option is with a point of117

P A R T F I V E

Figure 5:11

Figure 5:12

Figure 5:11, a chemin defer table.Figure 5:12, a punto bancotable. Chemin de fer andpunto banco are versions ofbaccarat, and both havebecome very popular inrecent years. Both gamesgive the player anopportunity to play thebank's hand. In chemin defer, players hold the bankby rotation. In punto banco,although the plaver mavpluv the bank's hand,there are no options.

118

5. It has been calculated that he has a slightlybetter chance of winning by standing thandrawing. A player who always draws is knownas a tireur, a player who never draws is a non-tireur and a player who varies his tactics is adouteur. The banker has an advantage if heknows the player is a tireur or non-tireur, sothe best policy is to vary the play and keep thebanker guessing. The option on 5, and thebanker's privilege of using his discretion,make the house edge in baccarat very difficultto calculate, but it is generally accepted to bearound 1 per cent.

Chemin der fer"Shimmy' is played on a table as shown inFigure 5:11. The main difference with bacar-rat is that the players hold the bank in rotation(the name derives from the sabot movinground the table like a railway train on rails).There are only two hands: the banker and theplayer. The first banker is decided by auction,and he holds the bank until he loses a coup,when it is offered to the player on his right.He need not accept it, but if he does he mustput up a bank equal to its amount whenpassed. If no other player wishes to hold thebank, it is auctioned again.

Since the casino does not operate the bank,it exacts a commission. In France and Nevadait is likely to be 5 per cent of the banker'swinnings per coup, in Great Britain it will be acharge per shoe, which will vary accordingto the size of the stakes.

The players put up their stakes, beginningwith the player on the banker's right, until thebank is covered. If the bank is not covered,the excess is removed. A player can cover thewhole bank by calling 'banco', in which casestakes already put up must be removed. Somecasinos, however, will not allow a call of'banco' if the bank has already been coveredby preceding players. A player who callsbanco and loses, is entitled to call 'bancosuivi' on the following coup, this call havingpriority over all other calls and allowing thelosing player to bet the total amount of thebank again.

The player holding the cards for theplayers is the player with the highest stake.While the banker retains the bank, he is notallowed to withdraw any of it unless its amoun'

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khtly ! exceeds the casino limit. However he can passthan the bank at any time and withdraw the bank|own ' plus winnings. Six packs of cards are used,ion- They are shuffled and cut and placed in a shoeis a with a marker between the seventh and eighth

he last cards to indicate the end of the shoe.so Play begins with the banker who deals two

1 the cards face down to the active player and twothe face down to himself. The player and banker

lion, examine their cards and if either has a pointpcult of 8 or 9 he will expose them on the table. If|o be neither has 8 or 9, the player must stand or

draw. If he has 0, 1, 2, 3 or 4 he must draw,if he has 6 or 7 he must stand, and if he has 5he has the option of drawing or standing. This

In m is the same rule as in baccarat, and thecar- banker's Table of Play is also the same, as set

Ition out in Table 5:2. In chemin de fer, the bankerIving as well as the player must obey the Table ofiils). Play: the player has one legal option, and the

the banker two.Some casinos in Britain will allow faux

tirages, or false draws, where both player andbanker can draw at their discretion, but this isallowed only when the player has called banco.He is not allowed to take risks with otherplayers' stakes. Settlement of bets is as forbaccarat. A point of 9 or 8, called in America

lank, a natural, wins against any three-card-hand,rada otherwise the point nearer 9 wins, with a tie<er's a stand-off.bea

ding Punto bancoKnown in Las Vegas as baccarat-chemin de

|ning fer, this game is a version of baccarat growingthe quickly in popularity on both sides of the

red, Atlantic, and likely to relegate both baccaratthe i and chemin de fer to minor positions in the

lease | casino. The punto banco layout is shown in|ome ' figure 5:12. In punto banco, as in chemin de

of fer, there are two hands, the players' and the|ered bank's. All players are given the opportunity:alls m rotation to play the bank's hand, while aînco croupier plays the players' hand, but in effect

Iving 'bank' and 'player' do not have the samethe ', significance as in the other baccarat gamesthe I described, as all bets are made against the

/ casino, and no player is required to put up athe t bank. Players may bet that 'bank' or 'players'

lake. wins. Stakes for bets that the players win arenot placed in the area marked punto (players on

)iint some tables), for bets that the bank wins in

the small numbered boxes, each player placinghis stake in the box relating to his position atthe table. Two or three cards are dealt to eachhand by the 'banker' from a shoe arranged asin chemin de fer, and the rules for determiningthe winning hand are the same as at baccaratand chemin de fer. However in punto banco,neither the player nor the bank has any options.The Tables of Play for both are set out in Table5:3.

Table 5:3. Tables oj Play for Player and Banker at Punto BancoPlayer Point

0, 1,2, 3,4, 56,78,9

Banker Point0. 1,23

5678,9

drawsstandsexposes cardsDraws if plover draws0, 1 ,2 ,3 , 4/5,6, 7, 8,90, 1, 2, 3, 4, 5, 6, 7, 92, 3, 4, 5, 6, 74, 5, 6, 76,7Standsexposes cards

Because there are no optional plays in theTable of Play, it is possible (it is a mammothcalculation) to calculate which side, playersor bank, has the advantage. In fact, there is aslight advantage to the player who bets on thebank, which John Scarne, in his book Scarne'sNew Complete Guide to Gambling, has cal-culated at 1-3333 per cent. Therefore thecasino pays out bets on the players at 1-1,taking a house edge of 1-3333 per cent fromthese bets. Unless the casino adjusted the oddsfor bettors on the bank, all astute gamblerswould back the bank and enjoy an edge overthe casino of 1-3333 per cent. The casinotherefore pays out bettors on the bank at19-20, in other words it deducts 5 per centof what would be the winnings if it paid at 1 -1.The casino therefore has a house edge overbank bettors of 1-2000 per cent, making thebank bet slightly the better of the two.

It has wrongly been calculated that the totalcasino edge in punto banco is the sum of thetwo house edges, or around 2\ per cent, but infact if the bets on the players and bank wereequally distributed, the casino edge would bethe average of the two edges, or 1-2667 percent.

Stands ifplaver draws

80, 1, 8,9

0, 1, 2, 3, 8, 90, 1, 2, 3, 4, 5, 8, 9

119

P A R T F I V E

» *# ** *

* »*

.SO.*;

Faro was the most populargame in the Americansaloons of the second halfof the nineteenth century.Figure 5:13 shows thestaking table and theabacus-like device withwhich the case-keeper keptaccount of the cards played.The photograph showscowboys playing faro in asaloon in Morenci, Arizonaterritory, in 1895. Thenut-like discs on top ofsome piles of stakes meanthat the bettor is betting acard to lose.

FaroAlthough it is rarely played nowadays, a fewgames of faro might be found in Nevada. Itwas popular in Europe in the seventeenthcentury, and in the late nineteenth century wasthe most popular gambling game in America.

A green cloth table shows representationsof each rank in a pack of playing cards,usually showing spades, although this has nosignificance. Figure 5:13 shows the layout.The other equipment is a dealing box, inwhich a standard pack of cards is placed faceup after shuffling, and a counting device, likean abacus, with which a casekeeper keepstrack of the cards played, for the benefit of theplayers.

Players can bet any rank of card to win,and any rank to lose. In each case the stake isplaced on the appropriate card; if it is to losea copper token is placed on the chips. When Nbets are placed, the first card is played fromthe box. It is called soda and has no effect onthe game. The next card is dealt from the boxand is a loser, the card exposed in the boxbeing a winner. Stakes on the winning rank

\\\ J

120

P A R T F I V E

Figure 5:14

DEALER

rCROUPIER

Figure 5:14, a trente etquarante table.Figure 5:15 i.f an imaginarydeal representing a win forrouge and inverse.

to win are paid off at 1-1, stakes on the losingrank to lose are also paid at 1 -1. Stakes on thereverse bets are lost. Stakes not affected areleft on the layout, and other bets can be made.The winning card is then taken from the boxand begins-a win pile. The next loser is thenplayed from the box on to the losing pile,exposing the next winning card. More betsare then settled. When only three cards areleft behind the 24th winning card in the box,players may bet on their order (the ranks ofthe three cards are known). If the three cardsare different 4-1 is offered against namingthe order (correct odds 5-1, house edge16-6667 per cent). If there is a pair, 1-1 isoffered (correct odds 2-1, house edge 33-3333per cent). Players who eschew these betswould have no house edge to beat, were it notfor the fact that when the losing and winningcards in a pair are of the same rank, the banktakes half of all stakes bet on that rank. Thisgives the house an edge of about 1^ per cent.

Trente et quaranteSometimes called rouge et noire, this is apopular casino game in France, but is rarelyplayed elsewhere, and not at all in America.It is played with six packs of playing cards anda table as shown in Figure 5:14. There arefour possible bets for the player: rouge, noir,couleur and inverse, and stakes are placed onthe appropriate spaces on the layout.

A dealer, who does not use a shoe, deals arow of cards, representing noir, until the pip

FigiNOIR

ROUGE

ire 5: 15

•* **

* #•

• »»* •

its*. ;» »

• »•

•» »» »» *;

'V****•** *:

•» »« ** *•

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= 38

S» »

= 33* »•

count of the row equals or passes 31. Courtcards count as ten. If the pip count reaches 26,and the next card is an eight, making 34, thedealer announces 'four' as the point represent-ing 'noir'. As the total for any row must bebetween 31 and 40 (hence the name of thegame), only the unit need be stated (exceptthat 40 would be announced as 'ten'). Thedealer then deals a second row below the first,again stopping when the pip count reaches orexceeds 31. This row represents rouge and thedealer again announces the point.

The winning row is the row with the lowerpoint, i.e. the row with a total nearer to 31.A bet on rouge is a bet that this row (thesecond), wins. A bet on noir is a bet that thefirst row wins. A bet on couleur is a bet thatthe first card dealt is the colour of the eventualwinning row. A bet on inverse is a bet that thefirst card dealt is the opposite colour to thewinning row. All bets are paid at 1-1 or evens.

Suppose the two rows dealt were as inFigure 5:15.

The dealer would announce 'rouge andinverse' and bets would be settled.

Should the two rows be equal, the bets arevoid and the stakes retained. However, shouldboth rows be equal at 31, known as refait, thecasino claims half of all stakes. Half will bereturned to the player, or, if he prefers, thewhole stake may be left 'in prison' and stakedon the next game, the player reclaiming all ofit if he wins or losing all of it if he loses. Thisrepresents the house edge. It has been esti-mated that a refait occurs approximatelyonce in 40 games, giving the casino an edgeof 1-25 per cent. It has been calculated moreprecisely as 1-28 per cent. A player can insureagainst a refait by buying a special chip fo_r

one per cent of his stake on each game, and »he does this he reduces the house edge to 1per cent, or more strictly 0-9901 per cent.

122

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G A M E S O F C H A N C H

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Figure 5:16

RouletteThe most alluring of casino games is roulette.The bright green baize cloth with its red, blackand gold lines and lettering, the polishedwood table, the wheel with its red and blacknumbered pockets, chrome fittings and ivoryball clicking round with each spin comprisea scene of subdued glamour. It is a simplegame, and although the action is in realityfast, it appears relaxed in comparison with thefrenetic activity of craps. It has been asso-ciated most with Monte Carlo, but is playedin casinos all over the world, although it hasnever been very popular in America, probablybecause the odds offered to American gam-blers are very much inferior to those availablein Europe.

The French wheel and table layout areshown in Figures 5:16 and 5:17.

The table layout is repeated each side of acentral wheel, and the game is administeredby three croupiers, one, called le tourneur, tospin the wheel, the others to collect and paybets at each end of the table. Stakes are placed°n the layout before each spin, and thecroupier spins the wheel and sets the ballrolling around the rim in the opposite direc-tion. While the wheel is spinning he will callr'en ne va plus' which means no more bets

Figure 5:17Figure 5:16, a Frenchroulette wheel. Nearly allroulette wheels outsideAmerica are of the Frenchpattern, with only one zero.Figure 5:17 Li a Frenchroulette table. The Frenchtable and the Frenchlanguage are not as oftenused outside France as theFrench wheel, and casinosin Britain, for instance, willuse the French wheel andthe American table.

may be placed. The ball eventually comes torest in one of the numbered pockets, andaccording to the winning number all bets aresettled. Settlement comes with each spin, andexcept for the 'in prison' rule, to be explainedlater, no bets are carried forward.

The bets at roulette fall into two cate-gories, those offering even money, and thoseoffering other odds. The even money bets areas follows:Rouge: a bet that a red number will win.Noir: a bet that a black number will win.Pair : a bet that an even number will win.Impair: a bet that an odd number will win.Manque: a bet that a low number (1-18) will

win.Passe: a bet that a high number (19-36) will

win.The stake is placed on the appropriate space

on the table layout, and if successful will bepaid at odds of 1-1. With each of these bets

123

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WG A M E S O F C H A N C E

there are 18 winning numbers and 18 losersplus zero. It is when zero appears that therule placing the stakes 'in prison' operates.Stakes are not immediately lost, but mayremain on the table for another spin. If the betwins on the next spin, the stakes are retainedby the player, without winnings. If the betloses, the stakes are lost. Alternatively, whenzero appears, a player may retain half hisstake and forfeit the other half, a conventionknown as le partage. The effect is the same.One even-money bets, the player will lose onebet in 74, a house edge of 1 -3514 per cent.

The other bets are as follows:En plein: Sometimes called a straight bet, thisis a bet on a single number, and the stake isplaced on the appropriate number on the lay-out. Zero can be backed. The odds paid are35-1.A cheval: Sometimes called a split, this is a betthat one of two adjacent numbers on the tablewill win, such as 28, 29. The stake is placed onthe line between the two numbers. Zero can becombined with 1, 2 or 3. Odds paid are 17-1.Transversale plein: Sometimes called a street,this is a bet on any three numbers in a row onthe layout, such as 19, 20, 21. The stake isplaced on the line at the edge of the row. Zerocan be backed with any two numbers of 1, 2or 3 by placing the stake on the corner com-mon to the three numbers. Odds paid are 11 -1.En carré: Sometimes called a square, this is abet on any four numbers forming a square onthe table layout, such as 5, 6, 8, 9. Zero can behacked with 1, 2, 3 (sometimes called thequart premiers) by placing the stake on theoutside corner common to the zero and therow. Odds paid are 8-1.Transversale simple or sixain: Sometimescalled a line bet, this is a bet on a group of sixnumbers forming two adjacent rows or streets,such as 1,2, 3, 4, 5, 6. The stake is placed on'he outside corner common to the two rows.Zero cannot be backed in a sixain. Odds paidare 5-1.Colonne: Sometimes called a column bet, this18 a bet that a number in one of the threecolumns will win, i.e. a bet might be placed onthe centre column 2, 5, 8, 11, 14, 17, 20, 23, 26,-9, 32, 35. The stake is placed in the boxwhich is unmarked at the foot of the column.The odds paid are 2-1.

Colonne a cheval: Sometimes called a splitcolumn, this is a bet on any two adjacentcolumns. The stake is placed on the line be-tween the two unmarked boxes at the foot ofeach column. The odds paid are 2-1 on or1-2.Douzaine: Sometimes called a dozen, this is abet on 12 numbers, the lowest (1-12), themiddle (13-24) or the highest (25-36). Thestake is placed in the boxes marked P12, M12

or D12, P (première) for 1-12, M (moyenne)for 13-24 or D (dernière) for 25-36. The oddspaid are 2-1.Douzaine à cheval: Sometimes called a splitdozen. This is a bet on any two adjacentdozens, the stake being placed on the linebetween the appropriate two boxes on thetable. Odds paid are 2-1 on, or 1-2.

Combinations of these bets are allowedprovided the intention is unambiguous. Forinstance, a popular bet is to back a numbersingly and in combinations with all eightnumbers which surround it, called completingthe number. Figure 5:18 shows such a bet onnumber 20. This is a single bet on 20, foursplit bets combining 20 with 17, 19, 21 and 23and four squares. Should 20 win, the return is144 chips, a profit of 135. If 17, 19, 21 or 23win, one split and two squares win, returning36 chips, a profit of 27. If 16, 18, 22 or 24 win,one square wins, returning 9 chips and noprofit.

The odds paid on all the bets listed above(i.e. all roulette bets except the even-moneybets) would be the true odds were there 36numbers on the wheel. As there are 37, includ-ing the zero, the casino will expect to win inthe long run one unit in 37, a house edge of2-7027 per cent. It is wrong to regard the zeroas the 'bogy' number which makes the casinoits profit. As stated, zero can be backed inmany ways, as can any other number. Thecasino's profit comes from the fact that thereare 37 numbers on the table, whereas the oddsare geared to 36.

Roulette is the system player's delight. Allthe systems described in Part Two are appli-cable to the even money bets, and there are atleast two other systems, based on fallaciouspremises, which can be seen in operation atroulette tables. One is called the Biarritzsystem, and involves keeping a check on

16 17 18

Opposite : The Frenchroulette wheel and table atthe Curzon House Club inLondon. Bets can he placedafter the wheel is spun, hutnot after the croupier hascalled 'rien ne va plus '.Figure 5:18 shows thecompletion of the number20 at roulette. The number20 is backed singly, àcheval with 17, 19, 21 and23, and en carré with eachof the three numbers withwhich it forms a square.

125


numbers which have not won for a givennumber of spins. Such numbers are called'sleeping' numbers. As any number, includingzero, can be expected to appear on averageonce in 37 spins, a Biarritz player might waituntil a number has not appeared for 111(3 x 37) spins, when he will consider it due.He will then back it until it wins. If it loses fora further 36 spins, he will be out of pocket whenit eventually does win, unless he increaseshis stake, so after 36 losses he will increase hisstake to two chips for the next 18 spins, andthen three chips for 12 spins, four chips fornine spins, five chips for seven spins, six chipsfor six spins, seven chips for five spins, etc.This looks complicated, but it is easy to cal-culate. If he wants to be in profit or level whenhis win at last comes he must not lose morethan 36 chips on any one stake. Eventuallyhis stake will reach 18 chips which he can staketwice, when he will have to begin increasinghis stake on every bet. On bets on single num-bers, the player might be able to raise his staketo 40 times the minimum before exceeding thetable maximum stake, but it is likely that hewill lose his nerve before he gets to this stage.The fallacy in the system lies in the assumptionthat a sleeping number is more likely to winthan the number which has won on the lastspin. In fact the probability of either winningis 57 on a true wheel.

Another popular system relies on the factthat the third column on the layout containse'ght red numbers and only four black.Players l ike to back this column and hedgetheir bets by also backing black. The idea isthat if their column bet loses, the stake will°e saved more often than not because the othertwo columns contain 14 blacks to 10 reds.And, of course, if any of the four black num-"ers in the chosen column wins, then bothbets win. In practice, the arithmetic of thehouse edge cannot be defied this way. Thej-olumn bet will still lose 2-7027 chips in everyhundred, the bet on black 1-3514 chips in everyhundred, a house edge of 2-0270 per cent.

'n practice, the big bettor at roulette willack the even-money chances to take ad-

J'antage of le partage. The nine chips required-° complete a number, as described above,'" lose to the bank at the rate, on average, of^430 chips per spin, whereas were they all

placed on an even-money chance, they woulddisappear at only half this rate.

Study of the roulette wheel in Figure 5: 16shows that black and red alternate, and thatalthough the zero prevents a perfect arrange-ment of the numbers, high/low and odd/evenalso alternate as far as possible. For the benefitof seekers of the infallible system, Figure 5:19is the tableau des voisons, showing which fournumbers appear each side of any particularnumber on the wheel. Some of the best

Opposite: the Americanroulette wheel and table,showing how it differs fromthe French arrangement onpage 124. The languageused by the croupiers willbe English, and 'no morebets ' will be called to endthe staking on each spin.Above : French roulette atCrockford's Club, London.

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P A R T F I V E

Figure 5:19, the tableaudes voisons. This is a chartshowing, in the centrecolumn, the 37 numbers ona French roulette wheel,and to either side of eachnumber its neighbours onthe wheel.Figure 5:20 is an Americanroulette wheel, which has adifferent arrangement ofnumbers as well as theaddition of a double-zero.Figure 5:21 is the Americanroulette table. Opposite : adouble-headed Frenchroulette table in the mostelegant casino in the world,Baden-Baden, is aglamorous sight, and it iseasy to forget that thegame itself is a simplegame of chance.

Figure 5:19

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casinos will supply clients with a table ofprevious results on roulette tables which willenable a systemier to check his system againstpast results. Any reader who does find aninfallible system is invited to share his goodfortune with the author.

Figure 5:21

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Figure 5:20 if/II

Roulette in America and many illegalcasinos all over the world is likely to be playedwith a different wheel and table layout. Theseare shown in Figures 5:20 and 5:21.

The main difference lies in the wheel havingtwo zeros, a single zero and a double zero.although there is no difference in their f1 L'tions. The wheel has a different arrange»of numbers, although those numbers whichare red on the French wheel remain red.

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P A R T F I V E

The two casinos in thephotographs on these pagesare in the same ownership.Both are in the CurzonHouse Group. Crockford's,above, was opened in 1972.The players are playingroulette on a French table.The Palm Beach Club,opposite, has some of theelegance oj the old Frenchcasinos, but the roulettetable shown is of theAmerican pattern. Thetable at Baden-Baden onthe following pagesillustrates why there ismore gambling lore andromance associated withroulette than withany other game.

The bets are basically the same, and theodds paid are the same. A difference comeswith the combinations allowed with the zeros.A bet on five numbers is allowed by combiningboth zeros with 1, 2 and 3. The odds paid are6-1, and as the correct odds are 33-5, thehouse edge is 7-8947 per cent. Americancasinos do not recognise le partage, andall bets are lost when either zero appears(except those actually staked on zero). Theeffect is that on every bet, except the singlebet on five numbers mentioned above, thecasino has an edge of 5-2632 per cent.

The French language is dispensed with inAmerican casinos, and the table reflects this.The table is rarely double-headed, and on thesingle layout the wheel is set at the end nearerto the zeros. The game is usually operated bytwo croupiers, one the wheel roller. It iscustomary when the American table is usedfor special roulette chips to be issued at thetable. They are in differing colours, so thateach player can use chips of a 'personal' colour,

130

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thus obviating any disputes arising from twoplayers claiming the same bet. The disadvan-tage, which is slight, is that chips are obtain-able only in fixed denominations, and mustbe cashed at the table when the player wishesto leave - they cannot be used elsewhere inthe casino.

In British casinos, the French wheel is usedbut the American table (without the doublezero) is more popular. Casinos do not recognisele partage but return half the stake on even-money bets when zero appears, which interms of the house edge amounts to the same

thing. When the wheel indicates the winningnumber, the number will be called and acroupier will either point to it on the table orplace a marker on the table until the bets aresettled.

It is customary in roulette for the payon5

on the even money bets to be stacked by tne

original wager. On the bets on specific num-bers the payoff will be placed in front of the

player, but the original stake left on the tableUnless the player wants his stake to rernai" ion the table for the next spin, he must rernov£ |it himself.

134

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77î<? English artist GeorgeCruickshank painted aseries of pictures on life inParis. This painting showsgambling at the PalaisRoyal, Paris, in 1822. Thegame is trente et quarante,or rouge et noir.

Inningind a

Ible orts are

layoffs,y thenum-

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forerunners of roulette'Wo games played with a ball and a wheelwith numbered pockets were popular gam-bling games in casinos before roulette wasinvented. In the early eighteenth century hocaWas played in casinos in Europe. There were4" numbered pockets around the edge of aC1rcular table. From the centre of the tablePr°jected a spindle from which six spokesInched halfway from the centre to the rim.when the ball was placed between the spokes|!nd the 'wheel' spun, the ball would shootrom the centre and speed round the rim of

the table before settling into a stationarypocket. Three of the forty pockets were zeros,from which the casinos took their profit.

E.O. (which stands for even-odd) waspopular around the same time, particularlyin England, where it became fashionable athealth resorts like Tunbridge Wells and Bath.The wheel was like a roulette wheel, withforty pockets alternately marked E and O.The perimeter of the circular table in whichthe wheel was set contained E and O divisionson which the stakes were placed. Odds paidwere 1 -1 , and the operators had to devise

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P A R T F I V E

Roulette in Las Vegas.Roulette has neverthreatened the popularityof craps and blackjack inNevada casinos, but thismight be becauseAmerican roulette, with itsdouble zero, offers acomparatively poor returnto the punter. On no betdoes the house edge dropbelow five per cent.

136


their own methods of taking a profit: one waywas to bar a pocket of each sort. If the ballcame to rest in the barred E pocket, E bettorswould retain their stake but O bettors lose.This gave the house an edge of 2-5 per cent.Two pockets of each sort barred would doublethe house edge.

Nineteenth century roulette wheels inFrance used the bar principle. Thirty-sixpockets included two zeros, one red and oneblack. When the black zero appeared bets onred lost, but bets on black were returned. Betson single numbers paid 34-1, so the houseedge on all bets was 2-7778 per cent, slightlymore than the edge on other than even betstoday. American wheels of the same period,operating like a hoca wheel with a spokedspindle, contained 31 pockets, including azero, a double-zero and an eagle, which couldhave been marked as a treble-zero. Bets couldbe made on single numbers, including thethree zeros, and were paid at 21 for 1, Ameri-can operators having early discovered thisform of quoting odds to mislead the unin-itiated. Any of four groups of seven numberscould be backed at 3 for 1, red or black at 2for 1. The house edges on the three bets were12-9032 per cent, 32-2581 per cent and 9-6774per cent. No wonder roulette has never caughton in America.

BouleThe "poor man's roulette' is boule, a gamewhich dates from the eighteenth century, andis still very popular in French casinos. It isplayed in a separate room apart from thearistocratic roulette salon. The dish and tablelayout are shown in Figures 5:22 and 5:23.

The game has replaced a game called petitschevaux, which was played in casinos inFrance up to the twentieth century and canstill be found in France and in Ireland. Inpetits chevaux the winning number wasdecided not by a ball, but by nine models ofmounted horses, each with a number, racingon nine individual concentric circular tracks.When the horses stopped revolving that near-est a fixed winning post was the winner. Neardead-heats naturally caused a great deal ofargument. The staking layout was the same asfor boule, except that there were no bets onrouge, noir, passe or manque.

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P A R T F I V E

Figure 5:22, a boule dish,and Figure 5:23, a bouletable. A rubber ball is usedin boule, which is rolledround the dish andeventually drops into one of36 pockets to decide thewinning number. Bets canbe made on single numbers,or on groups of fournumbers. The number 5acts like the zero in roulette.

Figure 5:23

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There are 36 cups in the boule dish, fourfor each number from 1 to 9. Numbers 2, 4,7 and 9 are coloured red, numbers 1, 3, 6, 8black. Number 5 is yellow and performs asimilar function to the zero in roulette. Thewinning number is decided by the croupier

spinning a rubber ball round the dish, whichdoes not have a revolving wheel, the pocketinto which the ball drops being the winner.

Bets can be made on any single number,including 5, by placing the stake on the num-ber in the layout. Winners are paid at 7-1.

Even money bets can be made on noir,rouge, manque or passe on the spaces marked,and on even or odd by placing the stake on thediamond arrangement of odd or even num-bers. These bets lose when 5 appears, and thereis no le partage convention. The house edgeon all bets at boule is 11 • 1111 per cent, makingit a much less attractive game than roulette.

Vingt-troisA new, more sophisticated version of boule tobe found in some French casinos is vingt-trois.The differences are that the wheel contains 27pockets and it spins, like a roulette wheel.It is enclosed in a plastic dome, and is spunby apparatus outside, so that neither wheelnor ball is touched by the croupier. The 27pockets are numbered 1 to 14 as follows:Numbers 1, 2, 3, 4 have one pocket eachNumbers 5, 6, 7, 8, 9, 10, 11 have two pockets

eachNumbers 12, 13, 14 have three pockets each

The pockets numbered 13 are white, andperform the function of zero at roulette. Theother pockets are alternately red and black,the only even-money bets allowed. These betslose when 13 appears, there being no le par-tage.For bets on any of the numbers with onepocket each, odds of 23-1 are paid.For bets on any of the numbers with twopockets each, odds of 11-1 are paid.For bets on any of the numbers with threepockets each, including 13, odds of 7-1 arepaid.

The house edge on all bets on vingt-troisis the same as for boule, 11-1111 per cent.Clearly French roulette is the least disadvan-tageous of the wheel and ball type games fromthe player's point of view.

HoggenheimerA card game of pure chance, played privatelyand not in casinos, is hoggenheimer, whichhas been called English roulette. It is playedwith a standard pack of cards from which

138


cards of the ranks 2-6 are removed, and thejoker added. If the pack is an old one, and thejoker cleaner than the rest, one of the rejectedcards must be used instead, as a joker recognis-able from the back spoils the game.

The pack is shuffled and cut and the cards|oir, are dealt by the banker into four rows of eight

cards each, the odd card being placed faceI the down to one side. The top row is for spades,-irn- from ace to 7, the next for hearts, the third for1ère ' diamonds, the fourth for clubs, all from the

Jdge I ace to the 7.}ing The players then place their bets on cards

'• [ or groups of cards which they think will be[ face up when the game ends. When all bets are! placed, the banker turns over the odd card,

; to I and places it in its position in the layout, tak-ïois. ' ing the card which it replaces and placing that

27 in its appropriate position, continuing thussel. unt i l the joker appears. If the joker is the odd3un card, the dealer wins all bets,leel Figure 5:24 shows a layout at the end of the

27 game, the joker having just been exposed.| The bets possible are as follows, and the

odds quoted are the true odds.kets 1 1. On a single card (stake 1 on the layout).

Odds 1-1.|h 2. On any pair of adjacent cards (stakes 2 and

3 on the layout). Stake 2 is a bet that both aceThe of hearts and ace of spades will be exposed,

lick, It has won. Odds 2-1.?ets 3. On four cards, either in a street (stake 4 ont>ar- the four queens) or a square (stake on the red

8s and 7s). Odds 4-1.lone 4. On a suit (stake 6 on the spade suit). Odds

8-1.two The odds quoted give no advantage to

either banker or player. It is best if the bankiree circulates, and if minimum and maximum

I are bets are decided beforehand. The odds forthis game are at first sight surprising. Onemight suppose that if ace and king of spadescan each be backed at evens, a double on thetwo of them ought to be 3-1. However, whenmaking this bet you are interested in the order°f three cards only, the rest being immaterial.There are six orders in which the ace, kingand joker can appear: AKJ, AJK, KAJ, KJA,

|tely JAK, JKA. Two win and four lose, makinglich the probability of winning |. or odds of 2-1.

jyed The probability is 2! (there being two cardshacked) divided by 3! (two cards plus the

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joker). Similarly, when backing a suit ofeight cards, say the hearts, you are interestedin the order of nine cards (eight hearts plusthe joker). These cards can appear in 9! orders.You win only if the joker appears last, orninth. Given the joker is ninth, the eighthearts can appear in 8! orders. Your chanceof success is therefore ff or 5. Odds are 8 1.

There are, of course, countless card gamesof pure chance on which money is gambled,the simplest being when two or more playerscut the pack of cards, the player cutting thehighest card taking all stakes. To describe themall, if such a task were possible, would requirea book in itself. It is hoped that readers of PartTwo will be able to calculate the chances andtheir expectation on all these games for them-selves - if they cannot perhaps they shouldavoid playing these games.

Four-five-sixJust like card games, dice games of chance areinnumerable. One popular in North Americawhich leads to a lot of gambling is four-five-six. Three standard dice are the only equip-ment necessary. The game requires a banker,and as the banker has an advantage, the bankshould pass among the players by rotation.

Once the banker has been decided, all theplayers put up their stakes, which should bebetween an agreed minimum and a maximum.

The banker then throws the three dice, andcontinues to throw until any of the followingcombinations appear:

Figure 5:24, the end of agame ofhoggenheimer.The joker has beenexposed with 17 of thecards in the layout face up.

139

P A R T F I V E

a. 4-5-6 or any triplet, in which case the bankerwins all betsb. 1-2-3 in which case he loses all betsc. Any pair and 6, in which case he wins allbetsd. Any pair and 1, in which case he loses allbetse. Any pair and 2, 3, 4 or 5, in which case thenumber on the odd die establishes his point.

If the banker establishes a point, then theother players in turn from the left must throwthe dice. The same combinations win and losefor the player as for the banker, i.e. if he throwsthe combinations in (a) and (c) he wins, thosein (b) and (d) he loses. The other alternativefor the player is (e), the establishment of apoint, and he wins if his point is higher thanthe banker's, loses if the point is lower, and thebet is a stand-off if he ties.

As the combinations which win and lose forthe banker and the player are the same, it iseasy to assume that the game is fair. In fact,the banker has an advantage by throwingfirst. There are 216 ways (63) in which threedice may fall. Of these, six will be a triplet( 6 x 1 x 1 ) , six will be 4-5-6 (3 x 2 x 1), and 15will be a pair and 6 (there are three dice whichcould be 6 with five possible pairs to accom-pany each). Therefore, on average, the bankerwins immediately on 27 of 216 games.

There are 21 ways in which the banker canlose immediately (calculated the same way butminus the six triplets).

There are 60 ways in which the banker canestablish a point (four points with five pairsthree times).

It is interesting to note that there are 108ways of making a significant throw, so exactlyhalf of all throws are decisive.

Converted to fractions, the banker wins ,loses y7^ and makes a point on f§.

The player will be required to throw on ffof all games and will win of them and lose376 without establishing a point. Of his points,the player will win f, lose f and ^ will be stand-offs.

The expectation of the banker, therefore, is

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A big six wheel in a LasVegas casino. The 54divisions round the wheeleach contain three dicenumbers. Each division isseparated on the wheel'srim by a projecting pin.The wheel is spun, andwhen it stops a leatherindicator between two ofthe pins gives the winningdivision. Players mayback any number. If thatnumber appears once in thewinning division, they arepaid evens, twice 2-1 andthree times 3-1, as inchuck-a-luck. The game iseven more disadvantageousthan chuck-a-luck, as notall 216 combinations ofthree dice are on thewheel - there are usuallyonlv six with no pairs, 24with a pair and 24 withtriples. The net resultis a house edge of22.22 per cent.

141


This equals 1-0247, an advantage to thebanker of 2-4691 per cent.

Four-five-six can be found in some Ameri-can casinos, when, of course, the bank will notcirculate but will provide the casino with itshouse edge.

Other games of chanceVast sums are gambled on events of chance sosimple, like the proverbial flies crawling up awall, that they could never be called games.Some extremely simple propositions havefrom time to time captured the imagination oflarge numbers of people for no identifiablereason. Two-up is a gambling game whichrequires two coins to be placed on a flat pieceof wood, like a child's ruler. A spinner thenthrows the coins in the air, and bets are struckthat the coins will fall two heads or two tailsuppermost. One head and one tail is a stand-off and nobody wins. The game is played inAustralia, and has achieved such popularitythere in the past that games were organised onwaste ground with look-outs watching out forthe police. Bets were enormous, and even theflat piece of wood had its name - the kip.

Fair grounds and carnivalsare places where a gooddeal of gambling of a mildsort takes place, and it islikely that most of it isoutrageously unfair to thecustomer. These shots ofHampstead Fair in Londonshow two of the commonesttypes of game. In the largerpicture ducks revolve roundthe stall, and the punterscatch one with a stick.Each duck has a number onits base, and according tothe number a prize is or isnot won. Sometimes threeducks (or they may befish) have to be caught, andthe numbers are addedtogether. In either case thenumbers on the ducks aresuch that the stall will notgo broke. On the other stallrings must be thrown overobjects on blocks to winthem. The rings mustcompletely encircle theblocks to win, and althoughthe rings are large enoughto do this, it is so difficultto achieve when the ringsare thrown from in frontthat there is little chance,even if the thrower leansover, that anything ofvalue will be won.

143

Another popular game onfair grounds requires thepunter to throw a ping-pongball into any one of anarray of goldfish bowls.Usually the prizes aregoldfish. This stall atPeterborough Fair allowsseven balls for 10p.Prizes are frequently won,but if a goldfish is worth5p to the stallholder, it islikely to cost on averagelOp to win one.

Before the Second World War, there was acraze in Britain and America for a game calledput-and-take, played with a metal octagonaltop. Any number could play, and before thegame started all contributed equally to a pool.By turns, the players would then spin the top,which would fall with one of eight sides upper-most. The sides were labelled PI, Tl, P3, T3,P4, T4, P-all, T-all. P stood for put, and theplayer throwing it had to put into the pool thenumber of units stated. T stood for take, andthe player throwing it took out of the pool.Whenever the pool disappeared, the playersreplenished it equally. Perhaps the ease withwhich gaffed tops were manufactured helpedkill this craze.

Fan tan is an ancient Chinese game in which

a random number of beans is placed under adecorative bowl. Gamblers place bets on oneof four 'corners' numbered 1 to 4. The bowlis then lifted and beans are taken from the pilefour at a time with a stick, so that they are nottouched by hand and all can see fair play.Eventually one batch of four beans will betaken away to leave only one, two, three orfour in the pile. The player who has bet on thatnumber wins. The game has been played byChinese for hundreds of years and is actuallyspreading to other parts of the world.

That such simple games, in which theplayer can exert no influence, can have com-manded the attention of millions, indicatesthe strength of the appetite men have f°r

any form of,gambling.144

3 -a o o

P A R T S I X

ny game of skill can be gambledupon. Games of skill have one great advan-tage over games of chance as betting proposi-tions and one great disadvantage. Theadvantage is that players largely control theirown destinies: the influence of Lady Luck isminimised. The disadvantage is the other sideof the same coin: for players of unequalability to bet fairly against each other, handi-caps have to be devised, which can make thegames less satisfactory and encourage thehustler. If a player's game improves dramatic-ally when the big money is down, suspicion isaroused that he has deliberately falsified hisform. Whether the suspicion is well-foundedor not, the game is spoiled.

In this part of the book are examined gamesof skill in which gambling is a necessary part,such as poker, and games in which gambling,while not being necessary, is more or lesscustomary, such as gin rummy and back-gammon.

BlackjackChance plays a large part in blackjack (other-wise it would not be found in casinos) but theskilful player still enjoys a big advantage overthe novice. Certain players have been bannedfrom blackjack in casinos, which is proof thatthey have, however temporarily, been able totransfer the hypothetical house edge from thebank to themselves. Blackjack is the mostpopular card game in Las Vegas casinos andis becoming more popular elsewhere. It is afast, calculating game which appeals to thosefor whom the high stakes and limited action ofbaccarat and chemin de fer are intimidating,or frustrating.

The origins of blackjack are unknown,except that its immediate predecessor was theFrench game vingt-et-un and the game wascalled vingt-un or twenty-one in its early daysin America. Vingt-et-un, became van John inBritain, a name which gave way to pontoon,which might itself be a corruption of vingt-et-un, or merely a corruption of punting. Thename blackjack arose when an Americancasino, to popularise the game, paid a bonusto any player holding the ace of spades andeither the jack of clubs or jack of spades; thehand, and later the game, took the nameblackjack.146

G A M E S O F S K I L L

George Cruickshank 'spainting of life in Londonshows whist plavers in1820. Whist has beenplayed in England sincearound 1500, and became afashionable game with thepublication of one of themost famous books inhistory, 'A Short Treatiseon Whist ' by EdmondHoyle. Whist remainspopular to this day, and'according to Hoyle ' hasbecome a description forthe correct proceduresin all games.

147

P A R T S I X

'Ay, rail at gaming - 'tis arich topic, and affordsnoble declamation. Go,preach against it in thecity - you'll find acongregation in everytavern '. So said EdwardMoore, in his eighteenthcenturv play TheGamester. The ancientGreeks gambled in saloons,and the cowboys of theWild West in the bars ofTombstone and Dodge City.Cards and dominoes can beseen in the traditionalBritish pub. The gamebeing played in theNorthamptonshire pub inthe large picture is shut thebox, a dice game played ona tray on which there arenine boxes numbered 1-9with lids. A player throwstwo dice and can shutwhatever boxes helikes which add up exactlyto his score. He continuesto throw until no moreboxes can be shut, and thetotal of the boxes still openis his score. The otherplayers have their turns,and the lowest scorewins the stakes.

148

P A R T S I X

Figure 6:1, a blackjacktable. Blackjack is a casinogame in which the skilfulplayer can reduce the houseedge, and even, in theopinion of some players,enjoy an advantage.

Only comparatively recently have rulesbecome standardized, and even now con-ventions differ in various casinos. The follow-ing description is of a version to be found inmany American casinos. It is played on thetable shown in Figure 6:1.

Four packs are used, shuffled by the dealerand cut by a player (by means of an indicatorcard). A second indicator is placed somefifty cards from the bottom of the combinedpack to indicate the end of the shoe, and thecards are placed in a dealing shoe face down.

The players (up to seven) sit at the spaces atthe table.

All cards have their face value, with courtcards counting as ten, except the ace, whichwhen held by the player has a value of one or11, at his discretion. When the dealer holdsan ace, it might also have a value of one or 11,but its value is governed by the casino rules,as will be seen.

The object of the game from the player'spoint of view is to obtain a total card count,with two or more cards, higher than that of thedealer, but without exceeding a maximum of21. Should the player's count exceed 21 he issaid to have busted, and loses his stake.Minimum and maximum stakes are imposed :in a large American casino they might be $1and $500.

Before the deal, each player puts up a stakein the betting space before him. A player mayplay at more than one space, but must playthe hands independently from his right to left.

The first card dealt is burnt, i.e. it is left facedown on the table and not used. The dealerthen deals a card to each player in turn, be-ginning on his left, and finally one to himselfall face up. He then deals a second face-upcard to each player, and a second card, facedown, to himself.

If the dealer's face-up card is an ace or a tencount, he must look at his other card (if it isan ace he must first ask players if they wish toinsure, as is explained later). If he has a total of21, he faces it and announces twenty-one orblackjack. A two-card total of 21 is known asa natural or blackjack. A natural 21 is thehighest hand, and the dealer wins all stakes,unless a player also has a natural, in whichcase his bet is a stand-off.

When the dealer does not have a natural,he deals with each player in turn, beginningwith the player on his left. If the player has anatural, he wins, and is paid at odds of 3-2, asthe table states. All other bets are paid at 1-1.

Otherwise he may stand or draw a furthercard or cards. He will stand if he is satisfiedwith his count, or if he judges a further cardjnight bust him. If he wishes to draw he willbeckon for another card, or, as is common inAmerica, say 'hit me', when the dealer willgive him another card face up. The player maycontinue to draw cards unt i l he is satisfied withhis count. If in drawing he busts, he mustannounce it, and the dealer collects the stakeand burns the cards, i.e. adds them to thediscard pile.

A third option is open to the player if thetwo cards dealt him are of the same rank. Anytwo cards of a ten count are regarded as beingof the same rank. This option is called split-ting pairs. The player may treat each card asthe first card of separate hands, putting hisoriginal stake on one and a stake equal to iton the other. The dealer then deals him aseparate face-up card to each hand, whereuponthe player plays each hand separately, be-ginning with that on the right. Should thesecond card in a split hand again form a paif-the hand may be split further.

If a player splits a pair of aces, he may notdraw a third card to either hand: the secondcard dealt to each hand completes the hands-If a split hand results in a natural, the playef

is paid at 1 1 and not at the 3-2 odds.150

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A fourth option open to the player afterreceiving his first two cards is to double down.This allows him to double his stake, andreceive a third card face down. This cardremains face down, and the player may notlook at it, until the dealer faces it when settling.Therefore a player doubling down receivesone additional card only.

The last option open to the player is open tohim wherever the dealer's face-up card is anace. He may insure against the dealer having anatural by putting up half his stake as insur-ance. If the dealer has a natural, this stakewins at odds of 2-1. Before looking at hisface-down card, the dealer asks if any playerwants insurance. When those that wish haveinsured, the dealer looks at his face-downcard. If he has a natural, he pays the insurancebettors and collects the other stakes. Other-wise, he collects the insurance bets and pro-ceeds as before.

The dealer treats each player in turn asstated above. He collects and discards thecards of all those who bust as he proceeds, andif any hands remain he then plays his owncards.

He begins by facing his second card, so thathis hand is exposed. The dealer has no optionsin playing his hand. If his count is 16 or less,he must draw and continue to draw until histotal becomes 17, 18, 19, 20 or 21. When histotal reaches any of these numbers, he muststand. It is important to note here that whilean ace may count as one or 11 for the dealer,if by counting it as 11 his total reaches one ofthe numbers on which he must stand, he mustcount it as 11. Thus if his hand is 6-ace, he muststand on 17, and not draw to 7. This is knownas a 'soft' 17. If the dealer busts, he pays allPlayers still in the game. When he stands, heP'ays all players with a higher point count andcollects the stakes of those with a lower. Whenthe dealer's and a player's point count is thesame, the bet is a stand-off.

VariationsThe commonest variations to the abovedescription are :a a dealer will draw with soft 17. It is not an

option, and the rule may be printed on thetable.

" some casinos do not allow insurance.

c in some casinos the players' initial two cardsare dealt face down. As the dealer has nooption in his play, it makes no differencewhether or not he knows the players'hands.

d some casinos restrict doubling down tohands of 9, 10 or 11 , 10 or 11, or 11 only.In Great Britain, the Gaming Board have

introduced restrictions designed to reduce thehouse edge against poor players, but it is notcertain that this aim has been achieved. Thevariations on the game described above to befound in Great Britain are:a the dealer deals one card only to himself in

the initial round. The players play out theirhands, standing, drawing, doubling downetc., before the dealer gives himself a secondcard.

b splitting is not allowed on pairs of 4, 5 or 10.c doubling down is allowed only on 9, 10 or

11.d insurance is allowed only when the player

himself holds blackjack.It is the first variation, known elsewhere as

the 'London deal', which causes controversy.The aim is to prevent the dealer cheating incollusion with a player by indicating to himthe value of his face-down, or hole card. Thisis a simple method of cheating the casinowhich has been practised throughout thehistory of blackjack. Unfortunately the Britishrule leads the player to increase his stake bymeans of doubling down or splitting pairswhen the dealer might ultimately declare anatural for himself. In Nevada, the dealerannounces blackjack before the players com-mit themselves to increased stakes. In London,when the dealer's face-up card is an ace or a10-count, it is advisable to split only aces andnot to double down at all.

Strategy at BlackjackTo calculate the house edge in blackjackexactly requires a computer. The player hasadvantages in that he has many options,whereas the dealer has none. Also, he caninsure against a natural for the dealer. Thedealer has one advantage, the biggest. That isthat the player plays first. The player alwaysloses when he busts, whereas the dealer maybust having already won the majority of thehands at the table. To say that a tie is a stand-

151

P A R T S I X

An English Pope Joanboard, with counters andcards, of the nineteenthcentury. Similar games toPope Joan are the Britishgame newmarket and theAmerican game michigan.The board is dressed by thedealer, before each hand,placing counters into theeight compartments, oneeach in the compartmentsrepresenting Ace, King,Jack and Game, two eachin matrimony and intrigue,and six in Pope Joan. Theplayer who manages toplay the Ace, King, Queenor Jack of the trump suitcollects the counter in theappropriate box. If thesame player plays bothKing and Queen of thetrump suit, he also collectsthe counters in matrimony ;Queen and Jack winsIntrigue. The first player toplay all his cards wins thecounter for game, and theplayer to play the nine ofdiamonds (Pope Joan)collects those counters.The large illustration showsBritish hand-tintedmoralistic plaving cards,c!788.

152

off is therefore not strictly true, as it doesn'tapply when both player and dealer bust.

Some players, notably Edward O. Thorp, aprofessor of mathematics, in a famous bookpublished in 1962 entitled Beat the Dealer,have suggested that card-counting techniques,combined with the optimum play, could giveplayers an edge over the bank. Thorp hasblackjack winnings to prove it. The edge heenjoyed was a small one, and could still beobtained at casinos where cards are dealt byhand from one pack (provided they are dealtfairly) but the use of four packs, with up to 50cards not used, destroys his edge. In any case,the complicated calculations needed are be-yond the scope of the average player.

All methods of giving the player an advan-tage rely on casing the pack, or counting thecards. The simplest is merely to count the10-value cards, which constitute nearly athird of the pack. If the unplayed part of thepack is rich in cards of value 10, and thedealer's faced card is below 7, he must drawand has a good chance of busting. The playermight decide to stand on a low count of 12 or13, knowing that he has a better than evenchance of winning. More complicated count-ing requires the player to calculate how manycards remain of various groups: aces, 10-counts, medium cards (6-9) and low cards(2-5) and vary his strategy accordingly. Thisis very hard work, and in most cases the order

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Playing cards ix aharmless enough popularpastime for travellers onlong sea voyages, butcheats used to take trips inorder to fleece the richpassengers on the luxurvliners. The players, ondeck in this photograph areenjoying a game of thewhist family.


of the cards played will be unexceptional andresult in no significant advantage in count ingthem.

It is more profitable to look at the bestplays assuming a normal proportion of eachrank of cards in the shoe.

Table 6:1 gives the best play in these cir-cumstances. There is still argument amongexperts about some of these plays. The tablein these cases takes the side of caution, advis-ing to double down only when most expertsagree it is best.Table 6:1 Player's optimum play atblackjack in Nevada

Plaver Dealer's face-up cardholds 2 3 4 '5 6 7 8 9 10 A

Hard2-cardTotal

17161514131211109

SSsssHDDD

SSsssHDDD

SSssssDDD

SsssssDDD

SsssssDDD

SHHHHHDDH

SHHHHHDDH

SHHHHHDDH

SSHHHHDHH

SSHHHHDHH

1 9 S S S S S S S S S S1 8 S S S S S S H H H H

Soft 1 7 D D D D D H H H H H2-card 1 6 H H H H D H H H H HTotal 1 5 H H H H D H H H H H

14 H H H H D H H H H H13 H H H H D H H H H H

Note: Always stand on hard hands of 17 ormore and soft hands of 19 and 20.S = stand, H = hit, D = double down.

The table does not apply to games (i.e. allthose in Britain) where the dealer does notdeclare blackjack before the players play outtheir hands. Most disagreement among ex-perts occurs with the best play when holding16 against a dealer's up-card of ace or 10-count, when some advise hitting, and with theplay on soft hands, when some advise alwayshitting with totals of 17 or less, and othersadvise doubling down with a count of 13 to17 whenever the dealer's up-card is 4, 5 or 6.

SplittingThere is almost as much difference among

155

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This showcard was fordisplay in the foyers ofcinemas sho wing ' TheCincinnati Kid'. SteveMe Queen, in the title role,tries to beat 'The Man',Edward C. Robinson, atstud poker. Much of thefilm consists of theirlong-drawn-out game, andthis still shows the finalhand, in which Edward C.final/y beats his opponentwith a straight flush to afull house. Although thedenouement is quiteunbelievable, gamblersremember the film withpleasure as the best to haveportrayed the psychologyof the gambler and thetension of the big game.

157

P A R T S I X

experts on the question of splitting, as on theother plays. All agree that aces should alwaysbe split, and that 2s and 3s should be splitunless the dealer's up-card is 8, 9, 10 or ace.All agree that 5s should never be split andmost that 4s should never be split.

Table 6:2 shows a consensus of expertopinion on the advisability of splitting.

Table 6:2 Advisability of splitting pairs atNevada blackjack

Player's Dealer's face-up cardpair 2 3 4 5 6 7 8 9 1 0 A

A1098765432

SXssssXXss

sXssssXXss

sXssssXXss

sXssssXXss

sXssssXXss

sXXssXXXss

sXXsXXXXXX

sXXXXXXXXX

sXXXXXXXXX

sXXsXXXXXX

S = split, X = do not split

InsuranceThe term insurance is deceptive. A stake oninsurance is best regarded as a side bet. It is abet that can profitably be made by a cardcounter, as whether or not it is a good betdepends entirely on the proportion of 10-count cards against non-10s remaining in theshoe. Were the cards in their original propor-tions, there would be 16 10-counts in the packto every 35 non-10s. The probability of thedealer having a blackjack is f, and as the oddspaid are 2-1 there is a house edge of 5-8824per cent.

In Britain, players may only insure when-ever they hold blackjack themselves, and manydo so on the grounds that they must win oneunit whether the dealer holds blackjack or not,i.e. if he does, the original bet is a stand-off,and the player wins one unit insurance; if hedoes not, the player loses \ unit insurance butwins \\ units on blackjack. When the playerinsures, the dealer will usually pass over onechip immediately. However, British playersinsuring, and players elsewhere insuring whenthey hold blackjack, are accepting odds of 2-1about a 34-15 chance, a house edge of 8-1633158


Three shots of PaulNewman playing poker in'The Sting'. Poker isthought by the uninitiated tobe a game of bluff, but theexpert knows that it isprimarily a game of rapidcalculation of chances. Thebest players calculate theodds of improving theirhand and compare themwith the stakes in the pot.They also estimate theiropponents' chances by thenumber of cards drawn. Itis necessary not to giveaway information byinadvertent mannerisms,but a 'poker face' is notessential. Paul Newmanshows (not necessarilygenuine) doubt, confidenceand triumph.

159

P A R T S I X

Omar Sharif does not likehis name to be associatedwith gambling, so perhapsan apology is due forincluding his picture inthis book. Bridge is thebest of all card games, andthe best players get morepleasure from theintellectual exercise thanfrom the incidental stakeswon. Omar Sharif is avery fine player indeed.

160


per cent. A player accepting bad odds to'insure' his bet when he is in a strong positionto win should not be playing at all, and insur-ance betting is not recommended except forcard-casers.

PontoonBlackjack can be played privately, and indeedin many parts of the world is the most popularprivate gambling game. In Britain and Aus-tralia the game is known as pontoon; else-where it might be called twenty-one, vingt-et-un or blackjack. The rules vary considerablyfrom region to region, and next-door neigh-bours might be found with different rules. Thefollowing is a version the author has foundwidespread in Britain. Naturally, all rulesshould be agreed by the players before playstarts.

The dealer has an advantage, and the firstdealer is found by shuffling the pack anddealing the cards face-up round the tableunt i l a player is dealt a jack. He becomes firstdealer until a player beats him with a natural,called pontoon, when the bank passes to thepontoon holder.

The dealer deals a card face down to allplayers including himself beginning with theplayer to his left. The first player looks at hiscard, and puts up a stake between an agreedminimum and maximum. The first playerthen plays out his hand. Cards have values as inblackjack, with ace counting one or 11 at thediscretion of both player and dealer, and theobject is to get nearer than the dealer to 21.After staking, the player is given a secondface-down card, and then has four options.

1. If he holds a pair of aces, he mav splitthem. Only aces are allowed to be split. Astake equal to the first is put on the secondace, and the two hands are played in turn.

2. He may buy a further card for a stakenot exceeding his original stake, and afterreceiving this card might buy another andafter this a fifth, although each card must bebought for a stake not higher than the pre-vious stake. The object of holding five cardsls that in pontoon a five-card hand beats any°ther except a natural. Bought cards are dealt'ace down. A player may not buy a fifth card'f his four-card total is 11 or below, becausehe cannot bust. He must 'twist' his fifth card.

3. At any stage he may stand, by announc-ing 'stand' or 'stick' although he must have ahand valued between 16 and 21 to stick.

4. Should he not wish to buy a card, but isnot satisfied with his total, he may receive afurther card or cards by announcing 'twist',when the dealer will give him a card face up.A player with a count of 14 might twist, as hehas a bad hand and does not want to buy. If heis twisted an ace, he must twist again, as hedoes not hold the necessary 16 to stick. Aplayer who twists may not subsequently buy.

If a player busts, he must announce it, whenthe dealer collects his stake and adds hiscards to the bottom of the pack. The cards areshuffled only when the bank passes.

When a player sticks, he places his stake onthe face-down hand, and the dealer proceedsto the next player. When a player has a natural,he announces it immediately by turning hishand face up and putting his stake on top.

When all players are satisfied, the dealergives himself a second card and plays his ownhand. If he has a natural he collects from allplayers, as ties are won by the dealer. Other-wise he may continue dealing cards to him-self until he wishes to stick. Unless he has afive-card hand himself, he can stick only witha hand of between 16 and 21. Since the dealerwins all ties, if his total is 17 he will announce'pay 18s' and all players with 18 or more willexpose their hands and be paid. If he has 21,he will announce 'pontoons and five-cardhands only'. Settlement is then made at evenmoney. A player dealt a natural takes thebank (he would be silly to refuse it) unless thedealer has a natural on the same hand. Thebank cannot be taken on a split hand.

The commonest variations found are thatsome schools pay double for a natural, andtreble for a hand made up of 1-1-1. Someschools allow any pair, not only aces, to besplit. Some schools prefer that the bank passesfrom player to player in a clockwise directionevery five deals, naturals not taking the bank.

Strategy depends very much on the cardsrecently played, but a player staking the maxi-mum on aces and 10-counts, and the mini-mum on other cards, will not go far wrong,although this mechanical approach will de-prive him of the pleasure of exercising hisjudgment.

161

P A R T S I X

Figure 6:2, classes ofpoker hand. The highest isat the top, and the lowestat the bottom. The numberof ways each class of handcan be made is in thesecond column, and theprobability of being dealtthe class of hand is in thethird column. That theprobabilities do not make100 per cent is due to thepercentages being given tofour decimal places only.

example of hand

Straight flush-V VV »

H> V* «

• »

Fours

***S>:

#*»•

5X 1Full house

'4, A * V**»**** *:*.** *;,

Flush

1•v*»** *f

* »*»***? & * *;

Straight

11+*+*+** *f

*****»

Three of a kind•V ¥

A A;

S - . •* *

* *• 1

•V y

Two pairsii;» »

* *; * +? ¥

Dne pair

1is :<•» **.»*#%* »5 H,

Slo pair

¥

10. .•*.*+***+****;

7

*« *

ways of probabilitymaking percentage

40 0-0015

624 00240

3,744 01441

5,108 01965

10,200 03925

54,912 21128

123,552 4-7539

1,098,240 42-2569

1,302,540 501177

2,598,960 999999

PokerThe most popular card game in America ispoker, and its following has spread through-out the world. There are many versions, andeach version is l ikely to have local rules. Twoversions are described here: draw poker andstud poker. Before play, all players shouldagree on the rules and minimum and maxi-mum stakes.

A poker hand consists of five cards. Thereare nine classes of hand, shown with theirprobabilities in Figure 6:2. These proba-

bilities relate to being dealt the cards; in drawpoker there are chances to improve theinitial deal. A normal 52-card pack is usedbut if there are more than six players, twopacks must be used. Ace counts high, but mayalso count low in straights. Thus A-2-3-4-5is regarded as a straight, the lowest, whereasA-K-Q-J-10 is the highest straight. Straightscannot be 'round-the-corner', thus 3-2-A-K-Qis not a straight.

Straight draw pokerThe object of the game is to hold the highestranking hand at the showdown. The handsare ranked in the order shown in Figure 6:2.Where two or more hands are of the sameclass, the winner is decided as follows:straight flush by the highest card held. A-K-Q-J-10 is the highest, known as a royal flush.Fours by the highest foursome held. Full houseby the highest threesome or priai held. Flushby the highest card held. If equal, by thesecond highest and so on. Straight by thehighest card held at the top of the straight.Threes by the highest threesome or priai held.Two pairs by the highest pair held. If two highpairs are equal, by the higher second pair. Ifboth pairs are equal, by the higher odd card.Pair by the highest pair held. If two pairs areequal, by the higher odd card, then the next,and so on. No pair by the highest card held. Ifequal by the second highest, etc.

The deal passes in rotation clockwise roundthe table. Before the deal, each player puts anante into the pot, perhaps a quarter of theminimum stake. The dealer distributes thecards, one at a time, beginning with the playeron his left, till each player, including himself,has five cards.

The first player to the dealer's left then hasthe opportunity of staking or throwing in hishand. In some games, a player may start byputting in either the minimum stake or doubleit. If he throws in his hand, he takes no furtherpart in the deal and he passes his cards facedown to the dealer who puts them to one side.

If he bets one unit, the next player has theoption of throwing in, staking one unit tostay in the game, called calling, or raising thestake to two units, which he signifies by saying'raise to two'. If he raises to two, then sub-sequent players must stake two units to stay

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162


in, or may raise further. Suppose when it isthe dealer's turn to play, he raises to threeunits. Play is now back to the first player again,who, if he staked only one unit , must nowstake two more to stay in the game or throwin. He may increase further to four units.Staking continues until no player left inraises, when all players will have an equalstake in the pot or have thrown in. A playerthrowing in who has bet before does notrecover his stake or his ante.

When staking has finished, all players leftin may exchange any number of cards in theirhand, although it would be rare for a playerto want to exchange more than three, since apair is usually regarded as the minimumrequirement to stay in. Frequently 'pot' dealsare played, which usually start at jack-potsand progress to ace-pots. A jack-pot meansthat a player needs a hand of two jacks orbetter to open the staking. Before the stakingbegins a player with less than two jacks neednot throw in; he may 'check' and put up thenecessary stake on the next round. A playerwho opens must be able to show, after theshowdown, that he held the requisite hand.

Players exchange cards by asking the dealerfor the number of cards they want, and passinghim the discards, face down, which he placeson the discard pack. The replacement cardsare dealt face down. When all players, includ-ing himself, if he remains in, have exchangedcards, the dealer sets the unused part of thepack to one side, as it will not be requiredagain in the deal.

All players still in the game now have theircompleted five-card hands, and a secondbetting interval takes place, beginning withthe player who first staked. He may raise thestake again, or he may 'check', which he doesby announcing the word 'check'. This meansthat he remains in the game without increas-ing his stake. However, as soon as one player,ln his turn, raises, all other players, on theirturn, must call, i.e. put in stakes equal to theraise, or raise further. A player who haschecked may subsequently call but not raise.°etting continues as before until no playerraises or un t i l a maximum stake agreed^forehand has been reached. If all playersexcept one throw in, then the remaining player

take the pot without showing his hand.

Priai

Running flush

Run

Flush

Pair

No pair

exampleof hand waysofmaking

52

48

720

1,096

probabilitypercentage

0-2353

0 2172

3-2579

4-9593

16-9412

74 3891

100-0000

No player need show his hand at any timeexcept for the showdown, except the playerwho opens on a pot-deal, who need show onlythose cards necessary to establish that he hada required minimum. On the showdown, theplayer who made the last raise shows hiscards (the player calling might say 'see' or 'seeyou' when calling the bet). The other player orplayers may then concede without showingtheir hands. The principle is that no playerneed show his hand unless claiming the pot.

Once the pot has been taken, the playersante again, and the player on the dealer's left,after the cards are shuffled and cut, deals thenext hands.

StrategyAlthough poker is often said to be a game ofbluffing, good play is more a question ofknowing the probabilities of improving ahand, assessing whether the stake required tostay in the game is worth risking in relation

Figure 6:3, the classes ofbrag hand, with thenumber of ways each classcan he made and itsprobability. This is amodern version of thegame. Brag as described inmany books of card gamesdoes not recognise runningflushes, runs or flushes, andwild cards, called braggers,are used.

163

P A R T S I X

A famous poker story toldby John Lillard has anout-of-town chump losing apot to a local who displaysa worthless hand called, heclaims, a lollapalooza,which according to houserules beats everything.When the chump has onehe is denied the pot on thehouse rule: only onelollapalooza a night.

to the pot and the probability of winning it,and assessing the possible value of theopposing hands by the play of the otherplayers. So far as the last is concerned, a goodplayer will try to work out the habits of theother players at the table. The probabilities ofimproving a hand are shown in Table 6:3.

In the first betting interval, if it requires 3units to stay in, and the pot is worth 15 units,or odds of 5-1, it would be pointless to stay in

Table 6:3 Odds against improving at draw pokerOdds Odds against

Holding before Number of Improvement against anydraw cards drawn to drawing improvement

One pair 3

One pair and a 2kicker

Two pairs 1

Three of a kind 2

Three of a kind 1and a kicker

Open-ended 1four straight

One-sided or 1inside straight

Open-ended 1straight flush

Two pairsThree of a kindFull houseFour of a kind

Two pairsThree of a kindFull houseFour of a kind

Full house

Full houseFour of a kind

Full houseFour of a kind

Straight

Straight

Straightflush

5-1 5-28-1

97-1359-1

5-1 3-112-1

119-11,080-1

11-1 11-1

15i-l 8^-122i-l

15-1 11-146-1

5-1 5-1*

11-1 11-1*

22^-1 22^-1*

One-sided or 1inside straightflush

Straight flush 46-1 46-1*

Four flush 1 Flush 41-1*

Three flush 2 Flush 23 1 23-1** The odds against improving to a pair, or in the case of a three flush to

threes or two pairs are not considered.164


STMIGHTS*

with an inside straight (i.e. a straight missingone of the inside cards, such as 3-4-6-7), sincethe probability of rilling the straight is 11-1(to be precise 10| 1). With a four flush, it isnot worth staying in unless the pot is four timesthe stake required.

When drawing, the table shows that it is notprofitable to hold a kicker (i.e. an odd card,usually an ace or other high card) when draw-ing to a pair or three of a kind. Many playersdo this automatically; good players do itoccasionally to keep the opposition guessing.When one card is drawn, most opponents willassume that two pairs are held, and holding alow priai or two pairs aces high themselvesmight bet heavily, only to be beaten by a highpriai.

Most good players would agree that thefollowing principles are sound.

1. With a poor hand, throw in. Do not holdon in the hope of improving because you wantsome of the action. Be patient until you have agood hand.

2. Remember there is no payout for secondbest hand. Do not keep betting on three of akind, merely because it's the best hand you'veheld all night, if you believe another playerhas filled a flush or straight. When beaten,throw in.

3. Don't throw good money after bad.Treat each round as if it were the first. Do notfeel obliged to stay in because you havealready contributed heavily to the pot. Onceyou think you're beaten, cut your losses andthrow in. Similarly, if you are down on pre-vious deals, do not bet heavily on poor handsin a frenzied effort to get it back.

4. When you have a good hand, do not getexcited and rush - it won't fade away. Don'tfrighten off the others; raise on the last round,try coolly to get the other players to call, andmaximize your winnings.

5. Learn the probabilities in Table 6:3.They are a better guide than hunches.

6. Do not overdo the bluffing. Goodplayers will not be bluffed too often intothrowing in winning hands. Bluff if you thinkyour opponent might be bluffing, and that youhave a good chance of winning, but do notbluff on the principle that you must keep theopponents guessing or in order to give them afalse sense of security for future hands.

165

P A R T S I X

Stud pokerThis is one of the most exciting poker varia-tions, as all but one card of each hand isexposed on the table throughout the game. Itis the game played by Steve McQueen andEdward G. Robinson in The Cindnatti Kid.

The classes and ranks of hand are as indraw poker, and the object is to win the pot.Stud poker is not usually played with an ante,but some players prefer to do so, as it helps thepot when many players drop out first time.As there is no draw in stud poker, up to nineplayers can play with a single pack : five toeight is best.

The dealer deals one card face down to eachplayer, including himself, followed by onecard face up. The down card is known as thehole card, and a player sees only his own.

When all players have one face-up card, theplayer with the highest card showing (ace ishigh) begins the betting. If two or more cardsof equal rank are showing, the player nearestthe dealer's left begins. This player must stakeon the first round he cannot throw in orcheck. It is usual to have a minimum andmaximum stake and raise.

As in draw poker, once the betting has be-gun, all players must in turn either throw in,pass, or raise. When the betting reaches thelast player to raise, i.e. no other player hassubsequently raised, then each player still inhas put an equal stake in the pot, and theround of betting ends. Thrown-in hands arecollected by the dealer and discarded facedown. Hole cards of players throwing inshould never be shown to the other players.

The dealer then deals a third card to eachplayer, face up, so that each player now hastwo cards showing. There is now a secondround of betting, begun by the player withthe highest hand showing, which cannot behigher than a pair, and might depend on thehighest card. In no betting round does a partflush or part straight have any significance: apair of 2s on the last round ranks higher thanA-K-Q-J of a single suit.

Players are dealt a fourth and fifth card,with further betting taking place after eachcard. After the last betting round, comes theshowdown, when the last player to raise showshis hole card and the remaining players con-cede or show a better hand.

StrategyThe principles given for good play at drawpoker apply equally to stud poker. A parti-cular fault is to stay in too long with a straightor a flush. Even if you hold a four-card flush,reference to Table 6:3 shows that the chancesof the fifth card completing the flush are 4^-1(to be precise 38-9). If another player has twoaces showing he is 4^-1 on to beat you.

The most important decision in stud pokeris made after the first up-card is dealt. Withsix players in, the odds that at least one has apair are only about 2-1. If your hole card isqueen and your second card is 8, you would dowell to throw in if an ace and a king are alreadyshowing and another player raises as if heheld two 9s.

On the next round, if a pair is showing, donot stay in without a pair. Do not bet on ahand which you know is not the best in thehope of improving. If after the last card isdealt you are sure you hold the best hand,raise. Make your opponents pay to see yourhole card.

Finally, to return to The Cincinaiti Kid.When Steve McQueen held a full house, aceshigh, in the final hand, he could fully expectto win. Edward G. Robinson's hole cardproved to be the jack of diamonds, filling astraight flush. Apart from the astoundingimprobability of two hands being dealt to-gether, neither smaller than a full house, aceshigh (about one chance in 10 million), why wasEdward G. Robinson staying in so long withsuch high stakes, and with a very small chanceof winn ing?

BragAn ancestor of poker, brag was the mostpopular card game of England in the six-teenth century, and is still very popular today.It is very similar to poker, played with anormal pack. The deal passes in rotation,each player including the dealer receivingthree cards face down. The dealer places astake up to an agreed limit in the pot, and theplayer on his left has the first option of throw-ing in, calling (i.e. equalling the dealersstake) or raising. When the stake is raised.each player in turn must raise his stake to thenew level to stay in, as in poker. When allbets are equal, there is showdown. There is

nclan]

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n Iprlcalcala ninalsaprlaltit

166


no draw for fresh cards. The classes of handsare shown in Figure 6:3.

In brag, a run, or straight, ranks higher thana flush. The probability of obtaining a flushwith three cards is greater than that ofobtaining a run, although with five cards, asin poker, the straight is more likely. A priaiin brag ranks higher than a running flush,although its probability is slightly higher.

When two hands are equal, the winninghand is determined on the same principle as inpoker. There are two exceptions. The highesthand is a priai of 3s, ranking above aces, andthe highest run is A-2-3, ranking aboveA-K-Q. These rules must be understood andagreed by all players before play begins.

Strictly, runs and flushes are not recognisedin brag, the classes of hand traditionally beingPriai (or pair-royal), pair, or no-pair (highestcard wins). More action is generated by threecards, known as braggers, being wild, the aceand 9 of diamonds and jack of clubs. Anatural hand ranks higher than a hand of thesame class with a bragger. Modern playersPrefer to play the game as described above,although some impatient players like to speed't up further with the use of black 2s as wild.

A popular version of brag is seven-cardbrag, which can be played by up to sevenplayers. Each player is dealt seven cards, dis-cards one, and makes the two best brag handshe can with the remaining six. Each playerputs an agreed stake into the pot before eachdeal. There is no betting, and a player mustwin both hands before he takes the pot. If thepot is not won, it remains for the next deal,when it is added to. Each successive deal inwhich the pot is not won makes the pot moreworth winning.

Little strategy can be practised'in brag, asthere is no draw and no indication of theopposing strength. Players must know theprobabilities in Figure 6:3 and the bettinghabits of their opponents. It is worth notingthat with four players, a hand of ace high willbe enough to win about half the deals, and apair of aces over two-thirds of them.

Gin rummyA game of recent invention, gin rummy wasdeveloped from the parent game of rummy,or rum, in the early days of the present century,and popularised in the 1940s when it becamea craze in Hollywood among the film stars.

These players are playingmichigan, a variation ofPope Joan, the board forwhich is illustrated onpage 152. A simple versionof the game is often playedwithout a board by usingcards from another pack,say an Ace, King, Queenand Jack from differentsuits, as the winning cardson which stakes are placed.

167

P A R T S I X

8*1

5*7

Me TVvet Me Me

Figure 6:4, the Hollywoodscore-card for gin rummy.How to enter scoresis described in the text.

It is a game for two players played with astandard pack of 52 cards, ace counting low.Each player draws a card to decide dealer, thehigher deals. Thereafter the winner of eachhand deals the next. Dealer deals ten cardsto each player, beginning with non-dealer,the remaining cards being placed face downbetween the players to form the stock, the topcard being turned over to become the up-card,and to begin a discard pile.

Non-dealer may take the up-card into his-hand, replacing it with a discard from hishand. If he refuses the up-card, dealer maytake it. If he declines it, non-dealer takes thetop card from the stock into his hand, anddiscards a card, which might be the same card.Thereafter each player in turn draws from thestock or the discard pile, and discards.

The object of the game is to form sets,either with three or four cards of the samerank, or three or more cards of the same suitin sequence. After drawing, a player mayknock, i.e. he lays down his hand in sets andmakes his discard. He is allowed to lay downunmatched cards if they total 10 or less. Eachunmatched card has its pip value, aces count-ing as one and court cards as ten. No playermay draw a card when the stock is down totwo cards; if the player who takes the fiftiethcard does not knock the hand is abandoned.If the knocker lays down all his cards withnone unmatched he is said to go gin.

When a player knocks, unless he has gone

gin, the other player shows his sets, and isallowed to lay off any unmatched cards on thesets of the knocker. For example, if theknocker has a set of three kings, his opponentmight lay ofT the fourth king if he holds it. Ifthe knocker has a sequence of 4-5-6 of hearts,his opponent might lay off 7-8 of hearts.

After laying off, if the knocker has the lowercount in unmatched cards, he scores the differ-ence of the counts. If he has declared gin, healso scores a bonus of 25. If the opponent hasan equal or lesser count, he is said to undercutthe knocker, and scores the difference, if any,plus a bonus of 20. A knocker going gin can-not be undercut : if his opponent discovers healso has gin, there is no difference in thecounts, but knocker scores the bonus of 25.

The Hollywood scoring is complicated, andis recorded on a card like that in Figure 6:4.

The first time that a player scores he entershis score in the first of the three columnsagainst box 1. The second time he enters hisscore in the second column against box 1 andalso adds the points to his score in the firstcolumn, writing the total opposite box 2.The third time he scores he enters the score inthe third column, and adds the points to thosealready scored in the first two columns. There-after, each score is added on to all three of thecolumns.

When a player's score reaches 100 in acolumn, he wins the column and scores 100points for winning it plus 20 points for eachbox he has won more than his opponent. Ifthe opponent has scored more boxes, 20points are deducted for each extra box. If aplayer fails to score in a column, he is said tobe blitzed, and the score of the winner of thecolumn is doubled. Once a column is won, nomore scores are added to it. A player blitzedin the first column must enter his first score inthe second column.

If a player wins all three columns, his finalscore is the sum of the three totals. If bothplayers win a column, the player with thehigher score wins by the différend1 in the twoscores. Settlement is at a rate per point, or tenpoints, to be agreed beforehand.

StrategyThe best play lies in remembering the dis-cards, so that no attempt is made to form a set

168


lnd is that is impossible or difficult to make because>n the i all or some of the required cards are buried in

If the the discard pile.[orient It should be appreciated that a combination

it. If Of ^6 +6 +5 affords four chances of a setpearts, I with^6-î-6+4 and + 7 whereas ^A+A+2

affords only three. A holding like +8+74-10|lower 4-8-Î-7 affords six chances of a set, includingiiffer- one of four cards, and whichever set is formed,

|in, he two matching cards can still be kept. A se-it has quence is more valuable than a set of three of aercut ' kind, as more cards can be added to it, two

If any, immediately at each end of a sequence, onecan- only on a threesome. The cards the opponent

lers he , takes from the discard pile, and the cards heIn the , discards, should be noted to form a picture of

25. his hand. Cards which might help him should1, and be kept both to block him and to afford laying>:4 . off opportunities should he knock. Otherenters things being equal it is better to hold low cards

f u m n s than high cards, so that any adverse score is1rs his kept down and also because they afford

1 and opportunities to knock. Most gin hands aree first won on two sets and three or four unmatched

lox 2. cards.lore in The early discards tend to be high cards,

I those and it is often worth holding potential high-There- card sets early in the game. If such sets are not

lofthe I formed after four or five discards, however.they might be expensive to hold. The longer

in a the game continues, the more wary a player|s 100 must be of knocking with a high total of un-

each matched cards, as it is likely that his opponentInt. If might undercut him. It is not usually good|s, 20 < policy, when it is possible to knock, to hold on

If a ' hoping for gin.ud to |)f the Napoleonl n . n o The game of Napoleon, or nap, is played with a[itzed standard pack of 52 cards, ace counting high,jre in I The first dealer is decided by any agreed

method, and subsequently the deal passes tofinal } each player clockwise.

I both \ All players, including dealer, are dealt fivethe cards, face down, one at a time. There is then

two one round of bidding, each player in turnr ten _ from the dealer's left being given the oppor-

tunity to contract to make a stated number of'ricks, with trumps the suit of his choice.After the first bid, subsequent bids must be in

dis- ^ending order. The bids are Two, Three,| a set Four or Nap (all five tricks).

The player who contracts to make the mosttricks (the declarer), then leads to the firsttrick. The first card led indicates trumps.Tricks are won in the normal manner of trick-making games, the winner of each trickleading to the next. The declarer receives orpays to all other players depending uponwhether or not he makes his contract. Paymentis at the following rate:

ContractTwoThreeFourNap

Declarer wins2 units3 units4 units10 units

Declarer pays1 units3 units4 units5 units

Overtricks and undertricks do not carrybonuses or penalties, and settlement is madeimmediately.

In order to give the game more variety,some players allow further bids. Misery, acontract to lose all tricks, there being notrumps, ranks between the bids of Three andFour, and pays or loses 3 units to each player.Wellington is a bid which can be made onlyabove nap, and is a contract to win all fivetricks at double stakes (i.e. it wins 20 andloses 10). Blucher is a bid which can be madeonly over Wellington, and pays triple stakesfor a contract of five (30 and 15). Peep napallows the player who has bid nap to exchangea card for the top card of the pack if he wishes.Purchase nap allows each player, if he wishes,to look at the top card of the pack beforebidding, by contributing one unit to a pool.The player who becomes declarer, if he haspaid to look at the top card, is allowed to takeit into his hand in exchange for another cardbefore leading.

StrategyThe best play comes from est imating the l ike l i -hood of missing cards being in the packor in another player's hand. With four or fivehands dealt, it is more likely than not that amissing card is sleeping, i.e. in the pack. Aplayer holding three of a suit, which he mightmake trumps, should know that it is about16| 1 against any specific other player hold-ing three or more trumps. Should there be sixplayers, it is about 4-1 against any otherplayer holding three or more trumps. There-fore a player with AKx in the trump suit and

169

P A R T S I X

Bridge ix thought by someto have received its namefrom biritch, or Russianwhist, described in apamphlet published inLondon in 1889. The finalpolish on the game whichled it to become to-day'scontract bridge was theinvention oj Harold S.Vanderbilt and his card-playing friends in 1925.Bridge soon became themost popular game in thehistory of card-playing, andhas acquired a worldwideliterature comparable tothat of chess. TheseAmericans are enjoying agame in the open air.

170


171

P A R T S I X

an outside ace can expect to make four tricksabout four times in five. A player holding AKonly in the trump suit against five otherplayers has a 6-4 on chance of clearingtrumps, and with an outside ace should makethree. A player with four small trumps, on theother hand, in a game of five players, will findit is 2-1 on another player holding twotrumps, and even with an outside ace cannotexpect to make more than three.

Red dog and shootAlso known as high-card pool, red dog is agame for up to ten players. Each player inturn deals. Before the deal each player con-tributes an agreed number of units to a pool.The dealer gives each player five cards, one byone, face down, and places the stock facedown in front of him. With nine or tenplayers, each player has four cards each. Theplayer on dealer's left examines his hand andbets a stake ranging from one unit to theentire pool that he has a card of the samesuit and higher than the top card of the stock.Dealer turns over the top card, and if theplayer can show a higher card in the suit, heis paid by the dealer from the pool the amountof his bet. If he loses, he adds his bet to thepool after showing his cards to the otherplayers. Ace counts high. When the firstplayer has won or lost, his cards and the topcard are placed face down in a discard pile andthe player on his left is the next to play. Whenthe whole pool is won, or if at the beginningof a fresh deal it has fallen below an agreedminimum, all players replenish it equally.

Shoot, or slippery sam, is a similar game tored dog, but is a banking game. Each player inturn, when dealer, puts a sum in the centre asthe pool. The amount of the pool can beagreed beforehand; otherwise a minimumshould be agreed. Shoot is possibly uniqueamong banking games in that the advantageis with the players.

The dealer deals each player three face-down cards, one by one, and each player athis turn, after examining his cards, bets anyamount from an agreed minimum to theamount in the pool that he can beat the topcard in its suit. A player betting the wholepool 'shoots the pool' by announcing 'shoot'.As in red dog, the dealer exposes the top card.

and the player takes from or adds to the poolthe amount of his bet. When the pool is taken,the player on the dealer's left puts up a pooland becomes dealer. Each player when dealerdeals three rounds, when he may withdrawthe pool and pass the bank to the next player.He has an option of a fourth and final deal ifhe wishes.

Strategy in red dog and shoot comes fromremembering the cards already exposed in thedeal and calculating how many cards remainto beat your hand and how many remain thatyou beat. A player holding ^A-î-J^lO inshoot knows that he can beat any diamond,nine of twelve clubs and eight of twelve hearts.Any spade beats him. If he were first to playhe would have 29 chances to win, 20 to lose.If four cards have been exposed, he mighthave 27 chances to 18 to win, or odds of 3-2on. He should bet heavily. The best stakingplan is to shoot every time the odds favour you,and to bet the minimum when they do not,but a player using this strategy will not bepopular with his fellow players.

Other card gamesThe former British Prime Minister, HaroldMacmillan, enjoyed a variation of red dogand shoot called farmer's joy, in which allplayers, including the dealer, put an ante intoa pool, and the dealer then turns up the cardsuntil a 7 or lower appears. He then dealsthree face-down cards to the players, whowithout looking at them bet in turn that theycan beat the up card in its suit. Ace countshigh. The bet must be between one unit andthe total units in the pool. The dealer dealsone round before passing the cards to the nextplayer. A player's chances depend upon thenumber and suits of the cards turned up by thedealer before the final up card. If the first cardturned is a 7, the player's chance of beating itis about 7-4 against. If it is a 2, his chancesare slightly better than 5-4 on winning. If thefourth card turned up is a 2, and it is the firstof its suit, the player's chance of winningbecomes 17-12 on. In the majority of deals,therefore, the player's chance will be between6-4 on and 6-4 against, and experience willsoon teach a player to estimate it fain)'accurately without doing the sums.

There are, of course, several other ca

I

172


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InningIdeals.tween

le will1 fairly

Black's outer board12 11 10

Black's home board3 2 1

Bar

12 11 10 9White's outer board

3 2 1White's home board

Figure 6:5, the layout atthe start of a game ofbackgammon. Traditionally,the home board is nearestthe window or other sourceof light. The actual boardis not marked with anyannotation, which isincluded to facilitate theexplanation of the game.

games designed specifically for gambling,many of them excellent games. Ecarté is agame for two players which Nico Zographoswas fond of playing for small stakes before hetook on the heavy punters at the Deauville andMonte Carlo baccarat tables. It is a game withendless scope for studying probabilities. PopeJoan is a very old gambling game originallyPlayed on an attractive decorated circularwooden table with compartments, some ofwhich are found today in museums andantique shops. It is a pleasant game played°n one of these tables. A modern simplervanation is the game known variously as new-market, boodle and stops in Britain, andl^'chigan, Saratoga and Chicago in America,'hese games and others could well be dis-ctissed in this book, did space allow. Descrip-lons of them can be found in authoritative°°ks on card games (see bibliography), and

the reader can have the pleasure of workingout the probabilities and optimum strategiesfor himself.

BackgammonThere is reason to believe that the first gamesplayed in which men were moved around aboard used the principle of throwing dice todetermine the movements of the men. Gamesof this sort have been played for 5000 years,and backgammon and pachisi (an early formof ludo) are probably the oldest of these gamesstill played in something like their originalform. The name backgammon first appearedin the seventeenth century, although theFrench name for the game, tric-trac. is older.The conception of doubling is about fiftyyears old, and has contributed to the presentpopularity of backgammon, on which a greatdeal of gambling now takes place.

173

P A R T S I X

Backgammon is one of theoldest of games still playedin something like itsoriginal form. Romanliterature refers to agame called 'LudusDuodecim Scriptorium ',the game of twelve lines,which closely resembledbackgammon. Variations ofthe game accumulatedmany names through theages, the commonest I c'ngthe word 'tables'bv whichit was known in variouslanguages. In France itbecame 'tric-trac', andlater 'jaquet'. Theillustrations on these pagesshow players at tric-trac,that above dating from thesixteenth centurv.

174

Backgammon is played on a board by twoplayers, each of whom has fifteen men (alsocalled stones or pieces). It is a race game, eachplayer trying to move his men round and offthe board before the other.

The starting position is shown in Figure 6:5.The triangular spaces on the board are knownas points. The points are numbered in theillustration to enable the moves to be de-scribed, and the raised ledge which divides theboard into two halves is labelled 'bar',although on the actual board there is noannotation. Each player has a home boardand an outer board. In the il lustration thehome boards are shown on the right, althoughthe board could be reversed from left to right,with the home boards on the left. Tradi-tionally, the home board is on the side of thewindow, or source of light. The men move inopposite directions towards their home board :in the set-up illustrated, black men moveclockwise and white anti-clockwise. The first

object of each player is to move all his men jinto his home board (i.e. on to his pointsjnumbered 1 to 6) whence he can begin to bearjthem off.

Each player has two dice. For the first rollonly each player throws one die. The playerwho rolls the higher number has the first move,and takes the numbers shown on the two dice Ias his first roll. Throughout the game, if a dieis cocked, i.e. resting on a man or against t h e jbar or the side of the board, both dice mustbe re-thrown.

On his turn , a player must move his meniaccording to the totals shown on his dice.'each total being independent. If he throws 1and 4, he cannot move one man five spaces.He can move one man one space and anotherfour, or he can move the same man one spaceand four, or four and one. Except when bear-ing off, a man can only be moved the exactnumber shown on the die. for instance if a (l

is thrown none of the men on the home 6-

P A R T S I X

Backgammon has enjovedmanv revivals and becamea craze throughout Europein the early sixteenthcentury. This engravingshows a domestic scene inwhich eating, drinking andsmoking accompany thepleasures of the game. Themen are playing puff,which was the Germanname for backgammon.

176


point can be moved, as a move of 6 wouldcarry it off the board. Another restriction isthat no man can be moved onto a pointalready occupied by two ormoreoftheopposingmen. A player with two or more of his menon a point is said to have made the point. Nopoint can be occupied by men of differentcolours. If a player has one man only on apoint, that man is known as a blot. An oppos-ing man can now occupy the point, when it issaid that the blot is hit. A man hit is removedto the bar, and the player with a man on thebar must re-enter him if possible on his nextturn. He is not allowed to move another manuntil he has re-entered the man on the bar.A man must re-enter on his opponent's homeboard. If the throw is 6-3, and the opponenthas made both these points (he starts thegame with his 6-point made) then the man onthe bar cannot be re-entered and the turn isforfeited. If a player throws a double, he mustmove the number thrown four times. Again,the four moves are independent.

Sometimes a player cannot move men inaccordance with the two numbers thrown (orfour if a double is thrown) in which case hemakes the move or moves he can and forfeitsthe other or others. It sometimes happens thathe can move in accordance with either of thenumbers thrown but not both, in which casehe must move according to the higher numberand forfeit the lower.

When it comes to bearing off, i.e. movingmen from the home board off the board,special rules apply. A player must move hismen according to the rules already given, withthe option, where applicable, of bearing off aman or of moving a more backward manforward. For example, if he has men on his6-point and on his 2-point, and one of his diceindicates 2, he may bear off a man from the 2-point or move a man from the 6-point to the4-point. Sometimes, however, he will not beable to move a man according to these rules.For example, he might throw 5-4, and havefour remaining men on the 1, 2, 3 and 4-points. In this case he may bear off the man onthe 4-point, corresponding to his throw of 4.For this throw of 5, he must bear off the manon the highest point remaining, in this casethe man on the 3-point. Now, with men onthe 1 and 2-points, he must win on his next

177

P A R T S I X I

Backgammon has retainedits popularity in the MiddleEast during periods when itwas practically unplayed inthe West. This game, withits interested kibitzer, istaking place in a hackyard in Cyprus.

throw (as double-1 will entitle him to Fourmoves of 1) unless his opponent bears all hismen off next turn, or unless his opponent has aman on the bar. which he can re-enter with athrow of 1 or 2 and hit the blot.

Betting and the Doubling CubeThe item not so far mentioned, and the onewhich has elevated (or reduced) backgammoninto a gambling game for high stakes, is thedoubling cube. The doubling cube is a die,usually larger than the others used in the game,on which appear the numbers 2, 4. 8, 16, 32and 64. At the beginning of the game, theagreed stake for which the players are playing

is one un i t (it might be that each player stakes£1 or $1, or £5 or $10 or whatever). Thedoubling cube is placed to one side of theboard showing 64 uppermost (since there is no1 on the cube). At any stage of the game aplayer who thinks he has the upper hand mayoffer his opponent a double before he takeshis turn. The opponent either declines, inwhich case he loses the game and pays oneunit, or accepts, in which case the cube isturned to 2 and the game continues with twouni ts as the stake. When a player accepts adouble, the cube is placed on his side of thetable, and only he is allowed to make the nextdouble. Therefore, in a game of much doub-ling, each player will double alternately. Theplayer declining a double pays the amountshown on the cube at the time.

There are three classes of win. A straightwin is when the loser has begun bearing off, inwhich case he pays the stake shown on thedoubling cube. The second class of win isknown as a gammon. If a player loses beforehe has begun to bear off his men he is said to begammoned, and pays twice the stake on thedoubling cube. If a player loses while he still |has a man in his opponent's home board, or jon the bar, he is backgammoned, and pays jtriple the stake on the doubling cube. The |maximum loss therefore is 192 units. Back-gammons are rare, and it is usual in Britain >not to play them. Players should agree before-hand whether or not to recognise back-gammons.

ChouetteThis is a means of enabling three or moreplayers to share a game. One player (called theman in the box) plays against the others, onlyone of whom actually plays the moves. He iscalled the captain. If the man in the box wins,he remains in the box, and the next player inline becomes the captain, the losing captaingoing to the back of the line. If the captainwins, he becomes the man in the box for thenext game, the next in line becoming captain-and the losing man in the box going to theback of the line. Other players may advise the jcaptain, but he makes all decisions on theplay and doubling. All players pay or arepaid by the man in the box, who if he 'splaying against two players is in effect playin?

178

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for double stakes. Any player may accept ordecline any double made by either the man inthe box or the captain, but he cannot doubleunilalerally. If he declines he pays Ihe man inthe box the stake shown on the cube. Shouldthe caplain decline a double, he pays up andmoves lo the back of the line, and the re-mainder of the game is played by the playerfirst in precedence to accept the double.

StrategyThe best players learn the best strategy bypractice and experience, but research byexperts has resulled in general agreement asto the best moves to be made on the openingrolls. These are set out in Table 6:4.Table 6:4 The best opening moves inbackgammon (for White)

The best movesBl to B12Bl to B l lBl to B I OB12 to W5B12lo W7; W8lo W7Bl lo B I OW8 to W3 ; W6 to W3B12to W8; B12to WllB 1 2 t o W8; W6to W5B 1 2 t o W9; B 1 2 t o W10W8 to W4; W6lo W4B12to W9; W6to W5B12to W10; B12to Wl lW8 to W5; W6lo W5B12 to W l l ; W6 to W5

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The first player cannot, by the rules, beginwith a double (although there is a variant inwhich the player who throws the higher diere-throws both dice for his opening roll). Thesecond player might begin with a double.Table 6:5 shows moves agreed to be good°nes when throwing a double at an early stage'n the game.'able 6:5 Good opening moves when'hawing an early double (for black)Th,

5-54-43-32-21-1

The best ectr/v movesWl to W7 (twice); W12 to B7 (twice)W12 to B8 to B3 (twice)Wl to W5 (twice); W12 to B9 (twice)B8 to B5 (twice); B6 to B3 (twice)W12 to Bl 1 (twice); B6 to B4 (twice)B8 to B7 (twice): B6 to B5 (twice)

The probabilities of throwing any particularroll or total can be calculated by reference toFigure 2:1.

There are two distinct overall strategies inbackgammon. The first is known as the for-ward or running game. In this strategy theplayer tries to move his men round the boardas quickly as possible ignoring within reasonhis opponent's play and the risk of leavingblots. Without interference a player should beable to bear off his men in around 24 throws.The reverse game, known as the back game, isa strategy which allows the opponent to runwhile concentrating on making points and ifpossible to build blocks or a prime. A blockis a succession of adjacent points made,making it difficult for the opponent to movepast. A prime is six adjacent points made,making it impossible for an enemy man topass. A block can sometimes be walked roundthe board by moving the men on the back-ward point to the forward point, keeping theblock intact. Players hold two good points forblocking at the start of the game in their 6-point and 8-point. If a player can make his7-point (as he can with an opening roll of 6-1)he can build a block on points 6, 7 and 8. Ifhe can make his 9 and 5 points he nearly has a

These men in Jerusalemare playing xhe.ih besh, avariation of backgammon.

Backgammon had a hoomin the 1970s, when itbecame the fashionablegame in many parts of theworld. On the followingpages, two famous playersreceive advice fromSolly Kerzner of theSouthern Sun HotelCorporation. They arePeter Sellers, the actor,left, and Dr ChristiaanBarnard, the heart surgeon.

179

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P A R T S I X

18


prime. The best players will usually combineboth strategies, trying to run their men and tomake points.

Do not be over-anxious to hit blots. If youhave a big lead in time, it is better to let youropponent's runners pass, so that they cannothit your blots. Take risks in leaving blots earlyin the game, when an adverse hit is lessdamaging. When the two armies of men passeach other, do not waste points - get your meninto your home board as quickly as possibleto begin bearing off, even if most stack up onyour 6-point.

Double when you have a firm strategicadvantage, like a big lead in a running game,or when you have important blocks on thebar or 5-points, or when you throw a double-6 in a close game. Do not decline a double justbecause you think your opponent has anadvantage. Try to assess his advantage. If it isless than 3-1 accept the double. If youropponent doubles first four times, and youdecline each time you lose four units. If eachtime his chance was 3-1 on, you can 'expect'to win one of the games, winn ing two uni ts andlosing six, again a net loss of four units. If hischances were less than 3-1, you will havegained the edge by accepting. This does notmean that a player should not double until heestimates he has a 3-1 advantage. A playerwith an advantage clearly wants the stakes ashigh as possible, and if he can force a faint-hearted opponent to decline doubles in gameshe would ultimately have won, he is gaining apositive edge!

Although knowledge of good strategy andthe probabilities when throwing two dice areessential to the good backgammon player,learning to apply this knowledge comesthrough playing, and practice is the bestteacher.

GeneralThe most popular dice game in Puerto Ricols known as general. Although it is oftenPlayed elsewhere, a variation known as yachtls more common. Any number may play and"ve dice are used. A score sheet is ruled up asln Figure 6:6.

The hands, which are based on poker hands.ar>d scores for them are as follows :

Five of a kind. All five dice showing the same

number. When thrown on the first throw of aturn, this is known as big general and auto-matically wins the game. When obtained on asecond or third throw, it is known as smallgeneral and is worth 60 points.

Four of a kind. Worth 45 points on firstthrow, 40 subsequently.

Full house. Three dice showing one number,and two another. Worth 35 points on firstthrow, 30 subsequently.

Straight. A throw of 2-3-4-5-6 or 1-2-3-4-5.Worth 25 on the first throw, 20 subsequently.In straights, a die showing 1 is partially wild,and can represent a 2 or a 6.

Point numbers. These are valued at theirtotal spot count, e.g. three 6s are worth 18,two 4s are worth eight.

Each player throws all five dice to determinethe order of play, the lowest total going first,the next second, etc. Ties re-throw. Eachplayer has one, two or three throws per turn,and a game consists of ten turns per player,unless a big general is thrown and wins.

The first player throws the five dice. If hethrows a full house, or straight, he enters thescore against that hand on the score sheet. Ifhe throws any other collection of numbers,he may put aside any dice and throw the othersagain, or he may throw all five dice again. Thisis similar to drawing cards at poker, the objectbeing to improve the hand. If he does notachieve a poker hand on his second throw,he may re-throw any of the dice a third andfinal time. If he throws four of a kind on hisfirst throw, he may enter 45 points immediatelyagainst four of a kind. Alternatively, he maythrow the odd die twice more in an effort toscore 60 for small general. If he fails, he willscore only 40 for his four of a kind.

If after three throws a player still has notthrown a poker hand, he may nominate anypoint, and score accordingly. For instance, ifhe ends his turn with 6-6-6-3-2, he mightnominate 6 as his point, and enter 18 againstsixes on the score-sheet. If he has 1-2-2-4-6.he might nominate 2 as his point and scorefour against twos. He could score six bynominating 6s, but a later turn might provemore profitable, and he does not forfeit manypoints by scoring only four against twos. Oncea player has entered a score against any of thehands, he cannot score for that hand sub-

Backgammon is a simplegame to learn, hut tidifficult game to master. Itis also an ideal game fortrain and plane trips, whichperhaps contributed to itsappeal for modern jet-setters. Hugh He/her, ofthe Playboy organization,playing a game with aplaymate on aflight to Los Angeles.

183

P A R T S I X

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Figure 6:6, the score-sheetfor the dice game general.This is a game in which thechance throwing of dice isallied to skill in calculatingodds. The use of thescore-sheet is describedin the text.

sequently. Thus, on his tenth turn, a playerwill have only one space on the score sheet onwhich he can make a further score. A playerwith a very poor hand after three throws, say2, 2, 3, 5, 6 when he has already entered a scoreagainst twos, has the option of discountingthe hand and scoring zero in any empty spaceon the score-sheet. He might select aces in thiscase, as he does not lose much by scoring zerofor aces, and stands to lose more by scoringonly five or six points in the appropriate space.

If a player has entered a score against smallgeneral, and throws small general again onhis second throw, he cannot score again in thisspace, and must throw one die again in aneffort to score four of a kind, or if this is alsoalready scored, two dice for a full house. If heends his turn still with a small general, he mustcount the hand as a point number, or as a zeroin any available space.

At the end of the game the points aretotalled, and all losers pay the winner unitsaccording to the difference in scores. A playerthrowing big general collects 100 units fromall other players.

Strategy arises in knowing dice proba-bilities and deciding which dice to re-throwin an effort to score in an empty space on thescore sheet, and which point to choose toenter a score against at the end of the turn.

Yacht is basically the same game, but theterms are different, and there are twelve scor-ing hands. Five of a kind is called yacht andscores 50. There is no big yacht and smallyacht. Straights are big straight (2-3-4-5-6) andlittle straight (1-2-3-4-5) and score 30 each.Each has a space on the score sheet. Acescannot be counted as wild. Full house andfour of a kind score the total number of spotsshown on the hand, including, in four of akind, the odd die. Thus 4-4-4-4-6 counts 22points against four of a kind. Point numbersscore as in general. An additional scoringhand is choice, where all spots shown arescored. A hand of 6-6-5-5-4, for example,might be better scored as 26 against choicethan 12 against sixes. The strategy and scoringare the same as in general, although yacht ismore complex, and consequently the bettergame.

Poker diceA set of poker dice consists of five dice onwhich are printed, instead of spots, six playingcard denominations: A, K, Q, J, 10, 9. A setis shown in Figure 6:7.

Any number can play. The object is toobtain a higher poker hand than any of theother players. The hands rank: five of a kind,four of a kind, full house, straight, three of akind, two pairs, one pair. Usually spades isthe only suit shown, so there are no flushes.The odd dice in four or three of a kind, orpairs, do not settle tied hands. The firstdealer is decided by all players throwing thedice once, the highest hand being dealer.Thereafter the deal passes clockwise.

All players put up an equal stake, and thedealer throws the five dice from a cup. He mayeither stand on the hand thrown, or set asideany number of dice and re-throw the re-mainder, equivalent to drawing in poker. The

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184


player on dealer's left then attempts to beatthe dealer's hand, hut he may not have morethrows than the dealer. If the dealer did notre-throw, no other player may. Each player inturn throws, the winner tak ing the pool. Ifthere is a tie, the pool is shared.

The dealer decides whether or not tore-throw. Table 6:6 indicates the best playagainst various numbers of players.Table 6:6 Dealer's advisability on re-throwing at poker diceHand Number of players

2 3 4 * 5 6

Three queensThree jacksThree 10sThree 9s2 pairs (aces up)2 pairs (kings up)2 pairs (queens up)2 pairs (jacks up)2 pairs (10s up)Pair of aces

SSSSSSSSSS

SssssRRRRR

SSsRRRRRRR

SRRRRRRRRR

RRRRRRRRRR

S = Stand, R = re-throw. With three kingsor above, stand. With a pair of kings or below,re-throw. Dealer is advised to stand when theprobability of winning is over 50 per cent.Liar diceThis game is played with a set of poker diceby any number of players. All pla? ers throwthe dice, and the highest hand becomes firstshooter. Each player puts three betting unitsin front of him, and the shooter begins thegame by shaking the dice cup and turning itupside down in front of him, so that the diceremain hidden. The shooter looks at the dice,being careful not to allow the other players tosee them. He then announces a poker hand(see poker dice), including any odd die or dice.He might say, for example, 'three jacks, ace,line'. The hand announced might be the handactually thrown, or it might be higher or lower.The player on the shooter's left has the option°f accepting or declining the hand (by declin-lng, he is, in effect, calling the shooter a liar).'f he declines, the shooter must expose hishand. If his hand is as good as, or better than,he said it was, the doubter puts a betting unitlrito a central pool. If the shooter was lying,

he puts a betting unit into the pool, and paysone to the doubter, who now has four bettingunits before him. The doubter then takes thecup and dice and repeats the process, an-nouncing a hand to the player on his left.

If a player accepts the hand, he looks at thedice, and may then re-cast all the dice or putany number aside, re-casting the remainder.He may put all aside and re-cast none. At notime should he allow the other players to seeany dice. He then announces a hand to his left-hand player, which must be higher than thehand he accepted. If the first player had called'three jacks, ace, nine', and the second playerhad accepted, the second player might re-castone die only and announce 'three jacks, ace,queen'. The third player decides to accept ordecline according to his opinion of whetherthe first player lied or not.

When a player loses his three betting units,he retires, and the last player in takes the pool.A fresh game is then begun, with the playeron the left of the preceding shooter becomingshooter.

Liar dice is essentially a game of bluffing, butthe good player should know that the 'average'hand is a pair of aces. A player accepting apair of aces or below has an even chance ofbeating the hand even if the previous playerwere lying. Accepting a straight is dangerous.A player accepting a low straight (K-Q-J-10-9)might re-cast one die and announce 'highstraight', but he has only one chance in six ofachieving it, and is certain to be called liar.He might re-throw none and announce 'highstraight', implying that the previous playerhad undercalled his hand. Undercalling canbe seen as a nice ploy whereby a player canset a trap for the player next but one to play.

DominoesAll games can be played for money, anddominoes is one of the largest family of games.The most common domino set is that of 28bones, using all numbers from one to six, butin theory there is no limit to the number in a

Figure 6:7, a set of pokerdice. These dice can be usedfor various games,including liar dice, bywhich they aresometimes known.

185

G A M H S O F S K I L L .

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set, and sets are commonly used in whichdouble-9 and double-12 are the highest.

One of the best games, matador, is describedas an example of domino games. It is bestplayed by two players, alternately being firstplayer. The dominoes are placed face downand shuffled, and each player draws seven, theremainder forming the bone-yard. The firstplayer lays a domino, and the second playercan play to either end a matching domino. Adomino matches if the matching ends total7. The second domino is laid as in Figure 6:8.Four dominoes are wild: 6-1, 5-2, 4-3 anddouble-blank, and these can be played at anytime, with either end forming the match. Theyare known as matadors, and only a matadorcan be matched to an end which is a blank. Aplayer on his turn may draw as many dominoesas he wishes from the bone-yard, and if hecannot go must draw unti l he can. However,the last domino must be left in the bone-yard,and a player who then cannot go loses histurn.

The game begun in Figure 6:8 might looklike Figure 6:9 after each player has playedfive dominoes. This illustration shows how amatador and a double is played. At one end ofthe chain a 4 is needed to match, at the othera matador, since only a matador can beplayed to a blank end.

The game ends when a player runs out, i.e.plays all his dominoes, or neither player cango. Payment is made at an agreed amount perspot, or per ten spots, left in the hand. Adouble-blank held by the loser counts 25:other matadors 10. If neither player goes out.he with the lower total wins according to thedifference in totals.

SpoofThe simple game of spoof can be played byany number of players. It is best for two. andhas the beauty of requiring only six coins, andso can be played anywhere.

Each player draws from 0 to 3 coins from

Dominoes were a Chineseinvention, hut are nowuniversal. The commonestset is the 28-bone set, witha double-6 as the highestdomino, but there are othersets. Chinese sets have noblanks, but some otherdominoes are duplicated.The men in the photographare playing the draw game,the simplest and best-known of the many dominogames. Figure 6:8 above isan example of matchingdominoes at matador, andFigure 6: 9 shows a game ofmatador in progress.

187

P A R T S I X

Iff

Ancestors of modern chess,which dates from about the

fifteenth century, wereplayed hundreds of yearsbefore the birth of Christ.Many believe it to be finestof all games, anddesigners have reflectedthis opinion withbeautiful equipment.

his pocket in his closed fist. The first playerguesses the total number in both hands, whichmight be any of seven numbers between 0 and6. The second player then guesses, but mustguess a different number from the first. Thetwo hands are then shown. If a player guessesright, he wins a point, and the first player towin three points wins the game. Stakes are oneunit per game. Throughout the game, playerstake turns in guessing first.

Although it is a simple game, two playerswho play regularly can exercise skill andderive pleasure in trying to out-guess eachother. The second player to guess has anadvantage in being able to get an idea of thetotal from the first player's guess. Should thefirst player guess two, he cannot be holdingthree. Should he guess five he cannot be hold-

ing less than two. However, the first playermight deliberately forego his chance whenguessing first by just such a ploy, giving him-self the advantage on the next round. This isknown as spoofing, and there is satisfaction inspotting the spoof and winning.

Spoof is based on the very ancient game ofatep, in which a player guessed the totalnumber of fingers extended by his opponentand himself on one hand held behind the back.The game is also called the match game, as itis frequently played with matches. When morethan two play, the concept of spoofing is lessvaluable, and the game becomes one of pur£

arithmetical calculation for the later guessers.

Other games of skillPerhaps the three best intellectual (as oppose"

188


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to physical) games in the world are bridge,chess and 'go'. Certainly the first two havethe most extensive literature. As hundreds ofbooks have been published on aspects of each,it would be out of place and useless in thisbook to attempt to give hints to players whowish to bet on the outcomes of games.

Bridge is usually played for small stakes perPoint. It is a partnership game and must beplayed by pairs of more or less equal ability ifbetting is to be satisfactory. Big bets have beenWade on challenge matches, the most famousbeing two matches in the 1930s played by ElyCulbertson's team against teams of SidneyLenz and Hal Sims. Culbertson won both.On the former he gave odds of 5-1, S6,000i . *—

being at stake, and the match received tre-iiendous publicity.

Chess is not normally associated withgambling. It is a game of pure skill for twoplayers, in which the better player's supremacyshould triumph in a relatively short series ofgames. Handicaps have been invented, buttend to alter the nature of the game. Never-theless, betting does take place, Ivan theTerrible being said to have gambled hugeamounts on his skill.

'Go" is the principle game of the Far East,being invented in China, where it is known aswei-ch'i, and becoming the national game ofJapan. It is played on a board which consistsof a grid of 19 horizontal and 19 vertical lines,the points of play being not the spaces but the361 points of intersection of the lines. Each ofthe two players has circular stones (181 forblack and 180 for white) and they alternately

Open air chess in America.Chess has so far escapedheavy gambling, but manvbets were struck on theFischer-Spasskv worldchampionship match.

189

P A R T S I X

place a stone on one of the points. Opposingstones can be captured by surrounding them,but the object is to acquire territory by com-pletely enclosing vacant points. The game hasrecently attracted serious players in the West.It is as subtle as chess, and requires as muchstudy to become a top player. In Japan andKorea there are professional players, and onemust serve an apprenticeship to join theirranks. All players have a grade, similar to thedan grades in judo, and not unlike the handi-cap classifications which golfers have. Thereis a system of handicapping based on thesegrades, which is more satisfactory than thehandicapping system used in golf or chess.Players of unequal ability can thus play eachother, and a good deal of gambling takes place.There have been crazes in the West for theOriental game of mah jong and more recentlybackgammon, both inferior games to go, andgo will doubtless one day enjoy a similarboom.

Mah jong is a name trade-marked in 1920for a Western version of a game played inChina under various names. It enjoyed a boomin the 1920s as great as the passion for back-gammon in the 1970s. The Western gameattempted to incorporate most of the varia-tions found in many local versions of the gamein China, and the proliferation of hands andcomplicated scoring made the whole th ing toocomplex. The game is for four players, whobuild sets and attempt to go out in a mannersimilar to that in the card game rummy. Thereare no universally accepted rules. A modernset might consist of 136 tiles, of which 108are in suits (bamboos, characters and circles)and the other 28 are honours (east, south.west and north winds, and red. green andwhite dragons). Some sets include eight addi-tional tiles called flowers or seasons. The localChinese games are simpler than the Westernversions, and much bett ing takes place onthem.

Whist is a simple card game of the trick-making sort, which offers scope for a con-siderable degree of skill . It is a medium formild gambling through the populari ty ofwhist drives, which are games played by anumber of people in local halls l ike theWomen's Insti tute, usually to raise funds forgood causes. It is a partnership game for four190

ïVitlLSI».

G A M E S OF S K I L L

M ah jong is a Westernname for a game playedin different ways in China.The appeal of the manykinds of tiles led to someinterest in the West, but itnever achieved thepopularity it enjoys inChina. It is similar inprinciple to the card gamerummy, and is a medium ofgambling in the East. TheseWestern players have somestakes riding on the result.

191

P A R T S I X

Snooker, billiards and poolbelong to the same familyof games, in whichside-bets are usually madeby the players. ThisAmerican player is sittingon a pool table whileawaiting his turn at snookeron the adjoining table.

players. In whist drives, games take placesimultaneously on a number of tables, partner-ships changing by rotation after each deal.Each player carries a 'travelling' score-card,and there are usually prizes at the end for thebest score and the worst (the booby prize).Despite the modest value of the prizes, whichmakes a drive more a social than a gamblingoccasion, addicts take the play very seriously,and woe betide a player who disobeys a con-vention which requires a certain card to beled from a particular holding, or plays lowwhen he should have played high.

Draughts, or checkers in America, is an oldgame which has had a literature since 1756,and which recently has attracted more andmore attention from serious games players. Itis played on a 64-square board, like a chess

board, by two players with twelve men each,the object being to capture all the opponent'smen. It is not as complex as chess, and inmany languages has been given a name whichtranslated means 'a game for ladies'. It is agame of pure skill, however, in which theexpert will nearly always beat the beginner.Betting is restricted to the result, but gamesfor small stakes are often played, sometimesin the open air outside cafes in Europe andAmerica.

Other games on which betting takes placeare games of physical skill such as snooker,billiards, pool or darts. Games are frequentlyplayed in clubs or bars for stakes which mightbe as small as a drink. Betting is not essential-but most players find that a small stake addsspice to the game.

192

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Some famous casinos

193

P A R T S E V E N

'égal casinos are to be found in mostcountries of the world, and many illegalcasinos thrive in the remainder. The oldestcasino still operating is probably that atBaden-Baden in West Germany, where casinogambling has been taking place for 200 years,though not continuously. Some of the newestsprang up in Great Britain after the GamingActs of the 1960s, which made Great Britainone of the most important gambling centresof the world.

However, when the world's casinos arediscussed, pride of place must go to MonteCarlo, the most famous and aristocratic ofthem all, closely followed by the complex ofcasinos in Nevada, centred on Las Vegas.Las Vegas has in a comparatively short timebecome a town synonymous with gambling,where, in typical American fashion, all thosequalities and vices which have come to beassociated with gambling - wealth, poverty,avarice, vulgarity and corruption - can be seento a degree.

A casino was built in Monaco in 1856, onthe initiative of Prince Florestan I, who badlyneeded to attract capital to the principality.It was a failure, as the bad roads and irregularboat service were deterrents to visitors. Mostof Monaco was annexed by France in 1861,which was a blessing in disguise, as the French

agreed to build a railway line between Niceand Monaco. Building began on the presentcasino in 1863, and Prince Charles III, afterwhom Monte Carlo was named, invitedFrançois Blanc, the very successful director ofthe casino at Homburg, to run his new casino.François Blanc was a financial genius whosegains were not always legally obtained. He andhis brother Louis had served prison sentencesfor fraud before making a success of thecasino at Homburg, where Louis died. Fran-

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F A M O U S C A S I N O S

J

Opposite above: theKurhaus, Baden-Baden.The impressiveness of theexterior is overshadowedby the magnificence of thespacious gaming roomsinside. Below: the last davsof rouge et noir at Baden-Baden in 1872, when thegovernment closed gaminghouses. Baden-Baden wasallowed to re-open 61 yearslater. Left: this photographis claimed to be the firstever taken of a group inplay in a Continentalcasino. The game is chemindefer in the main salonat Monte Carlo, 1870.

Overleaf: the casino atMonte Carlo, the mostfamous of all. For fiftyyears after its opening in1863, its fame grew as theworld's kings and princeswent to gamble andsocialise with the merelyrich and famous. Nowadaysthe casino itself has beensurpassed in style andelegance, but its nameremains supreme.

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Gambling at Monte Carloin the naughty nineties.The happy couple below areleaving the tables with theirwinnings. The engraving

from the painting by JeanBeraud, right, shows acommon scene as rows ofstanding gamblers andwould-be gamblers crowdbehind those seatedat the gaming tables.

cois offered 1,700,000 francs for the MonteCarlo casino, an offer which the nearly bank-rupt Prince Charles could not refuse.

François Blanc was an astute business man,and used to advantage the opportunities hewas given. Casinos were illegal in France, andBlanc financed a successful movement againstthe proposed new casinos in Italy. With nolocal competition, Blanc advertised his casinoin the prospering French resorts of Nice andCannes, and when the new railway wasfinished in 1868 the trickle of visitors toMonte Carlo became a steady stream.

The company Blanc formed to run thecasino was named the Société des Bains deMer et Cercle des Etrangers - the Sea BathingSociety and Circle of Foreigners. The last partof the name referred to the ban on locals from

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Eisa Maxwell, the famousparty-giver and socialite,was invited in the 1920sto lend her considerabletalents to re-building thereputation of Monte Carloas the playground of therich, a reputationinterrupted bv theFirst World War.

Previous page : thesplendour of the bestEuropean casinos. MonteCarlo and Germany set thestyle for luxurious interiors,and casinos in France,legalise din 1907,maintained the tradition.202


gambling in the casino. Blanc's Homburgcasino had met criticism because by taking themoney of the townspeople it was creatingmore hardship than prosperity.

The casino's growing success caused envyin the French resorts, but Blanc was good atpublic relations, and knew that money spentwith French newspapers would ensure goodreports of his enterprise. Nobody has donemore to make Monaco what it is to-day. Hebuilt hotels, imported soil to the barren rockfor gardens and used the casino profits toimprove the public services in all the ways hecould. Much publicity was given by his rivalsto the evils of gambling. Blanc arranged thatsuicides, if found first by casino staff, wouldhave their pockets filled with money toprevent stories of ruined gamblers killing

themselves. He was very generous to gam-blers who lost all their money but not theirlives, giving them funds to return home.Although the stories of money being planted°n corpses became widespread, it was lesswell-known that poisons and fire-arms werenot allowed to be sold in Monaco, and thathotel detectives searched visitors' baggagefor guns and ammunition.

Monte Carlo rapidly built itself around thecasino, and practically incorporated Monaco'tself. When the Prince of Wales, later to be-come King Edward VII, began in 1870 aseries of visits to Monte Carlo, the principality

became a centre of fashionable society. Fora number of years the Royal yacht Britanniawas to be seen in the harbour, and the AgaKhan, most of the crowned heads of Europe,and American millionaires like W. K. Vander-bilt and J. P. Morgan were to be found at thetables or in the Grand Hotel, where CésarRitz presided and Auguste Escoffier lookedafter the kitchens. Blanc died in 1877, andfor nearly fifty years afterwards his sonCamille maintained the elegance and prestigeof Monte Carlo, despite competition from thegreat French casinos, legalised in 1907.

Camille Blanc died in 1927, having just lostcontrol of the casino to Basil Zaharoff, thearms king, who saw ownership of the casinoas a means of ousting the Royal family andputting his intended bride, the Duchess of

Overleaf: 'Vegas Vie', thetrademark of the LuxVegas Chamber ofCommerce, stands outfrom the other neon signswhich make Las Vegas atnight a blaminginvitation to gamble.

Famous faces at MonteCarlo. The late Aga Khan(smaller picture) wasfrequently seen at thetables and race courses ofEurope. He gambledagainst the GreekSyndicate. AristotleOnassis gained control ofthe casino in the 1960s,and his yacht was usuallyin the harbour. Thegovernment created newshares to reduce his powerin 1966 and he sold theshares he owned.

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Villafranca, on the throne. However, theDuchess died in 1926, and Zaharoff sold hisinterest to a syndicate led by Dreyfus, thebanking company. The casino declined withthe end of the Blanc era. The Blancs builtMonte Carlo, and it is the golden years oftheir reign rather than its present attractionson which the glamorous reputation of theMonte Carlo casino rests.

In the 1920s, Prince Pierre invited EisaMaxwell, the socialite and party giver, tocome to Monte Carlo and help revive itsfading splendour. The Sporting Club, asummer casino, was built, and the wealthyreturned in greater numbers, film stars, states-men and industrialists rubbing shoulders withkings, princes and maharajahs. Monte Carlowas by now a complex of casinos and hotels.It was successful, but it was not the old MonteCarlo.

Business continued during the war, butprofits took a sharp drop in the austere yearsafterwards, when many countries limited theamount of currency which could be takenabroad. By 1953, the casinos were withstand-ing heavy losses, but Aristotle Onassis, theimmensely wealthy ship-owner, bought acontrolling interest in the Société des Bainsand set about the task of restoring the profits.Prince Rainier II, who had succeeded to thethrone, married Grace Kelly, the film actress,in 1956, and the world's newspapers treatedthe romance of prince and showgirl as a storywhich no reader would want to miss. Nearly2,000 reporters and photographers at thewedding kept Monte Carlo in the headlinesat a time when returning affluence meant thatpublicity would have a maximum effect onthe fortunes of the principality. Once again ayacht, Onassis' Christina, was frequently inthe harbour and in the news, as Maria Callas,the celebrated opera singer, and WinstonChurchill became guests aboard. But theimpetus again waned, and Prince Rainier wasforced to create new shares in the Society forthe government, so that development couldcontinue under government control. Onassissold out to the state, and the popularising ofthe resort begun by Eisa Maxwell was in-creased. A new Monte Carlo Sporting Clubwas opened on land reclaimed from the sea,and the whole complex now resembles its206


Nevada became thegambling state of Americawhen legal organizedgambling was resumed therein 1931. Other states haveallowed legal gaming in thepast, such as Arizona,California and Louisiana.No laws will preventgambling. These oldmen were gamblingin large sums in anAmerican bar in 1913.

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The down-town FremonlStreet area of Lax Vegas,known as Glitter Gulch.The conversion of LasVegas from a desolatedesert town to a glitteringgambling resort was begunby gangster Bugsy Siegel,who built the fabulousFlamingo in 1946.

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French rivals. The majesty and exclusivenesshave departed, and the fight is now on for thespending money of the middle-class holidaymaker.

Inevitably the casino has become a touristattraction, and nowadays the visitor mustPay to enter. Some of the old aura can befound in the salles privées, where big-stakegambling on baccarat, roulette and cheminde fer takes place in relative luxury and quiet.In the salles ordinaires, known collectively as

I the kitchen, are two salons, the Salon de''Europe, in which are found the trente etQuarante tables among the European games,and the Salon des Amériques, where Americanvisitors can play craps, introduced in 1949.'he craps tables offer prohibitive odds,

and are spurned by self-respecting gam-Wers. Visitors can play blackjack and boule,

I I and, perhaps the biggest indication of the way

cheapness has overcome grandeur, there is theultimate Nevada horror - a slot machinealley.

The phenomenon of the gambling empirein the Nevada desert is of recent origin. WhileFrançois Blanc was an opportunist whostooped to fraud, the man who began theLas Vegas boom was a gangster of the firstrank, Benjamin 'Bugsy' Siegel. Siegel servedan apprenticeship in crime, having his owngang by the time he was 14 years old. When20 he formed with Meyer Lansky the gangknown as the Bug and Meyer mob. They weremurderers by contract for such hoodlums asAl Capone and Johnny Torrio. Siegel andLansky joined the board of directors of thegroup known as the Combination, whichincluded Capone, Torrio, Lucky Luciano,Frank Costello and other gangsters whosenames are as infamous. Siegel was different

A gambling entrepreneurin life and death. Thephotograph of Benjamin'Bugsy' Siegel in his nrimedoes not do justice to hishandsome appearance. Heused the methods of agangster and the money ofthe mob to build his casino.

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77;e Mississippi steam-boats provided easypickings for professionalgamblers, both honest anddishonest, who weresometimes in collusion withthe officers. The photographshows the steamboat 'Cityof Louisville' in the 1880s,and the illustrations showthe gamblers at work froma book 'Forty Years aGambler on the Mississippi'by George Devol,published in 1887.

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from the others, not in ruthlessness but inlooks. He was as handsome as a film star, andmore vain than most. Silk monogrammedshirts, hand-made shoes and sharp suitscontributed to his film-star image, and in1937 he was sent by the board to organisetheir criminal activities in California. Bugsyhad paid many visits to Hollywood, andalready counted a number of stars as hisfriends, including the screen vamp JeanHarlow, whom he pursued. Now he was in hiselement, organising the mobs and mixingwith the Beverly Hills social elite. With drugs,Prostitution and bookmaking rackets bring-ing in a fortune for himself and the Combina-tion, Bugsy turned his attention to Las Vegas

his share in a fleet of gambling ships

operating off the Californian coast was madeworthless by state legislation. Gambling hadbeen legal in Nevada since 1931, but fewventured into the desert to play the crapstables and slot machines. Bugsy reasoned thatif gamblers were prepared to go three milesout to sea to gamble, they would brave thedesert if the facilities were attractive enough.He had a vision of himself as the gamblingking of America, and in 1946 set out for LasVegas and began to build the fabulousFlamingo Hotel. The cost reached $6 million,partly due to Bugsy having to pay heavilyon the black market for materials. Whilebuilding was in progress, Bugsy fell out withthe mob. Capone acquired the ContinentalPress Service, which provided a service to

Howard Hughes withGinger Rogers during hisyears as a film magnate inHollvwood. In the late1960s Hughes boughtcontrolling interests inseveral casinos in IMSVegas and Reno, but wasreluctant to meet the state'sgaming authorities and lostinterest in developingfurther the gambling city.

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A roulette wheel doing nobusiness at the HotelSahara, Las Vegas. A'carpet joint', the Saharahas an expensive decorwhich lacks the elegantintimacy of the bestEuropean salons.

The dealer at the crapstable at Harold's Club,Reno, is dressed tocorrespond with theWestern motif of the club.

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bookmakers, and wanted to close the rivalTrans-America Wire Service which Bugsyhad set up for the Combination. Bugsyneeded the revenue from Trans-America forhis operations and at a meeting of directors ofthe Combination demanded $2 million toclose it. The mob would not brook independ-ence, and from then on Bugsy's days werenumbered.

On Boxing Day, 1946, the casino part ofthe Flamingo opened. After losing $100,000in the first fortnight, it closed again. Bugsydecided to re-open when the hotel itselfwas finished. Meanwhile bookmakers wereobjecting bitterly at having to pay Caponeand Siegel for both the wire services. Siegelfell out with Lucky Luciano, who asked whenthe Combination's investment of $3 millionin the Flamingo would pay dividends. TheFlamingo re-opened in March 1947, and ina month or two profits began to roll in. Buton June 20, Bugsy, who claimed to havekilled 12 men, was himself the victim of themob. While sitting on a sofa in the BeverlyHills mansion of his girl friend, Virginia Hill,he was hit by four slugs fired through a windowby a hired killer. Spattered with blood, he laywith a message pinned to his newspaper,'Good night. Sleep peacefully with the com-pliments of Jack's'. Jack was never found.

While the police were arriving at the scene,the Flamingo was being quietly taken over byGus Greenbaum, Siegel's old friend andfellow-hood. He made $4 million profit in thefirst year. Eventually he, too, displeased themob, and ended with his throat cut, but bythen modern Las Vegas was on its way.

Most of the casinos which followed theFlamingo were owned and controlled bygangsters. The Desert Inn was the secondlargest casino-hotel to open. It began opera-tions in 1950, and was followed in 1952 by theSands and the Sahara. These are luxuryestablishments on the Strip, the Las Vegasmain highway, and have been joined by,among others, the Tropicana, Riviera, Thun-derbird, Stardust, Caesar's Palace and Dunes.They are known as 'carpet joints'. At thepoorer end of Las Vegas are the 'sawdustjoints', noisy, less elaborate casinos withnames like Golden Nugget, Horseshoe, LuckyStrike, Monte Carlo and Jackpot.

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Gambling in films.Opposite: Peter Sellersand Orson Welles faceeach other across thebaccarat table in 'CasinoRoyale'. Above: WalterHuston tries to restrain thegreed of Gregory Peck ashe wins a vast sum ofmoney at the roulette tablein The Great Sinner(1947). Left: MarleneDietrich in a morerestrained scene as sheplays chemin defer in'The Monte Carlo Story.'

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Alfred d'Orsay throwing amain at Crockford's Club,London, in the nineteenthcentury. The game ishazard, the forerunner ofcraps. The caster firstestablished a main point(5, 6, 7, 8, 9), then achance point (4, 5, 6, 7, 8,9, 10). If he duplicated hischance point first he won,his main point first, he lost.216


The gangland killings, together with briberyof police and officials, continued, and wereexposed to all in 1957 when Mafia chiefFrank Costello was shot in the foyer of anapartment house in New York. Detectivesfound in his pocket a summary of accountsof the Tropicana. The Nevada Gaming Con-trol Board was forced to tidy up the owner-ship of the Tropicana, but this event was ahiccup in the smooth control that ganglandheld over the casinos.

In the late 1960s the multi-millionaireHoward Hughes began buying control ofseveral of the Las Vegas casinos, and he wasfollowed by conglomerate businesses such asthe Hilton Hotels group and M.G.M. Manyof the casinos are now just one interest ofmulti-part concerns dealing in real estate,restaurants, building and so on.

The casinos on the Strip offer round-the-clock gambling at blackjack, craps, roulette,baccarat and keno, with countless slot mach-ines ready for the loose change. The complexprovides everything the visitor needs, fromgolf to swimming pools. Expensive but vulgarcabarets keep the customers amused. FrankSinatra, a former casino owner, Tom Jones,Barbra Streisand and Liberace are amongthe entertainers to appear on the Strip. Top-

Hogarth 's gaming housescene from his eighteenthcentury series 'The Rake'aProgress'. The atmosphereis oj dissolution, with therake ranting at his losseswhile other gamblers gloat.The setting was a well-known gambling den inCovent Garden.

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Brooks's Club in StJames's Street, London,was the scene of someheavy gambling by itsaristocratic members of theeighteenth and nineteenthcenturies. This painting byThomas Roniandson showscard games beingplayed in the GreatSubscription Room.

line boxing matches have been held in Caesar'sPalace; in the Circus-Circus trapeze acts andhuman cannonballs are part of the show.But these are the trimmings, the publicrelations, the advertising designed to givethe impression that sophisticated entertain-ment is provided for holiday-makers.

In fact, everything is secondary to gambling,and a man is as important as the size of hisbets. In the cocoon of the artificially-lit casino,the gambler will see no windows or clocks. Hecan enter the casino at whatever hour he likesand find the same artificial atmosphere. Thehooked gambler does not seek variety. He iscontent to spend hour after hour courtingLady Luck, and the Strip casinos cater for him.

The sawdust joints centred on FreemontStreet comprise the most dense area ofgambling opportunities in the world. Knownas 'Glitter Gulch' the area lacks the luxury ofthe Strip, and unashamedly gets down tobusiness. Elaborate neon signs lure the gam-blers inside the casinos, where there are no

distractions to compete with the tables, sidegames and thousands of slot machines. Thestakes are lower in Glitter Gulch, and herethe locals, the less wealthy, the players downto their last few dollars and the addicts ekingout their resources accumulate. Here slot-machine players can be seen operating fourmachines at once, perhaps wearing a gloveto prevent blisters on the hand, becomingalmost as automatic in their movements as themachines they feed.

To the north of Las Vegas are two otherNevadan gambling centres. At the holidayresort of Lake Tahoe are casinos which includethe large and rich Harrahs, one of the biggestmoney-spinners in Nevada. In the town ofReno, famous for Hollywood divorces, is acomplex of casinos dominated by HaroldsClub. While the gambling activities in thesetowns are not as obtrusive as at Glitter Gulch,where the casinos are back to back, gamblingis by far the biggest industry.

Around 20 million visitors go to Nevada

218


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The stately buildings whichhoused exclusive gamblingclubs of the eighteenthcentury, Brooks's Club and,inset, Arthur's Club. It wasat Brooks's that BeauBrummell was said to havewon a fortune when hebeat a brewer 25 timesrunning at hazard. 7 shallnever drink any porter butyours' he told him, andreceived the reply 7 wishevery blackguard in Londonwould tell me the same'.

i. ARTHUR'S CLUB. 2. BROOKS'S CLUB.

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annually to gamble. Few leave with morethan they brought and many leave withnothing. Some of those who lose stay,and many ex-convicts and down-and-outsgravitate to the towns where money changeshands quicker than anywhere else. Nevadahas the highest crime rate of all the states ofAmerica, and more policemen per head thanany other. The suicide rate in Las Vegas ishigher than that of any other city in the world.In this city of crime there is only one sin - thatof being without money.

The example of Las Vegas led othercountries to be wary when legalising gambling.The Betting and Gaming Act of 1960 led toa boom in British casino gambling, but thiswas carefully regulated through additionalActs of Parliament and the setting up of theGaming Board in 1968. Only through theselimitations could the Home Secretary besatisfied that gangsterism and tax evasionin gambling were being brought under control.In Britain casinos must be licensed as clubs,with gaming restricted to members and theirguests. Applicants to join clubs cannot beissued membership cards immediately, butmust wait two days for acceptance. Adver-tising for members is not permitted, and whiledrinks may be served, licensing hours must beobserved, and eating and drinking is kept

The Playboy Club openedin Park Lane, London, in1966. It caters for the'middle ' class of gamblers,like young executives, whocan eat a subsidised mealthere before playing at thetables. It is also popularwith foreign visitorsto the capital.

Opposite: One of London'snewer gambling clubs, theLadbroke Club. Ladbroke'sare an old establishedbookmaking companywhich since the Britishgaming acts of the 1960shas enlarged its scope toinclude betting shops andgambling casinos.

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The casinos at Deuuviiic,above, and Biarritz,opposite. As theirarchitecture suggests, thesecasinos belong to the charmof an earlier age. Togamble in the quietness oftheir palatial but fadedrooms is to exchange therush and vulgarity ofmuch modern gambling fora gentler, more leisurelyway of losing money.

separate from the gambling. The guidingprinciple is that gambling is provided forthose who must, but casinos must not attemptto attract custom.

The Gaming Board must examine thecredentials of a club applying for a gaminglicence, and be satisfied about the integrityand financial status of the applicant, beforeissuing a 'certificate of consent'. The locallicensing authority then has to approve thepremises and seek the opinions of localresidents and the police on the desirabilityof and demand for a gaming club. Licences aregranted on an area basis, so that gaming isreasonably accessible to the whole community,without there being a concentration of casinosin any locality. Therefore, whereas Britainmight be regarded in its entirety as a dilutedisland Las Vegas, it is impossible for a smallgambling centre within it to be built.

London, of course, has the most casinos,

some under joint ownership. The CurzonHouse group operates the Palm Beach Clubin Mayfair, and Crockford's, a new club usingan old name in British gambling. The Meccagroup, as well as having large investments inbingo, own among other casinos the GoldenNugget, a Soho club using a Las Vegas name.The Playboy Club has bunny girls to. take itsmembers' coats, and its modest minimumstakes at the tables allow young middle-classgamblers to bet shoulder-to-shoulder with itsricher cosmopolitan clientele. The Playboygroup own the more exclusive ClermontClub, where Lord Lucan played backgammonbefore his notorious disappearance.

While the London casinos offer a widerange in comfort and in the amounts that canbe staked, most are housed in buildings notdesigned as casinos, and generally are not asspacious or plush as casinos on the Las Vega5

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The casino at Estoril inPortugal looks modern and

functional, and if gambling,like convenience foods,could be plastic-wrapped,that would be the Estorilstyle. It is modelled onLas Vegas and includessome of the Americancasino side-games.

are forbidden, although muzak is ever-presentin many. The casinos in the provinces are oftenquite seedy, being housed perhaps in olddance halls. The segregation of live entertain-ment and gambling is a problem to casinoowners outside London, and particularly inthe north, where in the 1960s the gaming tableswere side attractions to the cabaret and danc-ing. The 1970 Act forced the operators tomove the gaming into separate premises whereit is less popular, and casino turnover outsideLondon is considerably smaller than that inthe capital.

Most British casinos contain roulette andblackjack tables; baccarat can be played atthe more exclusive ones, punto banco isincreasing in popularity, and craps, whilestill not popular with most British gamblers,is available at least in those casinos likely to bepatronised by American visitors. The various

Gaming Acts have been concerned withguaranteeing the punter a square deal, whichhas led to some strange legislation, but whichhas had the merit of eliminating the moreoutrageous sucker bets to be found in LasVegas and recently in Monte Carlo. In acomparatively short time, considering theassociations which gambling has always hadwith the criminal classes, modern Britishlegislation has done much to ensure thatcasinos are well-run and reputable. ScotlandYard and the Churches Council on Gamblinghave expressed satisfaction with the operationof the law and if the atmosphere is a littleclinical compared with the razzmatazz ofLas Vegas, the dedicated gambler will notmind that.

The Palace casino in Douglas, Isle of Man.just off the English coast, enjoys a curiousadvantage over mainland casinos. As the

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Roulette on a single-endedfrench table in the casinoof the Grand Hotel,Rhodes. The decor containsnothing extraneous ordistracting, and thecustomers can settle tosome straightforwardsimple gambling.

P A R T S E V E N

Iron curtain countriesgenerally frown ongambling although mostallow casinos, and lotterieswhich raise funds for thestate and in which theprizes are frequentlycommodities. Roulette ispopular. These players arein the Mamaia MelodyBar in Romania.

Isle of Man is outside the legislation ofWestminster in local matters, the casino isnot inhibited by British gaming laws. It isinteresting that it compares unfavourablywith British casinos. Some of the roulettewheels have single zeros, some double. Pon-toon is played alongside blackjack. Pontoonis primarily a private gambling game with abig advantage to the banker. It is not playedin any other casino, and the main differencebetween blackjack and pontoon, that thedealer wins all ties, ensures a substantialhouse edge for the Palace casino.

Casino gambling on the Continent, as inBritain, has sometimes been allowed, some-times banned. In France, public casinos havebeen legal since 1907, and the best are amongthe most stylish in the world. Casino complexesmust offer entertainment and dining of a high

standard before being granted the right ofgaming. The games to be found are baccaratand chemin de fer, roulette, trente et quarante,blackjack, boule and vingt-trois. Recentlycraps has been introduced. French casinosare the best regulated in the world, beingalways under the supervision of inspectors ofthe Ministry of the Interior. Over half thereceipts, which are counted in public, aretaken by state and local taxes, an arrange-ment very satisfactory to the citizens ofCannes, for instance, the biggest gamblingcentre with three casinos.

Although inflation has meant that theprofits of the casinos increase, the golden ageof French casino gambling was in the 1920s,before roulette was allowed, but when Fran-çois André was running the magnificentcasino at Deauville and Nico Zographos wasplaying the world's biggest gamblers at bac-carat for unlimited stakes. The traditions ofelegant gambling are continued in manyFrench casinos by André's nephew, LucienBarrière, who has holdings in casinos at bothCannes and Deauville. The Deauville complex,with its large restaurant, golf course, cinemaand theatre, has the height of its season inAugust, when the race-course provides first-class sport.

Other splendid casinos with an illustrioushistory are to be found at Biarritz and Aix-les-Bains, and there is a large casino atDivonne-les-Bains, near the Swiss border.In the old palatial casinos, the gambling takesplace in a sedate atmosphere, as if it were apastime for those of discernment and taste.Entrance fees are minimal, but all casinos havea list of interdits, people who are barred fromFrench casinos. The professional physio-gnomists, who stand at the doors with thefaces and physical characteristics of thousandsof interdits imprinted in their minds, arejustly famous.

Not all French casinos are on the grandscale. Of the 150 or so currently operating,many are in new or converted buildings atseaside resorts with no pretensions to class.But the selective gambler can find the mostcivilised and aesthetically satisfying gamingin France.

West German resorts contain some of themost beautiful casinos in the world, including

226


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There are gambling casinosin the Bulgarian holidavresorts on the Black Sea.The decor and atmospheredo not suggest thebattleground of kings andtycoons, which might bethought too capitalistic, butrather a genteel workingman's club. This is theGoldstrand casino.

Overleaf: the entrance tothe casino at Ai\-les-Bains,once owned by thelegendary Francois André,but not now part of theempire ruled by hisnephew Lucien Barrière.The gambling between thewars at the great Frenchcasinos, like André 'sDeauville and Aix-les-Bains, had a stvle thatowed something to theinnocence of the world, tothe rich and famous menwho enjoyed gambling andto the palatial casinos.

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that at Baden-Baden, perhaps the most elegantof all. Like Deauville, Baden-Baden has arace-course, where around Christmas the besthorse-racing Germany can offer takes place.The fine restaurants and other places ofrecreation to be found at a health resortcannot compete with the magnificance of theornate casino, in which roulette, baccaratand blackjack are the principal games. Dostoe-vsky gambled at the German casinos, andbased Roulettenburg, the setting of his novelThe Gambler, on Wiesbaden.

European countries outside Germany andFrance have fewer casinos, and they tend tobe more functional and less redolent of a moreleisurely and stylish age. The Cercle Privé inVienna is in the Palais Esterhazy, and has anold-world charm of its own. Italians gamble atSan Remo, Venice and St. Vincent, where ScanConnery brought off a notable coup. Thelarger Belgian resorts have casinos, the biggestbeing at Ostend, where the games are limited tochemin de fer and roulette, which is playedwithout a zero, the house deducting a six percent commission from winning bets. There area number of casinos in Portugal, the largest andmost vulgar being at Estoril, which is deliber-ately designed to attract American gamblers byoffering them the traditional games found inNevada. Spain does not permit casino gam-bling. The small island of Malta has one ofthe pleasantest casinos, in a palatial buildingat St. Julian's, where French and Americanroulette, chemin de fer, blackjack and boulecan be played.

In most iron curtain countries privategambling is forbidden, but casinos are foundin Romania, Yugoslavia, Bulgaria andCzechoslovakia. Nearby Greece allows casinobetting as do Morocco, Tunisia and Egyptacross the Mediterranean. Other Africancountries have casinos and those near SouthAfrica provide facilities for rich South Afri-cans, who have no casinos in their owncountry. Most Arab countries do not permitgambling and rich oilmen go elsewhere fortheir casino gaming.

China itself does not allow casinos, but thelavish gambling centre which has grown upon the Portuguese island colony of Macaohas many attractions for Chinese gamblersfrom nearby Hong Kong.230

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There are three casinos onthe tiny Portuguese islandof Macao. They attract bigbusiness from neighbouringstates, particularly theBritish colony of HongKong, where there are nolegal casinos. This is theHotel Lisboa casino,offering a variety ofEuropean-style gambling.

Australian gambling, like that in the UnitedStates, is controlled on a state-by-state basis.The first legal casino was opened in 1973 nearHobart in Tasmania, and has been a success.A hotel-casino complex, it is well-run accord-ing to strict legislation, which is enforced bygovernment agents. The state takes a share ofthe profits. The games offered are the usualones of French and American roulette, black-jack, pun to banco and craps. There is also acasino version of the popular Australiangame of two-up, described elsewhere. Thereis not a rush to Tasmania to gamble, as mostlarge cities in Australia contain illegal casinos,of varying luxury and fairness. These casinos,while risking occasional police raids, are moreor less tolerated by the state.

One of the world's largest casinos is in theMar del Plata, in Argentina, and the largerand richer South American countries permit

casino gambling, with the notable exceptionof Brazil. Although Fidel Castro closed thebadly-run but flourishing casino industryin Cuba, many other islands in the Caribbeanarea permit gaming, the casinos often beingrun in conjunction with hotels to attract theholiday-makers from North America. Thelargest group of casinos is found in PuertoRico. They are subject to government rulesand inspection and bear no relation to theNevadan casinos. Betting is with casinochips only, the hours of opening are limited(usually from 8.30 p.m. to 3.30 a.m.), appli-cants for licences are strictly investigated, lowmaximum stakes are enforced, and althoughlight refreshments and beverages may beserved, alcoholic drinks are forbidden. Thegames played are American roulette, cheminde fer, craps and blackjack, although, sur-prisingly, there are no slot machines.

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White's Club in London,the scene of some of themost extraordinary betsever recorded. So keenwere the members onbetting that on one occasionwhen a man collapsedoutside the door and wasbrought in, many bets weresoon struck at various oddsthat he would die. It wasdecided that he should notbe treated, as this wouldaffect the bet, and so hedied and the winnerscollected. A similar storyhas been told of Las Vegas,but the first version has thebacking of Horace Walpole,who recorded it in a letter.

ambling addicts are never stuck for abet. There might be no games to hand, theremight be a shortage of money, but a way willbe found to satisfy the need for a wager.

Two moneyless Chinamen were reportedto have bet their ears on which side a fallingleaf would settle, and the loser paid up. Therewere numerous stories of wives being the stakein a gamble. An Indian prince lost not onlyhis wife, but his slaves as well. The biggeststake is put up in Russian roulette, when asingle bullet is put into a chamber of a pistol.The cylinder is spun, the pistol put to the headand the trigger pulled. Some say that the oddsagainst an 'unfavourable outcome' with asix-shooter are longer than 5-1 against, as thechamber holding the bullet, being heavierthan those empty, is more likely to stop at the

bottom of the cylinder, and not be fired.Whatever the house edge, it seems a poor bet.A better idea was that of two Eastern princeswho, instead of going to war, staked theirriches on a game of chess, on the groundsthat the better strategist would win at chessor war, and the spoils could be won withoutbloodshed.

Monarchs can be lavish with their bets.King Henry VIII lost the bells of St. Paul'sChurch in a game of dice. Robbers can beequally lavish. The famous English trainrobbers of 1963, when holed up in a remotefarmhouse, amused themselves by playingMonopoly with real money: with nearly £3million in the bank, who cares about landingon Mayfair, even with a hotel?

The worst thing said about inveterate

gamblers is that they would bet on flies walk-ing up a wall, or raindrops running down awindow. John Gates was fond of the latter.According to legend, he won over $20,000during a train journey in the rain by astuteselection of the fastest drops. The attractionsugar cubes hold for flies has inspired manybored gamblers to set up cubes of sugar andbet which will be first visited by a fly. Ship-mates on a tedious voyage in the Fernandelfilm The Sheep Has Five Legs, having ex-hausted cards and dice as a diversion, dis-covered a fly in the cabin and played thesugar cube game. Additional excitement wasprovided for all by the fly deciding to tourthe body of a partly dressed young lady,who was not permitted to move in case sheinfluenced the outcome.

The members of White's Club in the eight-eenth century were famous for their eccentricbets. A particularly aged member would belikely to have a number of bets resting on the

I date he would become an ex-member. Anj expectant girl might carry not only a child- but several wagers on the date it would appear.

If she were unmarried, opinions as to thefather would be backed up with cash. Betswere recorded in a book. The feelings of thesubjects of the bets were not recorded.

In more modern times, betting on generalelections has become big business in GreatBritain, with millions of pounds being stakedon the winners and the majority. Bookmakersare not slow to make books on one-off eventswhich catch the public's fancy. In 1966, whena number of jail-breaks were causing both

1 concern and amusement in Britain, the public1 could bet on how many prisoners would bej reported missing that day, with double odds: paid for naming the careless prison. WagersI were also struck on the names the Queen1 would choose for her children. This idea

spread to Chicago, where American gamblersfailed to select Charles for the first-born,unlike British gamblers who had a betterknowledge of the form.

Italians have been moved, when the Pope. dies, to bet on his successor. Not to be out-

done, the British bet on the new Archbishopof Canterbury in 1974. A bet of £7,000 to £350struck on a 20-1 outsider, the Bishop ofDurham, caused his odds to shorten over-

night to 5-1. It was a misplaced bet, as the2-1 favourite, the Archbishop of York,became the new Archbishop of Canterbury.Cardinal Montini was also favourite beforehis election as Pope in 1963, so the religiousformbook is reliable.

Cheating has received little attention in thisbook. Obviously gambling is particularlyattractive to cheats, with large sums of moneychanging hands on chance events. Anybodywho has watched in close-up a top-classconjuror performing sleight of hand willrealise that dice, coins, even cards, can beswitched by a smooth operator at will. Theonly precaution one can take against beingcheated is not to play for high stakes withstrangers and always to be on guard.

A hustler is a particular form of cheat whowins not by cheating in the event itself but byone of two more subtle means. If he is aplayer of a game of skill, he might deliber-ately falsify his form so that he brings off asurprise win when the big stakes are down.It is no reflection on the game of golf to statethat some players do not strive too hard toimprove their handicaps in games playedonly for fun. Paul Newman, in the film TheHustler, was a pool player who deliberatelyallowed other players to gain a false impres-sion of his ability.

This amusing engraving islabelled 'Lady gamblerfleeces male sucker inPullman comfort on train '.The game appears to bepoker and it looks as if thelady has four aces and themale sucker might havefour kings, in which casehe has everv reasonto look outraged.

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O D D I T I E S

Paul Newman playing poolin 'The Hustler. ' Newmanwas the perfect exampleof a gambling hustler, asuper player who lost oneor two games when thestakes were low and wonthe big ones by justenough : tactics designed topersuade suckers that theycould beat him. Thehighlight of the film was atense match with JackieG Season as MinnesotaFats, the local champion.

237

P A R T E I G H T

It has long been a customon sea voyages for the .passengers to have a stakein the distance the linertravels during the day.Sometimes this takes the

form of a sweepstake,sometimes, as in the caseillustrated, passengers beton the last figure of theship's daily run. Passengersseem to prefer the numbers5,6,7 and 8, although allhave an equal chance.Bookmakers in Britainhave in recent years takenlarge bets on generalelections. This board (farright) shows some of theodds being offered by theWilliam Hill Organisationon an election which theLabour Party were hot

favourites to win. Bets werestruck on the overallmajoritv: 21 to 70was expected.

The other form of hustler does not cheat atall. His angle is to know the true odds aboutcertain events and to entice other gamblersinto accepting disadvantageous bets. Thebest propositions are those where the victimhas a little knowledge of the theory ofprobability, but not enough. He might thinkhe has the better of the odds, and put hislosses down to bad luck. Most people know,for instance, that if two dice are rolled, thelikeliest number to be thrown is 7. If a hustlersuggests that he can throw a 6 and an 8 beforetwo 7s, the victim might reason that as 7 ismore probable than either 6 or 8, the hustlershould be invited to back up his statementwith money. A little knowledge is a dangerousthing. What is overlooked is that the hustlercan throw 6 and 8 in any order. The probabilityof throwing 6 or 8 is Having achieved either,the probability of throwing the other is ^.The probability of throwing 6 and 8 with twothrows is the product of these probabilities,

50 . The probability of throwing 7 is ,__36_36>T36'

36x36and of throwing two successively

The hustler will win the bet therefore 50 timesto his victim's 36, an edge to him of 16-2791per cent.

A good hustler will introduce his proposi-tion casually into the conversation. Aftera game of cards, he might stand two packsface down and speculate on his chances offinding two identical cards on the top of eachpile if he turned over the cards one at a timefrom the top of each. Pity the innocent whoreasons thus: for each card in pile A thechances are 51-1 against the identical card in

238

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In fact, converse probabilities must be usedin calculating the probability that there willbe a match. If there are two cards in each pile,the probability of no match is 1 divided by 2!If there are three cards the probability is

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The fraction at the end of the expressiongets smaller and smaller, so that after 7 termsthe fraction being added or subtracted doesnot alter the value of the whole expression ifit is required to only four places of decimals.The probability of no match is only 0-3679,and the hustler's edge will be 26-4242 per cent.

Looked at another way, the 'break-even'j point for rinding a match can be worked out, in the way described in Part Two for thei problem of the Chevalier de Mere. The break-| even point is

log 2Tog 52 - log 51 or alternatively 0-6931 x 51

The hustler will need 36 trials to give him-

self an even chance. As he has 52, he has aconsiderable advantage.

The above propositions give the hustleran edge. He is not guaranteed to win eachtime, but over a period the percentage willwork for him. Some hustlers will presentpropositions in which they are sure to win.Van Gogh is said in a music-hall joke to havebet a Parisian 100 francs that he could bite hisown ear. The bet being accepted, Van Goghtook his ear from his pocket and bit it. Whenhis victim offered for 200 francs to do the same,Van Gogh accepted the bet, whereat the Paris-ian took out his false teeth and bit his ear.

The game of drawing matches from a pileis one which the hustler reckons to win. Apile of matches, of a number known to bothplayers, is set on a table. Each player in turnremoves one, two, or three matches. Theplayer who takes the last match wins. Thehustler wins the game by making sure thathis victim draws his last matches from a pileof four; then, no matter how many he takes,the hustler takes the rest. He makes sure thevictim is left a pile of four by ensuring that hisprevious draw is from eight. So long as thevictim draws from a pile divisible by four, thehustler can ensure that each pile he drawsfrom subsequently is a multiple of four,guaranteeing the outcome. If the victim wantsto change the game so that the player whotakes the last match is the loser, the hustlerensures that the victim always draws from amultiple of four, plus an extra match. Nomatter what number the victim takes fromhis last pile of five matches, the hustler candraw enough to leave one match. An un-scrupulous hustler can have a box of matchesprepared, containing a given number, so thathe can tip them onto the table and win froma pile of an apparently unknown number.This will make it more difficult for the victimto work out afterwards how he was duped.

A card game uses the same principle. Oneplayer has all the red cards and another allthe black. The players lay a card in turn,adding their values together and keeping arunning total. Cards are valued at their pipcount, aces counting one and all court cardsten. A player who can make the total exactly31 wins. A player who raises the total above31 loses. Any card played can have another

239

The odds against the'runners' in the 1970 MissWorld contest in London.At William Hill'sBlackfriars office, MissSweden was a firmfavourite at 7—1. Favouriteshave a poor record in thisevent, suggesting that theaverage gamblers' opinionson the forms of women areas diverse as their views onthe form of race horses.

added to it to make 11 ; therefore the playerforced to play when the total is 20 will lose,unless his opponent has already been forced toplay a pair. For example, if a player has toplay when the total is 20, but has alreadyforced his opponent to play both his fours, hecan safely play seven and win. The object of thegame is therefore to reach 20 without using apair.

Alternatively, a player can allow his oppo-nent to make 20, provided that he has to usea pair to reach it. If a player can force hisopponent to play from nine, he can then forcehim to play from 20. Unfortunately, to do thishe can be forced himself to use a pair to reach20, when he will lose, unless he has alreadyforced his opponent to use a smaller pair.

The game is extremely complex, but thehustler who understands the principles canwin consistently while his victim is graspingthe knack, and he has one certainty to fallback upon: when he goes first he can be sureof winning. He must play nine, and make thescore 20 no matter what his opponent plays.His opponent's only hope is to play two,

hoping the hustler will use his second nineto reach 20. The hustler however, plays seven,and now his victim can only reach 20 byplaying his second two. To vary the method,the hustler can first play eight. If his victimplays four to force a second eight, the hustlermerely plays four himself, forcing a secondfour from his victim.

The most famous swindle is that known asthe three-card trick, or three-card monte, orfind the lady. It is a game which depends onsleight of hand by the operator, who, however,does not work alone. A three-card-trick teamconsists of several members, collectively mak-ing sure that no member of the public will wineven by accident. The game arose from thethree-thimble game, in which a pea wasplaced under one of three thimbles, whichwere moved around on a makeshift tablebefore the onlookers were asked to pick thethimble hiding the pea. Because of trickery,none got it right.

In the three-card trick, one of the cards isusually a queen. This is the card the victimhas to pick, hence 'find the lady'. Severalmethods are used to fool the victim. If heguesses right by accident, one of the operator'scolleagues will usually bet on another card.The operator will decline to accept bets ontwo cards in one deal, his colleague willprovoke an argument and the operator willcancel the deal without exposing the cardsand start again. When a bystander doesappear to win, and to get paid, he is one of thegang.

Sometimes the queen acquires a bentcorner. The victim puts his money on thebent card only to find that an outside cardhas become bent.

Not content to fleece the public by trickery,the three-card trick swindle team usuallyincludes pickpockets too. While the crowd iscraning forward to watch the action, thepickpockets are busy removing wallets. Thethree-card trick is illegal, so one of the teamis a look-out. His job is to stop the game whenthe law appears, but he can also step in witha spurious warning when anything untowardhappens, like a customer missing his wallet.On his urgent instruction to 'fold', the gangquickly vanishes to reassemble elsewhere andbegin operations again.

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P A R T N I N E

ACCORDING TO HOYLE Played to a strict code of rules.ACCUMULATOR A cumulative bet, usually on four ormore events, called a parlay in America.ACE The playing card with one pip; the one-spot of adie.ACES UP A poker hand containing two pairs, thehigher of which is aces. Also kings up, queens up, etc.A CHEVAL A stake on two adjacent numbers on theroulette table ; a stake on both sides of the table atbaccarat.ACROSS THE BOARD A bet on win, place and show inAmerican racing.ACTIVE PLAYER The player who plays the cards for agroup of players in baccarat or chemin de fer.ALLOWANCE In a horse race, a reduction in the weightset to be carried, allowed to an apprentice jockey, orsometimes to a horse which has not won.ALSO RAN A horse which does not finish in one of thefirst three places in a race.ANCHOR MAN The player to the right of the dealer atblackjack, who plays last.ANTE A stake placed in the pool before betting begins.ANY RAFFLE A bet that three of a kind will appear athazard.ANY TO COME An instruction to a bookmaker that ifany money is to come from a bet, it is to be staked on asecond bet.APPRENTICE A jockey who has not ridden a stipulatednumber of winners, and who in certain races claims anallowance.AT THE POST Horses at the start of a race are said to beat the post.

BACK To bet on.BACK GAME In backgammon, the strategy of notadvancing runners, but of using them to hit adverse blotswhen the opponent is advanced.BACKGAMMON A win at backgammon when the loserhas a man on the bar or in the opposing home board.BACK STRETCH or BACK STRAIGHT In a horse race, thelong stretch on the opposite side of the course to thegrandstand.BACK TO BACK In stud poker, this is said of the holecard and first up card when they are a pair.BANCO A call at chemin de fer by which the calleroffers to stake the whole amount of the bank.BANCO suivi A call at chemin de fer by which thecaller, who has called banco and lost on the previouscoup, claims his right to stake the whole amount of thebank again.BANK The amount at stake in banking games ; theamount put up by the casino to finance a gaming table.

BANKER The person who operates the bank in bankinggames.BANKING GAME Any game in which the amount atstake is put up by one person (the banker), ororganization (the casino), for the players to bet against.BEST BET An American newspaper tipster's, or handi-capper's, selection as the winner of a race.BET THE POT To bet as many chips as there are in thepot.BETTING FORECAST A forecast, usually in a morningpaper, of the odds likely to be offered against the runnersin that day's races.BEVELS Crooked dice having one or more sides rounded.BIG six AND BIG EIGHT Bets at craps that a 6 or an 8will be thrown before a 7.BINGO The cry of the winner in the game of bingo.BLACKJACK A two-card hand of 21 in the gameblackjack, made up of an ace and a ten-value card.BLANKET FINISH A close finish to a race.BLIND BET A bet made in ignorance of its value, e.g.before examining the cards held in brag.BLOT A single man on a point at backgammon.BLOWER The telephone service by which bookmakerscan transfer bets to the course, thus ensuring that thestarting price reflects the betting.BLUFF To bet on a weak hand in order to mislead theopposition, especially in poker.BOAT RACE A crooked horse race.BONES Colloquial name for dominoes or dice.BONEYARD The stock of dominoes from which aplayer draws when unable to play from his hand.BOOBY PRIZE Prize for lowest score.BOOKMAKER A person who quotes odds and acceptsbets from the public.BOTTOM DEALER A card cheat who deals from thebottom of the pack.BOXCARS In craps, a roll of two sixes.BOXMAN The controller of a casino craps game.Box NUMBERS Those numbers at craps (4, 5, 6, 8, 9, 10)which establish a point for the shooter.BREAKAGE The amount left after the pool has beendivided arising from winners being paid to the nearestunit below the division, especially in American racing.BUCK The marker placed on a craps table to show theshooter's point.BUG A clip placed beneath a card table to hold cardsfor cheating.BURNED CARDS Cards taken from the top of a shuffleddeck and not used in the game.BUST To exceed a total of 21 at blackjack or pontoon.

CAGNOTTE The box beneath a slot in a baccarat orchemin de fer table into which the casino levy is dropped:the levy itself.CALCUTTA A method of betting at golf, wherebyplayers are 'auctioned' to gamblers.CALL In poker, to match the last stake.CALLER The operator at a bingo game who calls thewinning numbers.CARD SENSE Natural card playing ability.CAMERA PATROL The system used in Britain to record

242

G L O S S A R Y

a race on film from various angles to help the stewardsto adjudge on objections.CANADIAN A British 26-part bet covering five horsesin doubles, trebles and accumulators.CARPET JOINT A high-class casino or gaming club,especially in America.CARRÉ A stake on four adjacent numbers on theroulette table.CARTE BLANCHE A hand without a face card.CASK THE DECK To memorise some or all of the cardsas they are played, especially at blackjack.CASE-KEEPKR In faro, the person who records the cardstaken from the box.CENTRE BET In craps, the bet between the shooter andthe faders placed in the centre of the playing surface.CHECK A gambling token used instead of cash inAmerica.CHEF DE PARTIE The controller of a gambling table in aFrench casino.CHICANE A hand of cards void of trumps.CHIP A gambling token used instead of cash.

| CHOUETTE A form of backgammon in which more thanf two players can take part.I CLASSICS The classic horse-races for three-year-olds. InI Britain, the One Thousand Guineas (for fillies only), theI Two Thousand Guineas, The Oaks (for fillies only), the

Derby, the St. Léger.

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CLEVERLY Description of how a horse wins when thewinning margin suggests that it has not given itsmaximum effort.COLD DECK A pack, or deck, of cards secretly arrangedin a desired order for the purpose of cheating.COLONNE or COLUMN A stake on a column of 12numbers on a roulette table.COMBINATION TICKET In American horse-racing, a beton a horse for a win, place or show.COMBINATIONS The different ways in which a number ofarticles can be taken from a larger number of articles.COMMISSION A bet made on behalf of a racing stable.COME A bet at craps that the shooter will win, theshooter's next roll being regarded as the come-out roll.COME-OUT The shooter's first roll at craps.COME UP To win.COMING OUT The cry of the stickman at craps warningtha i the dice are about to be thrown and bets should bemade.COMPLET or COMPLETE A bet at roulette in which anumber is backed singly and in all the combinationspossible with the adjacent numbers on the table.CONSOLE A flat-topped electric slot machine which canbe played by several players simultaneously.

; Cot LEUR A bet at trente et quarante that the first carddeal t will be of the same colour as the winning row.

iCorp. One play or round of a game.I COUPLÉ An off-course pari mutuel bet in France in| Which two horses are backed in one race to finish in, the first two (win couplé) or the first three (place couplé).I COURT CARD Any king, queen or jack in a pack ofj cards.I COVER A BET To accept a wager.' CRAPS The totals 2. 3 or 12. which if thrown on the' come-out roll of the game of craps are immediate losers.

CRI ISS-EYES A throw of three at dice.,: CROUPIER A casino employee who directs the gaming•»t the tables and pays off and collects the bets.• Cup A receptacle used for shaking dice.• CURSE OF SCOTLAND The nine of diamonds.ICu i To divide a pack of cards into two parts andInverse their order.

DAILY DOUBLE A cumulative bet on a horse in each oftwo selected races in American horse-racing, operatedby the tote.DEAD HEAT A race in which two or more competitorsfinish level.DEADWOOD In poker, the discard pile; in gin rummy,the unmatched cards of a hand.DEALER The player or casino employee who deals thecards.DENOMINATION The rank or value of a card.DEUCE The playing card with two pips; the two-spotof a die.DEVIL'S BED POSTS The four of clubs.DICE The plural of die.DICE-STICK The stick with which the stickmanmanipulates the dice at craps.DOG A racehorse who quits under pressure.DON'T COME A bet at craps that the shooter will lose.the shooter's next roll being regarded as the come-outroll.DON'T PASS A bet at craps that the shooter will lose,made before the shooter's come-out roll.DOPE Drugs given to a horse or dog in order toimprove or impair its performance.DOUBLE A cumulative bet on two horses or dogs inseparate races; in backgammon to double the stake byusing the doubling cube.DOUBLE DOWN To double the stake at blackjack andreceive an additional card.DOUBLET A domino with the same number at eachend.DOUZAINE A stake on the 12 numbers at roulettemarked either première (1-12), moyenne (13-24) ordernière (25-36).DOZEN A stake on the 12 numbers at roulette marked1st dozen (1-12), 2nd dozen (13 - 24) or 3rd dozen(25-36).DRAW To ask for. or take, another card; a type ofpoker in which the player can discard and drawreplacements.DRY Broke, having no money.DUAL FORECAST A bet in horse-racing in which thefirst two horses to finish must be named in either order.DUTCH BOOK A list of odds unfavourable to thebookmaker, an overbroke book.

EACH-WAY BET In Britain, a bet that a horse will winor be placed - in effect two separate bets, one on a winand one on a place.EDGE The advantage held by the casino or bank ingames of chance, usually referred to as the house edge.

243

P A R T N I N E

ENGLISH The sliding and spinning action of the dicein a controlled cast.EN PLEIN A stake on a single number at roulette.EQUITABLE A game is equitable if it is fair for ailplayers.EVEN CHANCE When a favourable outcome to an eventis as likely to occur as not. it is said to have an evenchance.

FACE CARD Any court card, i.e. king, queen or jack; acard displayed or dealt face-up.FADE To cover the shooter's stake in craps.FAITES vos JEUX A call by the croupier for players toplace their bets.FALSE FAVOURITE A horse which is made favourite ina race, but does not fulfil expectations.FALSE PRICE Odds quoted about a horse or dog whichdo not represent its true chance.FAUX TIRAGE A draw made at chemin de fer orbaccarat which ignores the recommended table of play.It may be intentional and within the rules, as in the caseof the banker at baccarat, or it may be a mistake.FAVOURITE A competitor, particularly a horse,considered most likely to win, and therefore quoted atthe shortest odds.FIELD A bet at craps on the numbers in the field,usually 2, 3, 4, 9, 10, 11 and 12, with 2 and 12 payingdouble; all the runners in a race.FINALS The last digits of the roulette numbers. A beton the '6' finals is a bet on 6, 16, 26 and 36.FLAT RACING Horse-racing in which there are nojumps.FLATS Crooked dice shaved so that they are brick-shaped.Fix A swindle or bribe. A fixed game is one that isrigged for the purpose of cheating.FLOATING GAME An illegal game, especially craps,which moves from place to place to avoid the law.FLUSH In poker or brag, a hand in which the cards areof the same suit.FLUTTER In Britain, a bet, usually a small or casualbet.FOLD In poker, to drop out of the betting.FORECAST In racing, a combination bet which namesthe first and second to finish in the correct order.FORM The past performances of a competitor,especially a horse.FOUR OF A KIND In poker, four cards of the same rank.FRAME The board announcing the numbers of theplaced horses in a race, hence 'in the frame', meaningto be placed.FREE BET An additional bet at craps allowed in certaincircumstances to a player, in which winning bets aresettled at the correct odds, i.e. without a house edge.FRONT LINE BET A bet at craps that the shooter willwin.FRONT RUNNER A horse which sets the pace for theothers.FRUIT MACHINE A slot machine, especially in Britain.FULL HOUSE A poker hand containing three cards ofone rank and two of another.

GAFF To rig gambling equipment. Gaffed dice aredoctored for cheating.GAMMON A win at backgammon in which the loserdoes not bear off any men.GATK In horse-racing, the apparatus for starting races,or the start itself.GELDING A male racehorse which has been castrated.GET OUT To regain one's losses, especially in the lastrace of a meeting.GIMMICK Any device or method used in cheating.GIN A hand in gin rummy in which all ten cards aremelded.Go DOWN, Go OUT In gin rummy, to lay down thehand.GOING In horse-racing, the state of the ground, e.g.hard, firm, good, soft, heavy, etc.GOOD THING Said of a racehorse or greyhoundconfidently expected to win.Go THROUGH THE CARD To back every winner at aday's racing.LE GRAND A two-card point of 9 at baccarat orchemin de fer.

HANDICAP A horse-race in which the horses areallotted differing weights to carry with a view to givingthem all an equal chance of winning.HANDLE American expression for the turnover of cashin a business concern.HARD HAND A blackjack hand containing an ace whichis counted as 11.HARDWAY A bet at craps that a shooter with a pointof 4, 6, 8 or 10 will make it the hard way, i.e. by throw-ing a double.HARNESS RACES Races in which trotting horses pulldrivers seated in two-wheeled lightweight racing rigs.HEAD TO HEAD A game between two players only, orthe state of a game, e.g. poker, where only two playersremain in.HEDGE To transfer a bet, e.g. from one bookmaker toanother.HIGH ROLLER A big bettor, especially at craps inAmerica.HIT A request for an additional card at blackjack ; inbackgammon to send a man on a blot to the bar.HOLE CARD The face-down card of the dealer atblackjack; the first card dealt to a player at stud poker,which remains face-down until the showdown.HOME STRETCH or HOME STRAIGHT The straight part ota race-course leading to the winning post.HOT A player on a winning streak is said to be hot.and in craps the dice of such a player are said to be hot.HOUSE The casino or club operating a game.

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HOUSE ADVANTAGE The edge enjoyed by the house inoffering odds shorter than the true ones in games ofchance.HUNCH An impulse. A hunch bettor or player is onewho bets on impulse or irrational fancies.HURDLE The movable obstacle, lower than a fence,over which horses must jump in a hurdle race ; the raceitself.HUSTLER A gambler who preys on the ignorance of hisvictims, or who falsifies his form to mislead hisopponents.

ICE Money paid to police and officials to overlookillegal gambling.IF MONEY WAGER A bet conditional on a previous betwinning. In Britain usually called an 'any-to-come' bet.IMPAIR A stake on the odd numbers at roulette orboule.IN THE BAG Said of a sporting event that is considereda certainty, as 'the favourite has it in the bag'. InAmerica, it sometimes means that the event is fixed.IN THE FRAME, IN THE MONEY Said of the horses whichiinish in the first three in a race.INEQUITABLE A game which is not fair to all players isnequitable.INFORMATION 'Inside' information from a stable orother connections that a horse is expected to win. Hencenformation horse - a horse made the medium of a;amble.INSIDE STRAIGHT In poker, four cards requiring anan interior card to make a straight, as 6, 7, 9, 10.INSIDE TICKET In keno, a duplicate of the punched-out:icket, given to a player as a receipt.IN THE HOLE Losing, or having a minus score.'NSURANCE A bet at blackjack that a dealer with anace as his up-card will complete a natural or blackjack ;.he opportunity of a player at trente et quarante to guardagainst a refait by paying a premium of one per cent oflis stake."NTERDIT A player who is banned from French casinos.INVERSE A bet at trente et quarante that the first carddealt will be of the opposite colour to the winning row.

JACKPOT The top prize, especially from a slot machine.JETON A French gambling token, used instead of cash.JEU The French for game.JOCKEY The rider of a horse in a race.JOKER A playing card to which a player may attachany value.JUICE JOINT A crooked dice or roulette game in whichthe cheating is accomplished by electromagnets.JUMPER A racehorse which races over obstacles orjumps, a steeplechaser or hurdler.

G L O S S A R Y

KIBITZER A spectator at a card game.KICKER In draw poker, an extra card, usually an aceor king, kept with a pair for a two-card draw.KITTY A pool, especially of stakes for distribution tothe winner.KNAVE In card games, an alternative name for the jack,particularly in Britain.KNOCKER In gin rummy, the player who lays down hishand first.

LABOUCHÉRE A staking system named after HenryLabouchère, English editor and wit.LADDERMAN An inspector in a casino who sits on ahigh chair overlooking the gaming tables.LAYDOWN In America, a diagram of betting spaces onwhich stakes are laid, or the wager itself. In Britain, ahand at cards which cannot be beaten, and whichtherefore does not need to be played out.LAY OFF To pass on a bet, as from one bookmaker toanother; in gin rummy to get rid of cards by laying themon the knocker's melds.LAY THE ODDS To bet where the amount which can bewon is less than that which can be lost. To lay six to fouris to risk losing six for the chance of winning four.LAYOUT The arrangement of a gaming table on whichthe stakes are placed.LEFT In racing, describes a horse or dog which does notstart, or is slow to start.LET IT RIDE To leave winnings on the gaming table asthe stake for the next coup.LEVY A charge by a casino or bookmaker for theprivilege of playing, often exacted on winnings.LIMIT The minimum or maximum stake allowed at thegaming table.LINE BET A stake on six numbers in two adjacent rowson the roulette table.LONG ODDS Odds quoted of a competitor or horse withlittle chance, for example 100-1.LONG SHOT A competitior unlikely to win, especially ahorse.

MAIDEN A racehorse, of either sex, which has not wona race.MAKE A BOOK To offer odds, to set up as a bookmaker.

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MANQUE A bet on the numbers 1 18 at roulette or1-4 at boule.MARK A victim singled out to be swindled.MARKER CARD A card placed in the pack to indicatethe end of play. It is a device to ensure that a certainnumber of cards are not used in the game. At baccaratthe card indicates the end of the shoe, at blackjack thatthe cards must be re-shuffled.MARKET The betting on a race, especially a horse-race; the odds quoted on a race.MARTINGALE A staking system in which bets aredoubled after each loss.MATCH In horse racing, a race with two runners only,often privately arranged.MECHANIC A manipulator of cards or dice for cheating.MEETING The period of racing, usually of a few days,at a certain course, e.g. the Epsom spring meeting.MELD A combination of cards in rummy games, suchas three or more cards of consecutive rank and the samesuit; to make such a combination.MISS-OUT A losing roll for the shooter at craps.MIXED DOUBLES A method of backing several horses ordogs with each other in all possible doubles. Thus fourselections represent six mixed doubles.MORNING GLORY A racehorse impressive at morningexercises but which runs badly in races.MORNING LINE In America, a morning forecast of theodds likely to be offered on the horses running that day.MUDLARK A horse that runs well in muddy conditions.MUTUEL NUMBERS The numbers game.

NAP Short for the card game napoleon ; a British racingtipster's best bet of the day.NATURAL At craps, a winning roll of 7 or 11 on thecome-out roll; at blackjack, a two-card hand totalling21. consisting of an ace and ten-count card; at cardgames in which wild cards are used, a ranking handwhich does not contain a wild card.No DICE A roll of dice which is invalid, e.g. one inwhich a die is cocked.NOBBLE To get at a horse or dog and injure or dopeit to prevent it winning.NOIR A bet on the black numbers at roulette, boule orvingt-trois; a bet on the first row of cards at trente etquarante.NUMBER BOARD In horse racing, the board whichdisplays the jockeys and starting position of all horses in

ODDS A method of expressing probabilities as a ratioof the unfavourable chances to the favourable ; the pricequoted on a competitor in an event.

ODDS BOARD The board at an American racetrackshowing the approximate odds of the runners.ODDS ON A probability greater than an even chance ;a price quoted in which the stake is higher than theamount to be won.OFE-COURSE BET A bet made in a bookmaker's office orbetting shop, by telephone, or anywhere away from therace-course.ON THE NOSE Colloquial expression for a bet on a horseor dog to win only.ONE-ARMED BANDIT A slot machine.ONE-ROLL BET A bet at craps to be decided on the nextroll of the dice.OPEN In poker, to make the first bet.OPEN-ENDED STRAIGHT In poker, four cards in sequencerequiring a card at either end to complete the straight,e.g. 8, 7, 6, 5.OUTSIDER A horse or dog with little chance of winning,and therefore quoted at a long price.OVER-BROKE Describes a list of odds favourable to thepunter.OVER-ROUND Describes a list of odds favourable to thebookmaker; the amount of stakes which the bookmakercan expect to retain as profit.OVER THE STICKS Used at hurdle races or steeple-chases, the opposite of racing on the flat.

PACK The 52 standard playing cards. In Americausually called a deck.PAIR A stake on the even numbers at roulette orboule; two cards of the same denomination.PAIR ROYAL Three cards of the same denomination.PALETTE A wooden spatula used by the croupier tomanipulate the cards at baccarat.PARI MUTUEL A totalisator; the system of totalisatorbetting.PARLAY A cumulative bet. especially in America, ontwo or more events or horses. In Britain, called a double,treble or accumulator.PAROLI A staking system in which winnings are allowedto stay on the table to double. 'Parlay' is a corruptionof paroli.LE PARTAGE The convention in which half of thestakes on even-money bets at roulette are lost when zerowins.PARTIE A series of coups.PASS A bet at craps that the shooter will win. It is madeon the pass-line on the craps layout.PASSE A bet on the numbers 19-36 at roulette, or 6-9at boule.PAT HAND In draw poker a hand that cannot beimproved by the draw.PENALTY An additional weight to be carried by a horseon account of a recent win.PERCENTAGE The advantage enjoyed by a casino inoffering odds shorter than the true ones on variousgames is known as the house edge, or the percentage.PERMUTATION The arrangment of a number of items inevery possible order; a system of betting on the footballpools which entails combinations but is colloquiallycalled a permutation.

246

G L O S S A R Y

PHOTO FINISH A photo record of the finish of a racetaken through a narrow aperture as the field passes thepost, used to determine the winner in a close race; usedto describe any close race.PHYSIONOMISTE or PHYSIOGNOMIST A casino employeetrained to memorise the characteristics of all players, andto recognise those banned by the casino.PICTURE CARD A face card or court card.PIPS The spots on playing cards.PIT BOSS A supervisor of a group of gaming tables,especially in America.PITCH A bookmaker's stand or territory on a race-course.PLACE BET A bet at craps that a box number will winor lose; a bet in horse-racing that a horse will finish,(a) in Britain and most other countries, in the first four,three or two, according to the number of runners,(b) in America, in the first two.PLAIN SUIT Any suit which is not trumps.PLAQUE A rectangular gaming token used instead ofcash, usually of a high value.PLATER A poor horse which runs in minor races.PLUNGE To make a big bet.POINT The total pip value of a hand of cards at certaingames.POINT NUMBERS At craps, the numbers 4, 5, 6, 8. 9 or10.POLE A distance mark in a horse race. Thus the two-furlong pole is two furlongs from the winning post.LE PONTE The French term for a gambler or punter.POST The starting or finishing point of a horse race.POT In poker, the total amount bet on a hand; a k i t t yor pool.POUSETTE A form of cheating, usually at baccarat, inwhich the cheat pushes his chip or chips from oneposition to another in order to increase or decrease hisstake according to the cards held.LES PREMIÈRES The first four numbers (0, 1, 2, 3) on theroulette table, or a bet on them.PRIAL Three cards of the same rank, especially at brag.A corruption of pair royal.PRICE The odds quoted against a competitor, e.g. ahorse's price might be 7-2 against.PRICE LINE An American bookmaker's list of prices forbaseball or other sports. A twenty-cent line is a line thathas a differential of one point between the lay and takeodds, e.g. a bookmaker might offer odds of 6-7Yankees favourites, which means he offers 7-5 onYankees and 6-5 against their opponents, a differenceof one point in five, or 20 cents in a dollar.PRIME A series of six or seven points on a backgammonboard occupied by men of the same colour.PRISON A convention whereby a stake on the even-money chances at roulette is left on the table, or 'put inprison' when zero appears, to be either retained by thebettor or lost according to the next spin ; a convention intrente et quarante whereby on a refait all bets remain onthe table to be either retrieved or lost according to thenext deal.PROPOSITION BET At craps, another name for a one-rollbet, in which bets are determined by the next throw ; anancillary bet not covered by the rules of thegame.PULLING The holding back of a horse by the jockey.PUNTER In Britain, any gambler, or bettor; in America,usually one who plays against the bank.PUNTO A bet at punto banco that the bank will lose.PURSE The prize money, especially for a horse race or aprize fight.

QUARTER HORSE A horse which runs well for a shortdistance only, the implication being that it quits after aquarter of a mile.QUINIELA In American racing, a bet requiring thebettor to name the first and second horses to finish ineither order. Known in Britain as a dual forecast.QUOTATION The price quoted on a competitor in anevent.

RACING CERTAINTY Said of a horse that (in theory)cannot lose.RAFFLE A lottery; in hazard, three dice showing thesame number.RAISE In poker, to increase the stake by betting morethan the previous bettor.RAKE The implement with which the croupier at agaming table rakes in the chips.RANDOM DISTRIBUTION Distribution by chance.RANK The denomination or value of a card.READERS Marked cards; the lenses required to readsome marked cards.REFAIT The occurrence of both rows of cards in trenteet quarante equalling 31.REVOKE To fail to follow suit in card games.RIEN NE VA PLUS The announcement of the croupier,especially at roulette, that no more bets will be accepted.RIFFLE A manner of shuffling cards.RIG To tamper with gaming equipment for the purposeof cheating.RIGHT BET A bet at craps that the shooter will win.RING An enclosure at a race-course where bets aremade, e.g. Silver Ring; a syndicate of big bettors.RINGER A horse or dog running in the name ofanother, usually inferior.RING IN To introduce crooked equipment into a game.ROGUE An ill-tempered or unwilling horse.ROUGE A bet on the red numbers at roulette, or on thesecond row dealt at trente et quarante.ROUND ROBIN A series of cumulative bets in which allthe selections are bet in all combinations with each otherin parlays.ROUND-THE-CORNER Circular sequence of ranks ofcards whereby high and low cards are regarded as insequence, as in Q, K, A, 2, 3.ROUND THE HORN A craps bet on 2, 3. 11 and 12.ROYAL FLUSH The highest poker hand: the ace. king.queen, jack, ten of the same suit.RUFF To trump, to play a trump card on a lead of aplain suit.RUN A sequence of three or more cards, especially inbrag.RUNNER A participant in a race; an illegal bookmaker's

247

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employee who collects bets for the bookmaker; an agentin the numbers game.RUNNING GAME In backgammon, the strategy ofbringing all men into the home board as quickly aspossible.RUNT A poker hand of lower value than a pair.

SABOT A card-dealing box, also known as a shoe,from which cards are dealt in a casino.SALIVA TEST A test of a horse's saliva to determine ifit is doped.SALLE PRIVÉE A private salon in a casino, reserved forhigh-stake games.SAWDUST JOINT An illegal or low-grade gaming club orcasino, especially in America.SEE To cover the last bet at poker or brag withoutraising the stake.SEQUENCE In card games like rummy, a run of cardsof the same suit; in games of chance any series of eventsor results.SETTLEMENT The payment of losses and collection ofwinnings; the cashing in of chips.SETTLER An employee in a betting shop who calculatespayouts.SEVEN OUT In craps, to lose by throwing a seven.SHILL A casino employee who is paid to play at thetables to encourage other players.SHIMMY A colloquial term for chemin de fer.SHOE Another name for a sabot, a box from whichcards are dealt; the period of play, especially at baccarat.from the first hand until the cards in the shoe areexhausted.SHOOTER The player who throws the dice at craps.SHORT ODDS Odds quoted on fancied competitors, theopposite of long odds.SHOW A bet in America that a horse will finish in thefirst three of a race.SHOWDOWN In poker, the exposure of hands to decidethe winner.SHUFFLE To mix the cards in a pack prior to cuttingand dealing.SHUTOUT In America, to win a game without theopponent scoring. In Britian usually called a whitewash.SHY Short, usually used of a pot. A pot to which chipsare to be added is called shy.SIDE BET A bet made by onlookers at a craps game.SIDE CARD The highest odd card in a poker hand.outside of a pair or two pairs.SIDE SUIT A plain suit, i.e. not the trump suit.SIXAIN A bet on six numbers forming two adjacenttransversales on the roulette table; the six packs of cardsused in a shoe at baccarat or trente et quarante.SLEEPER A number which has not appeared for a longtime, especially at roulette; a bet left unclaimed on abetting layout.SNAKE-EYES The double-1 at craps and other two-dicegames.SODA In faro, the top card when the pack is placedin the dealing box.SOFT HAND A blackjack hand containing an ace whichis counted as one.

SPATULA A tool to assist the croupier to handle cards.SPLIT A bet on two adjacent numbers on the roulettetable.SPLITTING PAIRS A convention at blackjack whereby aplayer dealt a pair may split them and regard each as thefirst card of two separate hands, with an equal stake oneach.SQUARE A bet on four adjacent numbers forming asquare on the roulette table.STACK A pile of chips ; to fold or drop out of a cardgame.STACKED DECK A pack of cards pre-arranged in adesired order for cheating.STAND To play at blackjack with the cards held, i.e. todecline to draw a further card.STANDARD PACK OR DECK The ordinary pack of 52playing cards.STAND-OFF The situation in gambling games where twoor more players, or the player and dealer, tie, and therules state that no stakes change hands.STAKE An amount bet on an event.STARTING PRICE The final odds offered on a horsebefore the race begins.STEEPLECHASE A race run over fences.STICK To play at pontoon with the cards held, i.e. todecline to draw a further card.STICKMAN At craps, the casino employee who handlesthe dice and sometimes settles the proposition bets.STOCK The undealt portion of a pack of cards.STRAIGHT In poker, a run of cards in sequence, but notof the same suit ; in roulette a bet on a single number.STRAIGHT FLUSH In poker, a run of cards in sequenceand of the same suit.STREET The American term for a bet on three adjacentnumbers forming a row on the roulette table.STRIPPERS Cards that have had their edges stripped toform a convex or concave shape in order to facilitatecheating.STUD A form of poker in which the first card is dealtface down and the remainder face up and there is nodraw.SWEETEN THE POT Add chips or money to the pot.SYSTEM A plan of staking or betting.SYSTÉMIER One who employs a system.

TAB Totalisator Agency Board, which runs on- andoff-course tote betting in Australia.TABLEAU The layout of a gaming table.TABLEAU DES VOISINS A table showing each number ona roulette wheel in relation to its neighbours.TABLE OF PLAY The recommended standing or drawingprocedure for the player and banker at baccarat, cheminde fer and punto banco.TABLE LIMITS The upper and lower staking limits at agambling table.LE TAILLEUR The dealer, usually at trente et quarante.TAKE THE LEAD In stud poker, to make the first bet in around.TAKE THE ODDS To bet where the possible win isgreater than the possible loss. To take six to four is toaccept six for a win and pay out four for a loss.

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TALON In card games, the waste pile.TAP To pass in card games by tapping on the table.TIC-TAC A method of hand signals used in Britishracing in which a bookmaker's employees relate infor-mation about current odds and betting toeach other.TIERCÉ A combination bet in French racing in whichthe bettor must forecast the first, second and thirdhorses to finish.TIPSTER A person who sells his predictions of winnersto the public. A newspaper tipster is one who publisheshis selections in a paper.TIREUR A player who always draws to 5 at baccarat.TOTALISATOR, TOTE The machine which calculatesdividends by dividing total stakes by the winning stakes;the system of betting thus.TOTE BOARD The information board at a race coursewhich shows the amounts bet and the approximatepayouts for each runner.TOTE DOUBLE AND TREBLE A cumulative bet operatedby the totalisator in Britain in which the backer mustname the winners of two or three selected races, usuallythe third and fifth for the tote double and the second,fourth and sixth for the treble.TOTE JACKPOT A cumulative bet operated by the total-isator in Britain in which the backer must name thewinners of six races. If it is not won, the pool is carriedforward to the next day or meeting.TOPS AND BOTTOMS Gaffed dice which show only threenumbers, two of each.TOUT One who watches training gallops and exercisesat racing stables to spot future winners.TRANSVERSALE A bet on three adjacent numbers form-ing a row on the roulette table, known in America as astreet.TREBLE A cumulative bet on three horses or dogs inseparate races.TRFY A three-pip playing card.TRICK The cards played in one round of play in gameslike whist and bridge.TRIELLA A bet in Australian horse-racing requiring thefirst three in a race to be named in the correct order.TRIPLE A bet in American horse-racing requiring thefirst three in a race to be named in the correct order.TRUMP In trick-taking games, a card from a suit givena higher value than other suits.TURF Usually preceded by 'the'. The sport of horse-racing.TURF ACCOUNTANT A bookmaker who accepts bets onhorseraces.

UNDERCUT In gin rummy, to show a hand lower inpoint count than the knocker's.UNDER THE GUN In draw poker, the player who mustopen the betting is said to be under the gun.UNLIMITED POKER A poker game of unlimited stakes.UNMATCHED CARD In gin rummy, a card that is notpart of a meld.UPCARD In gin rummy, the first card turned up fromthe stock; in stud poker, any card dealt face up, asopposed to the hole card.

G L O S S A R Y

VIGORISH The percentage taken by a banking gameoperator as commission for running the game; anybookmaker's or gambling proprietor's percentage.VOISINS The numbers on a roulette wheel which areneighbours to any particular number.

WASTE PILE In card games, the talon or discard pile.WAGER A bet.WEIGHT The weight carried by a horse in a race,adjusted by the use of lead in the saddle.WELSH To fail to pay a gambling debt.WHEEL ROLLER The croupier who spins the wheel atroulette in an American casino.WHITEWASH In Britain, to win a game without theopponent scoring, usually called a shutout in America.WIDE RUNNER A greyhound which runs wide on thebends.WILD CARD A card to which its holder may attach anyvalue. It might be the joker, and is sometimes called ajoker.WIN A bet at craps that the shooter will win.WRONG BET A bet at craps that the shooter will lose,i.e. a bet on 'don't pass' or 'don't come'.

x A symbol used to represent a low card whose rankis immaterial, as in K-J-x-x.

YANKEE A popular bet in Britain in which four horsesor dogs are backed in all combinations of doubles,trebles arTd accumulators - six doubles, four trebles, oneaccumulator.YARBOROUGH In whist and bridge, a hand containingno card higher than a nine.

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IndexFigures in bold type refer to the main reference.Figures in italics refer to a caption reference.

Aabacus 120accumulators, horse racing

40,41,56,57ace-pots, poker 163across the board ticket, horse

racing 63Acts of Parliament 221addiction 22addict, drug 18,20

gambling 13, 18,21,234slot machine 106

Africa, casino in 230Aga Khan 28, 203, 203Aintree, Liverpool 53Aix-les-Baines casino, France

226, 227Aldin, Cecil 52Alembert D', system 47Aleppo 52Ali and Frazier fight 72, 72Ali Muhammad 73Allez France 60André, François 28, 226, 227ante-post bets 58

prices 58any raffle bet, hazard 114any specific total bet, hazard

114any to come bet, horse racing

56Aphrodite 8Arabs, horse racing 50Arab countries and gambling

230Araucanian Indians 13Aristotle 8Arkle 53, 54Arthur's Club 279Ascot, England 16Ascot, Melbourne 84astragals 8atep 8, 188Athens 27Australia 16, 21Auteuil 60

BBabylonia 8baccarat 25, 27, 28, 30, 85,

115-119, 146,2/5banque limitée 115banque ouverte 115-chemin de fer 115douteur 118non-tireur 118table of play 117a un tableau 115a deux tableaux 115, 777tableau un 115

250

tableau deux 115in Britain 85, 86, 224

France 226Isle of Man 226Monte Carlo 209USA 217West Germany 230

bacarrat-chemin de fer, seealso punto banco 119

back game, backgammon 179backgammon 92, 146, 173

183, 773, 174, 176, 178,179, 180, 183

back game 179block 179blot 177forward or running game

179prime 179strategy 179-183

backgammoned 178Baden-Baden casino 776,128,

130, 195, 230Bahram 53banco, chemin de fer 118banco suivi, chemin de fer 118bar principle (roulette wheels)

137Barnard, Dr Christiaan 750Baroda Squadron 24Barrière, Lucien 226, 227baseball 78basketball 78Bath 84, 135beat the dealer 114, 152

layout 775Beecher's Brook 54Bell's Life 82Belmont Park 62Belmont Stakes 62, 62Bentinck, Lord George 83, 84Beraud, Jean 198Bernhardt, Sarah 20Bet a Million Gates (see also

Gates, John Warne) 30Betting and Gaming Act, The

221betting, backgammon 178betting, craps 110-113betting, roulette 123betting shop, Britain 55, 58Biarritz casino, France 222,

226Biarritz player, roulette 127Biarritz system, roulette 125bicycle racing, France 69

Japan 70Big Six wheel 141billiards 192, 793bingo 10, 16,20,22,95,

99-101, 700halls 99variations 99

biritch 770birthday problem 37blackjack 25, 146-161

insurance 158pontoon 161strategy 151variations 151table 750in Australia 232

Britain 221Germany 230Isle of Man 226Malta 230Monte Carlo 209Puerto Rico 232USA 217

Blanc, Camille 27Blanc, François 194, 198,209Blanc, Louis 194Blancs, The 206blitz, gin rummy 168block, backgammon 179blot, backgammon 177Blucher bid, Napoleon 169Blue Peter 53Blushing Groom 60board games 8Bond, James 30bone-yard, dominoes 187boodle and stops (see also

Pope Joan) 173bookmakers 45-46

Olympic games 69soccer 75training 58

bought cards, pontoon 161boule 137

ball 138dish 735dish 735in Malta 230

Monte Carlo 209boxes, gin rummy 168boxing matches 72, 73, 218boxman, craps 108brag 163, 166-167

seven card 167'Brain, The' 88Brazil 232bridge 18,33,40, 160,170,

189Britain 15, 16,20,21,23,222Britannia 203British Gaming Acts 220British laws 15British Museum 8, 70, 11British Open Championship 8Britt, Edgar 23Brogue, The 24Brooklyn Jockey Club 62Brooks's 25, 275, 279Brummell, George Bryan,

'Beau' 25, 25, 279

buck dice 92Buda 52Bug and Meyer mob, The 27,

209Bula 54Bulgaria, casino 230Bulle Rock 52bullfighting, Spain 70, 70

Mexico 70Bunbury, Sir Charles 52buy bets, craps 111Byerley Turk 52cCalcutta pool system 80Callas, Maria 206Cambridge, Oxford and,

boatrace 45Canadian, a, horse racing 57cancellation system 47cancellation system backwards

48Cannes, France 226Canterbury, Archbishop of

22, 235Capone, Al 27, 21,209, 211,

213Captain, chouette 178Capua figurine 70CARBINE 66cards, cheating at 57

origin of 10-14Caribbean, gambling in 232'carpet joint' 213, 273carré, en 125Carruthers, Colin 74Casanova, Giovanni Jacopo

24, 25, 25Casinos 46Casinos in Africa 230

Arab countries 230Argentina, Mar del Plata

230Australia, Hobart 230Austria, Vienna 230Belgium, Ostend 230Brazil 230Britain 194, 222, 224Bulgaria 230Caribbean 230China 230Czechoslovakia 230Egypt 230France, Aix-les-Baines 226

Biarritz 226Cannes 198,226Deauville 226, 230Divonne-les-Baines 226

Greece 230Isle of Man, Douglas 224,

226

I

I

Italy, St Vincent 230San Remo 230Venice 230

Macao 230Malta, St Julians 230Monaco, Monte Carlo

194,198,203,206,224Morocco 230Portugal. Estori l 230Puerto Rico 230Romania 230South Africa 230Spain 230Tunisia 230USA, Nevada 100, 194, 230

LakeTahoe218Las Vegas 194,217,221,

222, 224Reno218

West Germany 226, 230Baden-Baden 194,230Homburg 194,203,230Wiesbaden 230

Casino Royale 215Castro, Fidel 232Caulfield Cup 64Caesar's Palace, Las Vegas

213boxing 218

Cercle Privé, Vienna 230chalker 55champion hurdle race 53Chantilly 60chariot races 50, 50Charles III, Prince 194, 198cheats and cheating 22, 87,

755, 235checkers 192Cheltenham 45, 53chemin de fer 30, 776, 775,

118-119, 146, 195,215faux tirages 119Table of Play 119in Beliiium 230Isle of Man 226Malta 226Monte Carlo 209Puerto Rico 232

chemmy, see cheminde fer 30

chess 188, 189, 189, 190betting 234

Chester, England 50, 53Chester Cup 50cheval, à, roulette 125Chicago (see also Pope Joan)

173Chicago White Sox 88China 8, 11, 15, 230

wei-ch'i 189chouette, backgammon

178-179Christ 8, 22

Christians 22Christina 206chuck-a-luck 114, 113, 114,

141church funds 22Churches Council on

Gambling 224Churchill Downs, Louisville

52, 62, 64Churchill, Winston 206Cincinatti 26, 88Cincinatti Kid, The 71, 157Circus-Circus, Las Vegas 218Citation 62, 62Citroen. André 28, 29City of Louisville 210Clermont Club, London 222Coborn, Charles 27, 27cockfighting 70, 71, 73coins, tossing 33, 34, 55, 37,

40colonne à cheval, roulette 125Columbus 13column, gin rummy 168Combination, The 2 1 1 , 2 1 3combination ticket 63combinations and

permutations 40-42combinations of numbers 42come bet, craps 108Computer Automated Real-

time Betting InformationNetwork 66

Connery, Scan 30, 30, 230Continental Press Service 211converse probabilities 36corrida 70corruption 21Costello, Frank 209, 217couplé, horse racing 61coursing 69Coyoumdjian, Zaret 27Covent Garden, London 277Coventry, Lord 86, 86craps, British-style layout 108

Nevada-style layout 772craps 29, 48, 106-113, 709, 276

floating game 107layouts 108private game 107strategy 113in Australia 232

Britain 224Monte Carlo 209Puerto Rico 232USA 275,217

cricket 80crime 82

in USA 21. 221criminal classes 21Crockett, Davy 707Crockford, William 25, 25,

83,53

Crockford's, London 25. 25,83, 730, 276, 222

crow 60crown and anchor 114, 774Cruickshank, George 735, 147Cuba 232Culberton, Ely 189cumulative bets, horse racing

55Curse of Scotland 752Curzon House, London 222Curzon House Group 730Cyprus 775Czechoslovakia 15

casino 230

DDagenham greyhound racing

track 85daily double, Australia 65Daily Mirror, England 2?. 23,

24Dandolos, Nicholas 29Daniels, Bebe 29Darley Arabian 52darts 192Deadwood, USA 26dealers, craps 108Deauville 28, 60, 115, 777,

173,222,226,227,230Delys, Gaby 28Dempsey, Jack 72, 72Derby, Epsom 52, 52, 53, 54,

60, 83, 53Derby, Italian 27Derby, Kentucky 62, 62Derby, Lord 53Derby, 12th Lord 52Desert Inn, The, Las Vegas

213Detroit, Nathan 107Devol, George 26, 270Diamonds are Forever 30Dice 92

buck 92cheating 57game 11, 36

Dice Players, The 92Dickens, Charles 20Dietrich, Marlene 275Divonne-les-Baines, France

226do bet, craps 109Doctrine of Chances, The 38Dodge City, USA 26Dodge City Peace

Commission 26Dolly Sisters 28dominoes 8, 185-187, 757Doncaster, England 52Doncaster Handicap 65

Doncaster St Léger 85don't come bet, craps 108don't pass bet, craps 109Dostoevsky 77, 18, 20, 230double, craps 108double, horse racing 55, 56double down, blackjack 157double pool, horse racing 63doubling cube, backgammon

178douteur, baccarat 118douzaine, roulette 125douzaine à cheval, roulette

125draughts 192

in Europe 192draw poker 162dreams, winning 23Duke University 24Dunes Casino, Las Vegas 213duos, Australia 65Durham, Bishop of 22, 235

Eeach-way bet, horse racing 56each-way doubles 56Earp, Wyatt 25, 26, 26Edward VII, King 55, 203Egypt 50, 230Egyptians, Ancient 8electric hare 50Electronic Random Number

Indicator Equipment 97Eliopulos, Eli 27Elizabethan brothel 77en carré, roulette 125en plein, roulette 125EO (even-odd) 135equipartition 42-44Ernie (see also Electronic

Random NumberIndicator Equipment) 97

Escarté 173Escoffier, Auguste 203Estoril casino, Portugal 30,

230, 224Eton, England 25Etruscans 8Europe 120even bet, hazard 114exacta 64Exbury 60

Ffactorial number 239fan tan 144farmer's joy 173faro 24, 26, 29, 30, 120-123,

120, 720251

Farouk of Egypt, Ex-king 30faux tirages (chemin de fer)

119Paye, Julia 29Federal Reserve Clearing

House 98Fermât, Pierre de 33, 35, 39Fernande! 235Fey, Charles 103, 705field bet, craps 110fifinella 53fighting 70-71find the lady 13, 240First World War 27Fischer-Spassky 189fish, fighting, Siamese 70Fitzgerald, F. Scott 86Fitzsimmons, Bob 26five of a kind, general 183Flamingo, The, Las Vegas

205,211,213flat-racing 52 """""~"~Fleet Prison 83Flegenheimer, Arthur 27Flemington, Australia 64, 65,

67floating craps game 107Florestan I, Prince 194flush, poker 162football 18

in Britain 79in USA 78, 79pools 16, 18,45,61,72treble chance 40, 41

football pools in Australia 75,77

Continental Europe 75Britain 74, 75, 75

forerunners of roulette135-138

fortune telling 8, 11Forty Years a Gambler on the

Mississippi 26, 210forward or running game,

backgammon 179four-five-six 139four of a kind, general 183fours, poker 162Francascal 84France 13, 21, 25, 27, 118

betting in 60casino in 230

Franco British CasinoSyndicate 85

France, King of 25Frazier 72free bets, craps 112Freemont Street, Las Vegas

706,205,218front-line, craps 109fruit machines 103full house, general 183full house, poker 162252

GGalileo 35, 36Gam-Anon 19Gambler, The 18,230gambler casual 18, 21

compulsive 20, 21occasional 22pathalogical 77, 18, 20, 22professional 23regular 22serious 22

Gamblers Anonymous 19, 20gambler's expectation 43, 44

fallacy 39gambling industry 21gambling organisation's

advantage 44gambling, USA 207games of chance 33games of skill 33Gamester, The 148Gaming Acts, British 194, 224Gaming Board of Great

Britain 101, 151,222Gaming Laws, British 226gammon, backgammon 178Gates, John Warne 30, 235general 183-184, 184

big 183small 183, 184hands, five of a kind 183

four of a kind 183full house 183straight 183point numbers 183

general elections 235, 238German casinos 230Germany 13gin, gin rummy 168gin rummy 146, 167-169, 168

strategy 168-169Gleason, Jackie 227Glengall, Lord 25'Glitter Gulch' (see also

Freemont Street, LasVegas) 208, 218

go 189, 190God 10, 22Godley, John 23, 23, 24Godolphin Arabian 52Gogh, Vincent van 239Gold Cup, The 53, 54, 54Golden Miller 54Golden Nugget, London 213,

222Goldstrand casino, Bulgaria

227golf 80, 80, 190,235

British Open Championship8

Gombard, Antoine 38

Goodwood 53Gordo, El 21Gordon-Gumming, Sir

William 86, 86Gordonstoun 86Grand Critérium 60Grand Hotel, Monaco 203

Rhodes 225Grand National 24, 52, 53,

54, 56, 60Grand Prix de Paris 60Grand Steeplechase de Paris

60Great Britain 118Great Gatsby, The 86, 88Great Sinner, The 215Great Subscription Room 218Greece 8, 10,230Greek mythology 8Greek Syndicate 27, 29, 30,

115, 777,203Greeks, Ancient 8, 8, 10

wrestling 70Greenbaum, Gus 213greyhound racing 41, 67-69,

58,66in Britain 67, 69in Continental Europe 67in USA 67, 69

greyhounds 50Grundy 53Guildhall, London 90Gully, John 83, 83Guys and Dolls 107

HHabgood, D. John 22Hades 8Hamlet 40handicaps 59Hanuman 11Hampstead Fair, London 143hardway bets, craps 108, 110Harlem, numbers game 97Harlow, Jean 211Harold's Club 709, 273 218Harrahs, Lake Tahoe 218Harrods, London 188Haydock Park, England 16hazard 773, 114, 113-114,

216, 219heavyweight championship of

the world 70Hefner, Hugh 183Heinz, the 57Hennessey, James 28Henry VIII, King 234Hialeah Park, Miami, Florida

61,64Hibbs, Albert 83Hickok, Wild Bill 26

high bet, hazard 114high-low 103Hill, Virginia 213Hill, William Bookmaking

organization 58, 240Hilton Hotels Group 217Hobart casino, Tasmania 232hoca 135

wheel 137Hogarth, William 27 7hoggenheimer 138, 139hole card, blackjack 151Holliday, Doc 25Hollywood, USA 25Home Secretary, British 221Homer 8, 50Hoover, Herbert 88horse racing 16, 22, 30, 40,

44, 45, 57, 50-67betting 45

horse racing in Australia64 67

in Britain 52-59France 59-61Germany 230USA 61 64

Horseshoe casino, Las Vegas213

housey-housey 99Hoyle, Edmond 747Hughes, Howard 277, 217human canonballs (see

Circus-Circus) 218Hunts 52Hustler, The 227, 235hustler 22, 235-240, 227Huston, Walter 215Hyperion 53

IIdomeus and Aias 50if money bets, horse

racing 64Iliad, The 8impair, roulette 123increasing stake system 47independent or mutually

exclusive events 36India 8, 11inequitable games 44in prison stake, trente et

quarante 122insurance, blackjack 150, 151,

158Ireland 23Irish Hospital Sweepstakes

96Irish Sweeps Derby 96Italy 13Ivan the Terrible 189Ivanjica 60

I

JJackpot casino, Las Vegas 213jack-pots, poker 163Jaggers, William 82jai alai Spain 78

Latin America 78USA 78

jail-breaks, betting on 235Japan, go 189, 190jaquet 174Jerusalem 779Jews, ancient 10Jimmy the Greek 29Jockey Club 52, 84John Player Classic 80Jones, Tom 217judo 190

KKelly, Grace 206Kelso 63Kennedy, Attorney General

Robert 21keno 700, 101, 707, 702

in USA 217Kenyon, Lord 15Kerzner, Solly 180Kibitzer 178Kilbracken, Lord (see also

Godley, John) 23King of Gamblers, The 88, 88kip, the (two-up) 143Knucklebones 8, 10Korea 11, 13, 190

LLabour Party 238Ladbroke Club 220Ladbrokes 80LakeTahoe, USA 218Lansky, Meyer 209Las Vegas 29, 101, 102, 146,

209,211,218,222,224casino 27, 700

Las Vegas Chamber ofCommerce (see also'Vegas Vie') 203

Laurel Park, Maryland, USA62,63

law of large numbers, the 33,39-40, 42, 44

law of averages 39lay bets, craps 111legality 15Lenz, Sidney 189Levy, Goodman 83lair dice 185, 185

Liberace 217Liberty Bell 103Liberty Bonds 88Liberty chess set 188Light of Other Days, The 13Lillard', John 764Littlewoods pools 75, 77logarithms of factorials 41lollapalooza 164London, gaming 222London deal, blackjack 151Long Island, USA 50lotteries 15, 16,22,44,90,

90-97, 94in Britain 95French national 94Greek national 96Italian State 95New Jersey state 94Puerto Rico 90, 94USA 95lugo 21mechanical 103

lotto 98, 99German 101

low bet, hazard 114Lucan, Lord 222lucky charms 18Lucky Luciano 27, 209, 213Lucky Strike, Las Vegas 213Ludlow race course, England

76ludo (see also backgammon)

173'Ludus Duodecim

Scriptorium' 174Lugo, Spain 21Luke, Gospel of 22

Mmacao 25Macao 230, 232Maccabeus 83Macmillan, Harold 172Mafia 217mahjong 190, 792Maisons-Lafitte 60major arcana, tarot pack 75Malta, St Juliens 230Mamaia Melody Bar,

Romania 226'Man, The' 757Man That Broke the Bank at

Monte Carlo, The 27Manchester United 75manque, roulette 123Man O'War 62Mar del Plata, Argentina 232Maribyrnong River 65Marmeluke 83Martingale system 46-47

matador 70, 187, 187match game, spoof 188, 239mathematicians 33, 35maturity of chances theory 39Mauritius 237Maxwell, Eisa 202, 206Meadowbank, Stadium 68Mecca Group, London 222Melbourne 64Melbourne Cup 64, 65, 65Meld 53Mere, Chevalier de 37, 38,

239Mesopotamia 8MGM217mice 709michigan 752, 767, 173Mill House 54Mill Reef 53, 60Ministry of the Interior,

French 226Minnesota Fats 227misery bid, Napoleon 169Mississippi 25

steamboats 270Miss Sweden 240Miss World contest 240Moivre, Abraham de 38, 39Monopoly 234Monte Carlo 20, 24, 27, 28,

30,82,55, 115, 795, 198,202,203,213,224

baccarat 173roulette 123

Monte Carlo Story, The 275Montini, Cardinal 235Moore, Edward 148Moores, John 75Morenci, Arizona 720Morgan, J. P. 203Morocco 230mouse race, Brixton 69Mr What 24McCall, Jackie 26McQueen, Steve 757, 166

NNapoleon, or nap 25, 169

Misery 169Wellington 169Blucher 169Peep nap 169Purchase nap 169Strategy 169

National Hunt 45, 52, 53National Museum, Rome 70natural, blackjack 150natural, see also pontoon 161Nevada 16,62, 106, 107, 115,

118, 120,218,211,221,232

blackjack 151gaming 230

Nevada Gaming ControlBoard 217

Newman, Paul 759, 227, 235Newmarket, see also Pope

Joan 52, 752, 173New Orleans 700New York 16,24New York Racing Association

62Nice 194, 198Nick the Greek 29Nijinsky 53, 55noir, roulette 123non-tireur 118no pair, poker 162noughts and crosses 33numbers game, the 97, 97

0Oaks, The 52, 60objections, to gambling 21odd bet, hazard 114odds 34odds or free bets, craps 112off-course betting 54, 56off-course bets 57off-course bookmaker 55, 64Off-Track Betting Corporation

63Old Curiosity Shop, The 20Old Testament, The 10Oiler, Pierre 44Olympic Games 50, 69Onassis, Aristotle 203, 206one-armed bandits 103, 707One Thousand Guineas race

52Orlando 84Orsay, Alfred d' 216Ostend 230Oxford and Cambridge

Boatrace 45Oxford University 23

Ppachisi, see backgammon 173pair, poker 162

roulette 123Palace casino, Isle of Man

224, 226Palace Club, Reno 83Palais Esterhazy, Vienna 230Palais Royal, Paris 135Palm Beach Club, London

730, 222Palm Springs Golf Course 80Pan8

. 253

pari mutuel 16, 44, 60, 61. 62.63, 64, 67, 75

pari mutuel or totalisatorsystem 44-45

pari tiercé 61Paris 24, 25, 27, 44, 60parlay, place 64

win 64partage, le, boule 138

roulette 123. 125. 127. 130.134

Pascal, Biaise 33, 38. 38, 39Pascal's Triangle 40, 41, 41,

42, 46pass bet, craps 109passe, roulette 123patent, thé 56Patroclus 50Patterson. Floyd 73Pawnese 60Peck, Gregory 275peep nap, Napoleon 169pelota. Cuba 78

USA 78periodic events 37-39Perov V. G. 77Persian War 54pessomancy 8Peterborough Fair, England

148petits chevaux 137Phar Lap 65Pick em line 80pickpockets 240Piggott. Lester 55, 59Pimlico. Baltimore, Maryland

62pin table 31Pinza 53place couplé 61place number to lose bets,

craps 1 1 1place number to win bets,

craps 110Playboy, The, London 227,

222Playboy organisation 183Player John, Classic 80point numbers, general 183point-to-point, horse racing

52poker 26, 29, 30. 33, 146, 759,

162-166, 762, 164, 225straight draw 162, 166stud 757, 166stake 163bluffing 163, 165strategy, straight draw 163

poker hands : flush 162fours 162full house 162inside straight 165kicker 165

254

no pair 162pair 162royal flush 162straight 162straight flush 162threes 162two pairs 162

poker dice 184-185, 185poker hands in general 183Pokerpolis (see Cincinatti) 26Polland, Eddie 80Pollard, James 52pontoon (twenty-one, vingt-

et-un, blackjack) 146,161-162

bought cards 161'natural' 161'stick' 161'strand1 161'twist' 161in Isle of Man 226

pool 192, 795Pope 235Pope Joan 752, 767, 173Portugal 230Poseidon 8Post Office 24pot deals, poker 163

ace-potsjack-pots

pousette, la 86Powderhall Sprint 68, 69Preakness Stakes 62Premium Bonds 95Pretty Polly 53prime, backgammon 179Prime Minister, British 172Princeton 78, 80private craps game 107Prix de l'Arc de Triomphe 53,

55, 60, 60Prix de Diane 60Prix de Jockey Club 60Prix Morny 60Prix Robert Papin 60prize fighter 50probabilities, graph of 40probability curves 40probability theory 33-36, 39prohibition 21proposition bets, craps 112Protestant belief 22psychology 48Puerto Rico, casino 232

general 183puff 7 76punto banco (baccarat-chemin

defe r ) 115. 119in Australia 232in Britain 224table 118

purchase nap, Napoleon 169put-and-take 144

Qquadrella 65quart premiers, roulette 125quinella 65quiniclas 69quiniela 63

Rrabbit's foot 18race tracks, USA 61raffle bet, hazard 113raffles 22, 90raindrops on window panes

30Rainier II. Prince 206Rake's Progress, The 217Randwick 64

Easter Carnival 65Ratan 83red dog and shoot 172Red Rum 53. 54refait 122Reformation 15Regent, Prince 25. 25religious argument 22Reno, USA 709,218restrictions on gambling 15Rhine, Prof. J. B. 24Ribot 60Richards, Gordon 53right bet, craps 108Ritz, César 203Riviera casino, Las Vegas 213Robinson, Edward G. 757,

166Rogers, Ginger 277Roman Catholic Church 22Roman mosaic 10Romania, casino 230Romans, the 10Rome 8, 10Roodeye 50Roosevelt, Franklin D. 88Rothschild, Baron Henri de

28Rothstein, Arnold 21, 88, 88rouge, roulette 123rouge et noire 135, 195roulette 43, 48, 123-135, 138,

213,215, 226,231salon in France 137wheels 43in Australia 232

Belgium 230Britain 138,223France 725, 727. 128, 225,

226Germany 230Malta 230Monte Carlo 209

Puerto Rico 232USA 727, 128, 136, 217

Roulettenburg 230round robin bets 64round-the-clock bet 56round-the-corner straight,

poker 162Rowlandson. Thomas 218Royal Ascot 53Royal children's names 235royal flush, poker 162ruination, prospects of 44rummy 167, 792running game, backgammon

179Running Rein scandal 83Runyon. Damon 107Russian roulette 234

whist 720

Ssabot 776, 117. 118Sahara Hotel, Las Vegas 213.St Andrews. Scotland 80. 80St Léger, The 52, 53. 83St Paul's Church bells 234St Vincent, Italy 30, 230Salisbury races 80Salles ordinaire. Sporting

Club, Monte Carlo 209Salles privées. Sporting Club,

Monte Carlo 209Salon de l'Europe, Sporting

Club, Monte Carlo 209San Francisco 26San Remo 230Sands, The, Las Vegas 213Santa Amaro 84Saratoga (see Pope Joan) 173Saturn 10'sawdust' joints 213Scarne, John 39. 119Scarne 's New Complete Guide

to Gambling 39, 119Sceptre 53Schmidt, Helmut 24Schultz, Dutch 21, 27, 97Scotland Yard 224Sea Bathing Society and

Circle of Foreigners 198Sea Bird II 53, 54, 60Second World War 103, 115,

144Secretariat 62, 62Selfridge, Gordon 28, 29Sellers, Peter 180, 215Sergeant Murphy 52Shakespeare, William 40Sharif, Omar 160Sharkey, Tom 26Sheep Has Five Legs, The 235sheshbesh 779

shimmy (see chemin de fer)118

shoe 117, 118, 122Shoot, or Slippery Sam 172Short, Luke 26Short Treatise on Whist, A 147shut-the-box 148Siegel. Benjamin 'Bugsy' 21.

20X.2W. 209, 211. 213Siever, Robert 67Signorinetta 53Silver Bell 50Sims, Hal 189Sinatra. Frank 217Sir Ivor 53Skol Sprint 68'sleeping' numbers, roulette

127Slippery Sam, or shoot 172slot machines 46, 103-106,

105, 106, 107Monte Carlo 209Puerto Rico 232USA 46, 211,217

snap 33snooker 192, 795soccer 72-78Société des Bains de Mer et

Cercle des Etrangers 27,198, 206

Society for Psychical Research24

South Africa 230Southern Sun Hôtel

Corporation 180Soviet Union 15Spain 21,230spatula 776split hand, blackjack 150splitting, blackjack 155splitting hairs, blackjack 151spoof 187-188Sporting Club, The, Monaco

206Sporting Life, The 82'stand', pontoon 161Stardust, The, Las Vegas 213starting price 59steeplechasing 52Stewards Cup 53'stick', pontoon 161stickman, craps 108Sting, The 159straight, general 183straight, poker 162straight draw poker 162straight flush, poker 162straight win, backgammon

178Streisand, Barbra 217Strip, the, Las Vegas 213, 217,

218.222stud poker 162

stud poker, strategy 166sugar cubes 235suicide rate, Las Vegas 221Sultan 83Sun Chariot 53Sunday Pictorial 24Sweden, Miss 240sweepstakes 97, 238Sydney, Australia 50, 64Sydney Cup 65systems 18, 22,46

TT.A.B. (see Totalisator

Agency Board) 65tableau des voison, roulette

127Tacitus 8Tantieme 60tarotpack 11, 13, 14, 15tax 45, 54, 59tennis 80tennis champion 50theory of probability 33thimble-rigger 52Thorp, Edward O. 152three bags problem 37three card trick 13, 240three thimble game 240threes, poker 162Thunderbird, The, Las Vegas

213Tiresias 83tireur 118tombola 99Tombstone 26Top Rank Bingo and Social

Club 99Torrio, Johnny 209Totalisator Agency Board

64, 66, 65Tote 16,44,45,54,55, 56,57,

59,64tickets 5*

Tote, Hialeah 61Touquet. le 28Tour de France 68, 70Tour, George de la 92tourneur, le, roulette 123Train Robbery 234training for bookmakers 58Tranby Croft 85, 85, 86Trans-American Wire Service

213Transversale plein, roulette

125simple or sixaine 125

trapeze acts (see Circus-Circus) 218

treble, a 56tremble chance 74

trente et quarante 18, 122.722, 735

Monte Carlo 209tric-trac, backgammon 173,

174triellas 65triple, the 64Triple Crown 53, 62, 62Trodmore Hunt 82Tropicana 213, 217Troy 50Tunbridge Wells 135Tunisia 230Tuscany, Grand Duke of 36twenty-one, pontoon 161'twist', pontoon 161two pairs, poker 162Two Thousand Guineas,

horse racing 52, 53two-up 143uUgly Buck. The 83under and over seven 115, 115unfair games 44United States of America 21.

22up and down bet, horse

racing 56Ur. Mesopotamia 8

YVagliano. Athanese 27. 28Vaguely Noble 60Vanderbilt, Harold S. 170Vanderbilt W.K. 203van John, see vingt-et-un 146'Vegas Vie' 203Venice 230Victoria, Queen 85Villafranca, Duchess of 206vingt-et-un 146

or pontoon 161vingt-trois 138

Isle of Man 226Volstead Law 21wWales, Prince of 85, 85, 86,

86, 203Walford. Roy 83Walpole, Horace 234Warner, Jack 30Waterloo Cup, Altcar 69Washington International 60,

63invitation race 62

wei-ch'i 8, 189Wellington bid, Napoleon

169Welles, Orson 215Wells 30Wells, Charles 26, 27Werribee, Melbourne 45Westminster. London 226What. Mr 24whist 147, 155. 190White's Club. London 25,

234, 235Wiesbaden 230Wild West 25Willard. Jess 72. 72Williams. General Owen 86William Hi l l Bookmaking

Organization 58, 238Wimbledon 50, 80, 80win bet, craps 109win, couplé 61Wolfsheim, Meyer 86, 87Women's Institute 190Wood, Alexander 84World. Miss, contest 240World's Series 86, 88, 88wrong bet, craps 108

Yyacht, see also general 183,

184Yale 78, 80Yankee bet. horse racing 55.

56Yankees, the 78Yarmouth. Lord 25Yemen 52York 53York. Archbishop of 235Yugoslavia 15,230

IZaharoff, Basil 203, 206Zeus 8Zographos, Nico 27, 28, 115,

173, 226

255

i

AcknowledgementsReading from left to right and from top to bottom

Page 6/7 Photoresources ; 8/9 Photoresources; 10 Photoresources;11 Mary Evans Picture Library; 12/13 Mary Evans Picture Library:13 American History Picture Library; 14 Spectrum Colour Library;15 Spectrum Colour Library, Mary Evans Picture Library; 16 TheHamlyn Group/Exchange Telegraph; 17 Novosti Press Agency; 18The Hamlyn Group; 19 courtesy Gamblers Anonymous; 20 MaryEvans Picture Library; 21 Freelance Photographers" Guild. AmericanHistory Picture Library, Freelance Photographers' Gui ld: 22 MaryEvans Picture Library; 24/25 Mary Evans Picture Library; 26 WesternAmericana; 27 Radio Times Hulton Picture Library; 28/29 RadioTimes Hulton Picture Library. Popperfoto; 30 John Kobal; 31 CameraPress; 32 The Mansell Collection; 36 The Mansell Collection; 38 TheMansell Collection; 45 The Hamlyn Group, Racing InformationBureau. Australian Information Service; 49 Moira Clinch: 50 51Michael Holford; 52 Cooper Bridgeman/British Museum, Mary EvansPicture Library; 53 Ron Hammond. Gerry Cranham; 54 The HamlynGroup/Associated Press; 55 Popperfoto; 56 Spectrum Colour Library,Picturepoint; 57 Picturepoint; 58 Camera Press. Horserace TotalisatorBoard; 59 Camera Press; 60 Mike Busselle. Gerry Cranham; 61 Zefa;62 American History Picture Library. The Hamlyn Group/AssociatedPress; 63 The Hamlyn Group, Associated Press; 64 Zefa, Picture-point (below left), Spectrum Colour Library; 65 AustralianInformation Service; 66/67 Australian Information Service. TheHamlyn Group/Colorsport; 68 Capital Press; 69 Leo Mason, ChrisSteele-Perkms; 70 Zefa; 70/71 National Film Archive: 72 RadioTimes Hulton Picture Library, Keystone; 72/73 Associated Press;74 The Hamlyn Group/Littlewoods Pools; 75 Littlewoods Pools;76 Littlewoods Pools; 77 Littlewoods Pools: 78 79 Photri;80 Leo Mason. Camera Press/Les Wilson; 81 American HistoryPicture Library; 82 Mary Evans Picture Library; 83 MansellCollection; 85 National Portrait Gallery; 86 Radio Times HultonPicture Library; 87 American History Picture Library; 88 FreelancePhotographers' Guild; 89 Mike Busselle; 90/91 Mary Evans PictureLibrary; 92 Mary Evans Picture Library; 92/93 Cooper Bridgeman/Teesside Museum. Cleveland: 94 M a r y E\ans Picture L ib ra ry ; 94 95The Hamlyn Group; 96 John Topham Picture Library, FionnbarCallanan; 97 Freelance Photographers' Gui ld; 98 Mary Evans PictureLibrary: 99 Camera Press/Peter Mitchel l ; 100 Western AmericanaPicture Library; 104/105 Chris Steele-Perkins; 106 Homer Sykes;107 Homer Sykes; 1 1 0 / 1 1 1 Camera Press/N Farbman; 116 MikeBusselle; 120/121 Western Americana Picture Library; 124 Zefa; 126Curzon House Club; 127 Crockfords' Club; 129 Mike Busselle; 130Crockfords' Club; 130 131 Palm Beach Casino; 132 133 Mike Busselle;134/135 Mary Evans Picture Library; 136/137 Photri; 140/141 Photri;142/143 Robert Estall; 143 Spectrum Colour Library; 144 Picture-point ; 145 Cooper Bridgeman; 146/147 Mary Evans Picture Library;148 John Topham;Fotogram, Mike Peters; 148/149 Mike Peters; 152Cooper Bridgeman/Private Collection; 152/153 Cooper Bridgeman,British Museum; 156/157 M.G.M.,Cinema Bookshop; 158,159 CinemaBookshop; 160 Popperfoto; 164/165 Homer Sykes; 167 SpectrumColour Library; 170/171 Homer Sykes; 174/175 Mary Evans PictureLibrary; 176,177 Mary Evans Picture Library; 178 Spectrum ColourLibrary; 179 Spectrum Colour Library: 180,181 Camera Press/JanKopec: 182 Camera Press; 186/187 Bill Holden; 189 Homer Sykes;190/191 Spectrum Colour Library: 192 Homer Sykes; 193 MikeBusselle; 194 Zefa, Mary Evans Picture Library; 194/195 RadioTimes Hulton Picture Library; 196,197 Spectrum Colour Library;198 The Mansell Collection; 198,199 Mary Evans Picture Library;200/201 Mike Busselle: 202 Keystone; 203 Popperfoto, 204/205Spectrum Colour Library; 206/207 The Bettmann Archive; 208 MoiraClinch; 209 American History Picture Library; 210 WesternAmericana Picture Library; 211 Camera Press; 212 /213 WesternAmericana; 214 John Kobal; 215 National Film Archive,, M.G.M.,John Kobal; 216 Mary Evans Picture Library; 217 Mansell Collection;218 Mansell Collection; 219 Historical Picture Service; 220,221Camera Press/Les Wilson; 221 Playboy Club; 222 John TophamPicture Library/Fotogram; 223 Picturepoint; 224 225 Spectrum ColourLibrary: 226,227 Zefa; 228/229 Spectrum Colour Library; 230/231Camera Press;P Morin; 232 Picturepoint; 233 Bill Holden; 234Historical Picture Service; 235 Western Americana Picture Library;236 237 John Kobal: 238/239 Camera Press; 240 Keystone

Bibliography

As befits a fascinating pastime which is at the same timea big business, gambling has inspired many books,varying from the dispensable to the necessary. Thepresent author acknowledges a debt to most of the bookslisted below. All of them are enjoyable and authoritative.

The most comprehensive is Scarne's Complete Guideto Gambling, published in 1961 and revised and re-issuedas Scarne's New Complete Guide to Gambling in 1975.This is published by Simon and Schuster in New York,and Constable in London.

For the clearest exposition of the rules and playingstrategy of more than 500 games played with dice, cards,boards and counters, The New Complete Hoyle byAlbert H. Morehead, Richard L. Frey and GeoffreyMott-Smith is especially valuable. This was publishedby Doubleday, New York, in 1964.

Casino games are described by Barrie Hughes inThe Educated Gambler, published by Stanley Paul,London, in 1976. The Casino Gambler's Guide by AllanN. Wilson, published by Harper and Row, New York,in 1971, is a penetrating analysis. Beat the Dealer byEdward O. Thorp, is subtitled 'A Winning Strategy forthe Game of 21'. It caused anxiety among Las Vegascasino owners, and amendments to the method ofplaying blackjack, when it was published by Blaisdell,of New York, in 1962.

Gamblers' Handbook by E. Lenos Figgis was publishedin 1976 by Hamlyn, London, and Domus Books,Northbrook, Illinois. This work covers the arithmetic ofgambling and the various gambling activities with a lotof useful statistics and tables. The same author'sChallenge to Chance, published by Arco Publications,London, in 1957, uses the device of fictional charactersplaying poker and roulette and discussing other gamblingpastimes to impart good advice in an entertainingmanner.

The history of gambling and games is told by AlanWykes in Gambling, published by Aldus Books, London,in 1964.

The life and times of the Greek Syndicate and thegolden era of baccarat at Deauville from 1922 onwardsare recreated by Charles Graves in None But the Rich,published by Cassell, London, in 1963. The developmentof the Monte Carlo casino is the subject of The BigWheel subtitled 'Monte Carlo's Opulent Century', byGeorge W. Herald and Edward D. Radin, published byWilliam Morrow, New York, in 1963 and Robert Hale.London, in 1965. The growth of Las Vegas, withparticular reference to the way casinos were manipulatedby the underworld, is described by Ed Reid and OvidDemaris in The Green Felt Jungle, published by TridentPress, New York, in 1963, and Heinemann, London, in1965.

An account of the theory of probability and thestatistics of chance is Lady Luck by Warren Weaver,published by Educational Testing Services, Inc., U.S.A.,in 1963 and in Britain by Heinemann EducationalBooks, London, 1964 and Pelican Books,Harmondsworth, 1977.

Good sense on getting the most for your money is thetheme of Oswald Jacoby on Gambling, published byHart. New York, in 1963.

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The encyclopedia of gambling - University of Calgary PRISM

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