BELIEF IN LUCK

Waipa Post, Volume 43, Issue 3391, 22 December 1931, Page 7

BELIEF IN LUCK

MAN’S POWERS OF SELF-DE-CEPTION. Recent cable messages from London have described the excitement in Dublin in connection with the drawing of the Irish sweep on the Liverpool November Handicap, in which the prizes distributed totalled a sum of nearly £2,000,000. Such a huge sum of prize money is impressive; but what is more astonishing to the mathematical mind is the way in which the public continue to buy tickets in sweeps and lotteries, when the odds against winning even a small prize are very great. Mr Norwood Young, in discussing the average man’s powers of self-de-ception in regard to his prospects o± winning a big prize in a lottery or a swt ep in which he has bought a ticket, writes as follows in his little book, “ Fortune,” which is one of the “ Today and To-morrow ” series, published in London:—

“ The buyer of a lottery ticket knows that he is only one of a large number of persons theoretically equal to himself, but he thinks that he has a better chance than any other ticket holder. However clearly he may see that he is only one of a thousand, he buys the ticket because he feels that there is something in him which no other man has. All staking is governed by the expectation of winning. There may be anxiety, fear, despondency; but they are overcome by a secret conviction that the staker is on terms of special intimacy with the scheme of things. This egotism is the ultimate inspirer of all appeals to the goddess Fortune. Few will admit that they have been fortunate in life. Most men, however successful they may have been, suppose that they have not received the rewards that are their due; that they have merits which their fellows have not perceived. They feel that when Fortune is appealed to the pangs of despised worth will be exchanged for the crown of divine recognition. Every staker believes that the risk of loss which affects the mass of the people is in his own case overborne by a special, individual, gift of luck. If he did not think so, he would not risk his money.” POPULAR FALLACIES.

Most people who “ invest ” in lotteries or sweepstakes are under the delusion that the longer they continue to put money into such ventures the more chance they have of winning a prize eventually. But it is a mathematical fact that the odds against winning a prize in a thousand sweeps are exactly the same as the odds against winning a prize in the first sweep in which the gambler buys a ticket. That is to say, he may go in for a thousand sweeps without reducing the odds against winning a prize, provided the number of tickets in each sweep and the number of prizes do not vary. For instance, the chance of winning a prize in a sweep of 100,000 tickets, in which there are 800 prizes, is 124 to 1; and the odds remain the same no matter how often the investor ” goes in for a sweep of that kind, provided he buys only one ticket in each sweep.

For the same mathematical reason the odds against a coin spun in the air showing “ heads ” or “ tails ” when it falls are always the same. Most people believe that after a coin has shown “ heads ” half a dozen times the odds are in favour of the next throw being “ tails.” But this is a delusion. A sequence of a hundred or a thousand “ heads ” would not alter the fact that it is even money against the next throw beirig “ tails.” The same irrefutable mathematical logic applies to roulette, one of the simplest of the gambling games which is played at Monte Carlo and other European casinos. The roulette wheel is divided into 37 stalls, numbered from zero to 36 inclusive; and they are coloured alternately red and black, except zero, which has no colour. The even chances, so called because a successful bet upon one of them earns the value of the stake, are red against black, odd numbers against even, and the first eighteen numbers against the second eight-

een. _ '"IW&W. ' >• “ The visitor to the gambling rooms at Monte Carlo will notice that many of those seated around the .tables mark the result of each throw in a note book, or on cards obligingly printed and supplied by the .authorities of the Casino,” writes. Mr Long. “ If the use oftsthese cards ! gave the staker any adv<%ge, they would not be so readily ; -;him; but that reflection, even when put before the note-taker, makes-no impression upon him. His industry is; m fact, wasted; he believes-that by noting the results that have • been ; obtained he may be able to foretell the results fjjat will be obtained. This is the, ' Iflgk delusion upon which the prosof Monte Carlo depends. Among who are unable , to cast off .its influence, who may be seen recording with care what they; see occurring, m order to deduce therefrom what will occur, are some of the ablest men of the day. It is a strange spectacle, for a reflection would enable them to perceive that » a S^me of chance the past cannot affect the - • IsKsi®

future—that each spin is separate, unaffected by what has gone before—is, in fact, incontestible, certain, sure —and incredible; for it means that if red has appeared once, ten times, a hundred times, the next throw is as likely to be red as black. It is frankly difficult to believe that the complete failure of red (or black) to appear at the roulette tables at Monte Carlo for a whole year is as likely a result as any other. Very few, indeed, would be able to resist the conclusion that such an eventuality would be conclusive proof that the machinery was out of order. Yet a run of red continued for a year is not only possible with a perfectly-balanced machine, but its ultimate occurrence, if the trial is prolonged, may be confidently expected. It is not certain, for in games of chance there cannot be any certainty; but we know of no cause which could prevent a perfect machine from confining itself for a year to red and ignoring black altogether.” But in actual fact the longest run of any one colour at any of the roulette tables at Monte Carlo in the history of that great gambling centre, which dates back to 1878, is 26. Why has there never been a sequence of 27 reds or blacks ? Mr Long’s answer is that “ A series of 26 repetitions of a colour should occur once in about 67,000,000 throws, and a series of 27 once ini about 134,000,000 throws.” It has been roughly estimated that since the Casino at Monte Carlo was opened in 1878 there have been about 100,000,000 throws or spins of the roulette wheel. Therefore the recorded occurrence of a run of 26 reds and the non-occurrence of 27 is in accordance with mathematical expectations. MATHEMATICAL EXPERIMENTS. From time to time men of scientific eminence have studied the records of the roulette wheel at Monte Carlo, as recorded in “ Le Monaco,” for the information of gamblers who want to compile winning *' systems ” of staking their money. Professor Karl Pearson, of London University, studied these roulette records over a period of eight weeks. His study covered 33,000 spins of the wheel, and he found that the actual proportions of red and black were not unexpected, but that alterations and long runs were much in excess of what one would expect. On the other hand, Dr Karl Marbe examined the records of 80,000 roulette spins at Monte Carlo and elsewhere, and, unlike Professor Pearson, found that the long runs Were much fewer than a mathematician would expect. Mr J. M. Keynes, commenting on these opposing conclusions in his “ Treatise on Probability,” states that m both cases the results are relevant only to the defects in the tools with which the data for the investigations were obtained.

Comte de Buffon, the famous French naturalist who lived in the eighteenth, century, tossed a coin into the air 4066 times (with the welcome assistance of a small child),.and found that it turned up “ heads ” 2048 times and “ tails ” 1998 times. A pupil of Professor Augustus di Morgan, the English. mathematician, tossed a coin 4098 times, and got 2044 “ tails ” and 2044 “heads.” In 1887 Quetelet drew 4096 balls from an urn, replacing them each time, and recorded the results at different stages, in order to show that the precision of the results tended to increase with the number of experiments. He drew altogether 2066 white balls and 2030 black. William Jevons, the British economist, made 2048 1 throws with ten coins at a time, and recorded the proportion of “heads” at each throw and the proportion altogether. Of the total! number of 20,480 single- throws, he obtained “heads” 10,353 times. Wolf, the Swiss astronomer, carried out similar experiments to an extent that; .has dwarfed the efforts of his predecessors. He threw two dice 100,000 times - and recorded the results. Subsequently, he threw two dice 20,000;times; and four, dice 10,000 times. / He' studied' particularly the number;, of. sequences with each dice, and the; -relative fre- , quency of each of the 36 eombinations of the two dice in the;2o,ooo throws. He found that the sequences were somewhat .fewer titan they ought to have been, and the relative frequency of the different: combinations very different indeed-from what one would expect. “ The explanation of this is easily found,”, comments Mr Keynes, “for the records;.^!. the relative frequency of each face, show that the dice must have irreplar,' the six face of tne ?white, dice, for example, cent more often than the four fape of the same dice. This, then,' is the sole conclusion of all these ipfleiisely laborious experiments-Mhat yvfejlf’s dice were ;• very ill-made.” WINNING SYSTEMS. All the systems oVer which gamb-; lers pore in the -hope of finding one which will win them a fortune are utterly fallacious, in regard to- games, of chance, because in such games what has happened in the past pannot affect the future. At ..Monte Carlo books containing many systems jlze on sale everywhere in the town, and at the Casind'itself. “V/hen Pa- . . . mm Mm

>, I mille Blanc (son of the founder of the - Casino at Monte Carlo) was in the 2 plenitude of his power, and ruled t Monte Carlo like a benevolent auto- , crat, there was nothing that pleased 3 him more than to hear of a new sys--3 tem,” writes Mr Charles Kingston in 2 “ The Romance of Monte Carlo.” “It > was said that he produced the Inter- }• national Sporting Club because he i hoped it would become the resort of - wealthy gamblers with a system to ■ play, which required quieter surroundi ings than the Casino itself afforded, ■ and that a little extra comfort and : luxury would make them bolder and r more avaricious. Years ago there used 1 to be an under-sized Frenchman, bald- , headed and obese, who had been a noted gambler in his middle age, and , had parted from a fortune at trente-et-quarante, and now existed on the small wages attached to the position ; of hotel clerk. Camille Blanc was , fond of pointing him out to his friends as the only man who had made money out of systems. When the inevitable question, ‘ How does he do it ? ’ was asked, the answer was given with a chuckle, ‘He sells them.’ It is indeed the only way of turning system to profitable account, for, just as men will purchase hair restorers from a bald-headed barber, so will gamblers buy systems from those who have been ruined by them.” “ MONTE CARLO” WELLS. Some readers will remember the music-hall song, “ The Man Who Broke the Bank at Monte Carlo,” which was first sung in London in 1891 by Chas. Coborn, in connection with the sensational stories in the English newspapers of the phenomenal winnings of Charles Wells, who broke the bank at Monte Carlo Casino many times in the space of a fortnight, through a remarkable run of luck, and was christened by the newspapers “ Monte Carlo ” Wells. He had collected £4OOO by means of a series of- swindles in England, where he had previously served a term of imprisonment, and he arrived at Monte Carlo in July, 1891, when the season was at Its height, and won £IO,OOO on his first visit to the tables. He came back on the following morning, and in less than an hour broke the bank —that is, Won the 100,000 francs (then worth £4000) with which each table started the day. When the table was again furnished with funds Wells broke the bank again in less than half an hour. His success, which continued with slight interruptions for a fortnight, created a sensation at the Casino, and gamblers of both sexes flocked round the table at which he was seated, and flung their money on numbers which he backed. Others fought to get near_ him in order to touch him for luck. He was a man of vulgar manners, who could not use the King’s English grammatically, but he was courted by the European aristocracy asserhbled at Monte Carlo, in the hope that he ( would divulge his system. '• Experienced gamblers studied his play, and so did members of the staff of! the Casino, but they could not discover his secret. As a matter of fact, he had no system beyond the hackneyed one of “coup des trois,” which consists in allowing a stake to accumulate until three successive wins have been recorded, and then withdrawing the lot. This system has ruined many a gambler, but it favoured Wells. It was supposed that he had some subtle manner of staking which eluded those who studied his play. He always pretended he had an infallible system, but in reality his success was due to an extraordinary run of luck. Wells went back to Monte Carlo in the following year in a private yacht, with a large party of friends, but on this occasion his luck failed and .he lost heavily. He went back to. England, .and in the following year was made a. bankrupt, with liabilities of £35,000 and negligible assets. Thirteen years later he stood in the dock .£t\the?6ld Bailey, London, in company with an unfrocked clergyman named Moylel-|They were charged with fraud and false pretences in connection with a get-rich-quick scheme. Wells was sentenced to three years and his companion to eighteen months. Wells to Paris after his release, floated another get-rich-quick scheme out of which he netted £40.000. He was sent he invested in annuities. He was sent to prison for five years, and his creditors took over his annuities. When they learned after his release that he was in a state of destitution they allowed hlmi £1 a week that he might continue to live and thereby enable them to draw the annuities. He died in Paris in 1922 at the age of 81 years. f