Jas. 13, 1SS2.] 



KNOWLEDGE 



223 



The mistake made by my friend on this occasion is one 

 of the commonest fallacies respecting the laws of chance. 

 Of course, it requires no mathematical knowledge or reason- 

 ing to show the opinion to he quite erroneous that past 

 events can in any way inliuenee events which are of their 

 very nature entirely independent of them. If there is an 

 urn in which we know that there are a number of white 

 and a number of black lialls, and we draw one after another 

 several white balls, 7wl reticrniiitj (hem, we have some 

 reason for thinking that ■we are more likely to draw 

 a black ball at the next trial, for every white ball 

 drawn diminishes the chance that the next one drawn 

 will be white. But if each ball after being drawn is 

 replaced, it is evident that the chance of drawing a white 

 ball at any given trial must be the same as that of drawing 

 it at the first or at any other trial. Or take the tossing of 

 a coin. Antecedently it seems so unlikely that head (say) 

 will be tossed ten times running, that we can easily imagine 

 how anyone who had tossed head nine times running might 

 entertain for a moment the idea that he was less likely 

 to to.'^s head the tenth time. But if he had any reasoning 

 power at all, and used it, he would see that no number of 

 past trials could in any degree affect the next tossing. 



There is a fallacy equally common, and held commonly by 

 the same persons who make the mistake just considered, 

 which yet is opposite to it in character — in fact, directly 

 contradictory to it. Tlie mistake we have dealt with above 

 may be called belief in the change o£ luck, and in a some- 

 what disguised foriii it is this foolish fallacy which leads 

 the weak-minded piceon to fall an easy prey to the rooks, 

 from the fond delusion, in whicii, of course, they encourage 

 him, thst though he has lost — or rather because he has lost 

 for a long time — he must presently begin to win. The 

 fallacy we have next to mention is faith in luck. You will 

 hear people say tliat they never have luck in games of 

 chance, or that they always have luck ; and you will find 

 hundreds ready to believe in the good luck or bad luck of 

 others. We say that this belief is contradictory to the 

 other. If it Ije considered for a moment, this is seen 

 to be the case. \Miat does belief in a man's good or 

 bad luck mean but that, because he has been foi'tuuate 

 or unfortunate for a long time he will continue to be so ? 

 and what does the other belief mean but that, because the 

 luck has been one way for a long time, it will no longer 

 continue to be so ? One would suppose that two ideas so 

 incompatible with each other could not exist in company ; 

 that everyone must see one or other to be fallacious, or 

 (which, of course, Ls the actual case) that both are so. 

 Both views are in fact ridiculous, though both, with many 

 other equally preposterous superstitions, are entertained by 

 persons who are not supposed to be wanting in keenness of 

 perception, and in other matters are intelligent enough. 

 Here, for instance, is an account given by one keen card- 

 player of another who was as keen, or keener. " He was 

 very particular about cutting the cards ; he always insisted 

 on the pack Ijeing perfectly square before he would cut, 

 and that they should be placed in a convenient position. 

 There is an old adage that a slovenly cut is good for the 

 dealer, but whether there is truth in the statement 

 we know not. He was superstitious to a degree that was 

 astonishing." (It must be a rather startling superstition 

 that would seem astonishing to a man who could gravely 

 ask whether there is any truth in the preposterous adage 

 just quoted.) " We are not aware that any one has ever 

 attempted to solve the problem why so many great minds " 

 (among card-players, fighting men, and men who have to 

 work much at odds ^\^th fortune) " are superstitious. This 

 is not the time or place to attempt that solution. We 

 record the fact He believed in dress ha^'ing something to 



do with luck, and if the luck followed him, he would wear 

 the same dress, whether it was adapted to the weather or 

 not. He believed in cards and seats. He objected to any 

 one making a remark about his luck. He had the strongest 

 objection to our backing him, because of our bad luck, and 

 we have often had to refrain from taking odds, because of 

 this fad. He was distrcss(!d beyond measure if any one 

 touched his counters. His constant system of shuiiling 

 the cards was at times an annoyance." This was a great 

 card-player. 



It will be asked, perhaps, how cases of notoriously 

 lucky men are to be accounted for, if there is no such 

 thing as luck. If the laws of probabilities say that no., 

 man can be regarded as a lucky or unlucky man in matteis. . 

 of pure chance, how is it that so many men have been. 

 lucky or unlucky 'i But science by no means denies that 

 men have been or will be lucky or unlucky ; on the con- 

 trary, the laws of probability can prove that among the 

 millions who try their fortunes in matters of pure chance, 

 thousands must be exceptionally lucky or unlucky, and a 

 few must have luck perfectly marvellous to all who witness 

 it. Given the nature of any chance game and the num- 

 ber who play at it, science can tell, within very narrow- 

 limits of error, how many will have ordinary luck, how 

 many will have moderately good, or moderately bad luck, 

 how many will be very lucky or very unlucky, and how- 

 many will have absolutely astounding luck of one sort or- 

 the other. When Science is asked how, with her absolute 

 rejection of all faith in luck, she can account for men who 

 have had amazing runs of good or bad luck, Science can 

 reply not only that she has no difliculty in accounting for 

 them, but that she can prove this to be to all intents and 

 purposes inevitable. 



What, then, is it that science rejects as untenable, or 

 how, with such views, can science be truly said to have no 

 faith in luck ? The answer is, that the laws of probability 

 — and (rightly understood) the laws of common sense — 

 forbid our belie\'ing that a man is either lucky or unlucky. 

 He may have been so ; but, so far as matters of pure 

 cliance are concerned, the man who has been most unlucky 

 is as likely as not to be lucky at any given trial as one who 

 lias been exceedingly lucky. He is not more likely to be 

 so, as the fallacy respecting change of luck implies, nor is- 

 he less likely, as the fallacy of faith in luck implies ; he has 

 simply just the same chance as another, neither better nor 

 worse. 



If twenty million persons in England were to begin 

 tossing a coin, each stopping so soon as he tossed " tail," 

 and each to receive a pound for one head, two for two 

 heads, four for three, eight for four, sixteen for five, and so 

 forth, it is practically certain that several would win a 

 prize of o£131,072 after tossing head eighteen times running, 

 and all but certain that some would get the prize of 

 £262,144 for tossing head nineteen times running, and one 

 or two perhaps the prize of £524,288 for tossing head 

 twenty times running. These would all have been very 

 lucky persons (and as long as they kept their winnings, we 

 may say that they were in luck afterwards as well as before). 

 The laws of probability show that among so many trials 

 there must be some such lucky persons. But, supposing the 

 experiment repeated, science assures us that those persons 

 who had been so lucky would have neither a better nor a 

 worse chance of success than those who had had but moderate 

 luck, or the unfortunates (some ten million in number) 

 who had tossed tail at the first trial. What would be- 

 lievers in the two fallacies we have considered, think 1 If 

 they had watched one of the luckiest tossers, would they 

 say that, as he had tossed head so many times running, he 

 was unlikely to toss a single other head in the second trial 



