December 1, 1886.] 



KNOWLEDGE ♦ 



20 



be futile, because the seas and oceans would be Eolid. 

 Opposing the force which attracts evervthicg into inert 

 union, the solar energy sets up the separative motions, the 

 ceaseless redistributions, which give rise to the grand climatal 

 and vital phenomena of nature. Expanding the air, it causes 

 the inrush to which winds and storms are due ; heating the 

 water, it excites tlie warm currents and draws lieavenward 

 the aqueous vapour, which, driven by the wind, returns, 

 when its energy is lost, as rain and snow, those silent yet 

 mightiest agents of mechanical, chemical, and vital changes. 

 But the full significance of the work done by the sunbeams 

 that strike the earth's surface will appear when we treat of 

 the relation of the living to the not-living. 



Ok, 



MARTINGALES ; 



SURE (?) GAMBLING SYSTEMS. 



Mm 



N previous pages I have considei-ed, under the 

 head of " Gamblers' Fallacies," certain plans Ijy 

 which some fondly imagine that fortune may 

 be forced. I have shown how illusor}' the 

 schemes really are which at first view appear 

 so promising. There are other plans the fallacy 

 in which cannot be quite so readily seen, though 

 in reality unmistakable, when once the conditions of the 

 problem are duly considered. 



Let me in the first place briefly run through the reasoning 

 relating to one of the simpler methods already considered at 

 length. 



The simplest method for winning constantly at any such 

 game as rouge et noir is as follows : — The player stakes the 

 sum which he desires to win, say \L Either he wins or 

 loses. If he wins he again stakes \!., having already gained 

 one. If, however, he loses, he stakes 2/. if this time he 

 wins, he gains a balance of 1/., and begins again, staking 1/., 

 having already won 1/. If, however, he loses the stake of 

 '21., or .'5/. in all (for 11. was lost at the first trial), he stakes 

 ■il. If he wins at this third trial, he is 11. to the good, and 

 begins again, staking 1/. after having already won I!. If, 

 however, he loses, he stakes 8/. It will readily be seen that 

 by going on in this way the player always wins IJ. when at 

 last the right colour appears. He then, in every case, puts 

 by the 11. gained and begins again. 



It seems then at first as though all the player has to do 

 is to keep on patiently in this way, starting always with 

 some small sum which he desires to win at each trial, 

 doubling the stake after each loss, when he pockets the 

 amount of his first stake and begins again. At each trial 

 the s;ime sum seems certainly to be gained, for he cannot go 

 on losing for ever. Sj that he may keep on adding pound 

 to pound, acZ ivjinilum, or until the "bank'' tires of the 

 losing game. 



The fallacy consists in the assumption that he cannot 

 always lose. It is true that theoreticall}' a time must 

 always come when the right colour wins. But the player 

 has to keep on doubling his stake practically, not theoreti- 

 cally ; and the right colom- may not appear till his pockets 

 are cleared. Theoretically, too, it is certain that be the 

 sum at his command ever so large, and the stake the bank 

 allows ever so great, the player will be ruined at last at this 

 game, if— which is always the case — the sum at the com- 

 mand of the bank is very much larger. It woidd be so 

 even if the bank allowed itself no advantage in the game, 

 whereas we know that there is a certain seemingly small, 

 but in reality decisive, advantage in f^ivour of the bank at 

 every trial. Apart from this, however, the longest pocket 

 is bound to win in the long run at the game of speculation 

 which I have described. For, though it seems a tolerably 



sure game, it is in reality purely speculative. At every trial 

 there is an enormous probability in favour of the player 

 winning a certain insignificant sum ; but, j)er contra, there 

 is a certain small probability that he will lose, not a small 

 sum, or even a large sum, but all that he possesses — sup- 

 posing, that is, that he continues the game with steady 

 courage up to that final doubling which closes his gambhng 

 career, and also supposing that the bank allows the doubling 

 to continue far enough ; if the bank does not, then the last 

 sum staked within the bank limit is the amount lost by the 

 player, and, though he may not be absolutely ruined, be 

 loses at one fell swoop a sum very much larger than that 

 insignificant amount which is all he can win at each trial. 



Although this gambling superstition has misled many, yet 

 after all it is easily shown to be a fallacy. It is too simple 

 to mislead any reasonable person long. And indeed, when 

 it has been tried, we find that the unfortunate victim of the 

 delusion very soon wakes to the fact that his stakes increase 

 dangerously fast. When it comes to the fifth or sixth 

 doubling, he is apt to lose heart, fearing that the luck which 

 has gone against him five times in succession may go against 

 him five times more, which would mean that the stake 

 already multiplied 32 times would be increased, not 32 times, 

 but 32 times 32 times, or 1,02-4 times, which would either 

 mean ruin or a sudden foreclosure on the bank's part and 

 the collapse of the system. 



For the benefit of those who too readily see through a 

 simple scheme such as this, gamblers have invented other 

 devices for their own or others' destruction, devices in which 

 the fallacy underlying all such plans is so carefully hidden 

 that it cannot very readily be detected. 



The following is a martingale (as gamblers call these 

 devices for preventing fortune from rearing against them) 

 which has mLsled many : — 



The gambler* first decides on the amount which he is to 

 win at each venture — if that can be called a venture which 

 according to his scheme is to be regarded as an absolute cei'- 

 tainty. Let us say that the sum to be won is 10^. He divides 

 this up into any convenient number of parts, say three ; and 

 say that the three sums making u]) 10^. are 3^., 3^., and U. 

 Then he prepares a card on the annexed plan (tig. 1 ), where 

 w stands for winnings, l for losses, and m 

 (for martingale) heads the working column 

 which guides the gambler in his successive 

 ventures. 



The first part of the play is light and 

 fanciful : the player — whom we will call 

 A — stakes any small sums he pleases until 

 he loses, making no account of any winnings 

 which may precede his first loss. This 

 first loss starts his actual operations. 

 Say the first loss amounts to 2/. : A enters this sum in 

 the third column (see fig. 2) as a loss, and akso in the 

 second under the cross-line. He then stakes the sum of 

 this number, 2, which is now the lowest in column m, and 3, 

 the uppermost — that is, he stakes bl. If he loses, he enters 

 the lost ."i/. in columns m and l ; and next stakes 8/., the 

 sum of the top and bottom figures {ol. and bl.) in column 

 M. He goes on thus till he wins, when he enters under the 

 head w the amount he lias won, and scores out in column m 

 the top and bottom figures — viz., the 3?. (at the top), and 

 the last loss (at the bottom). This process is to be continued, 

 the last stake, if it be lost, being always scored at the 

 bottom of column m, as well as in the loss column, the last 

 win being always followed b)- the scoring out of the top and 



* The account of the system here considered appeared in the 

 Cornhill Magazine under the heading " A San Carlo Superstition," 

 and was in that place described as "a pretty little martingale" 

 recently submitted to me by a correspondent of Knowledge. 



Fig. 1. 



