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a certain seemingly small, but in reality decisive, advantage in favor 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 favor of the player winning a certain insignificant sum; but, per 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--supposing, that is, that he continues the game with steady courage up to that final doubling which closes his gambling 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, he 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 1,024 times, which would either mean ruin or a sudden foreclosure On the
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