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run is actually allowed him. It may be a short run, or a fair run, or even a tolerably long run; but the question for him is, will it be long enough ? And note that it is not only
the limitation which the bank may assign to the stakes which we have to consider: the gambler's possessions assign a limit, even though the bank may assign
none.
Let us see, then, what prospect there is that in this, as in the other case, a run of bad luck may ruin the player -or rather, let us see whether it be the case that in this, as in the other system, patient perseverance in the system may not mean certain ruin, which ruin may indeed arrive at the. very beginning of the confident gambler's career.
Instead of alt but certainty of success in each single trial which exists in the simpler case, there is in the case we are considering but a high degree of probability. It is very much more likely than not that in a given trial the gambler will clear the stake which he has set himself to win. (This is why we so often hear strong expressions of faith in these systems: again and again we are told with open-mouthed expressions of wonder that a system of this sort must be infallible, because, says the narrator, I saw it tried over and over again, and always with success.) Granted that it is so; indeed, it would be a poor system which did not give the gambler an excellent chance of winning a small stake, in return for the risk, by no means evanescent, that he may lose a very large one.
Observe, now, how the chances for and against are balanced between the two systems. Suppose such a run of ill-luck as in the simpler system would mean absolute defeat, because of the rapid increase (by
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