Hoyle's Games, Improved And Enlarged - online book

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the former must necessarily win. Thus, if a player has been fortunate enough to win a consi­derable sum on one coup, it will dwindle away in detail; and, vice versa, what he had won in detail, a la martingale, he would lose en yros; for this reason—that of whatever number of coups the martingale may be composed, it will break in a proportion equal to what it may produce.
The number of combinations that may be com­posed in a series of 26 coups is immense. There are no less than 67108864 different ways in which a taille consisting of 26 coups may happen.
Thus, whatever wray we may determine on, there are (67108864—1) other ways, all equally possible. In this number there is but one chance for Noir winning, and one chance for Rouge; one that there may be no interruption commencing with Noir, and one that there may be no interruption commencing with Rouge. It is possible that by dint of tailles these events may sometimes occur; but the period in which we may reasonably look for them is too long ; for supposing 10 tailles per diem, it would require a space of 18500 years to see them once happen.
If a player has had the good fortune to double, triple, or quadruple his martingale, we must not imagine that his system of play is better than an­other, since it is in reality but the same degree of luck as the winning of a paroli et sept et le va, seven times the original stake.
Every progression comes to the same thing; and that which increases the most is nothing more than deeper play. He who imagines that he is only staking a sovereign because the first coup of his martingale commenced with that sum, is in eality playing more deeply than he conceives;
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