It is an indubitable result of the theory of probabilities that every gambler, if he continues long enough, must ultimately be ruined. Suppose he tries the martingale, which some believe infallible, and which is, as I am informed, disallowed in the gambling houses.

In this method of playing, he first bets, say, $1; if he loses it he bets $2; if he loses that he bets $4; if he loses that he bets $8; if he then gains, he has lost 1 + 2 + 4 = 7 and has gained $1 more; and no matter how many bets he loses, the first one he gains will make him $1 richer than he was in the beginning. In that way, he will probably gain at first; but, at last, the time will come when the run of luck is so against him that he will not have money enough to double, and must therefore let his bet go. This will probably happen before he has won as much as he had in the first place, so that this run against him will leave him poorer than he began; sometime or other it will be sure to happen. It is true that there is always a possibility of his winning any sum the bank can pay, and we thus come upon a celebrated paradox that, though he is certain to be ruined, the value of his expectation calculated according to the usual rules (which omit this consideration) is large.

Roman soldiers gambling over Christ’s tunic, detail of *The Crucifixion*, by Andrea Solario, 1503. © Godong / UIG / Bridgeman Images.

But whether a gambler plays in this way or any enough he will be sure sometime to have such a run against him as to exhaust his entire fortune. The same thing is true of an insurance company. Let the directors take the utmost pains to be independent of great conflagrations and pestilences, their actuaries can tell them that according to the doctrine of chances the time must come at last when their losses will bring them to a stop. They may tide over such a crisis by extraordinary means, but then they will start again in a weakened state, and the same thing will happen again all the sooner. An actuary might be inclined to deny this, because he knows that the expectation of his company is large, or perhaps (neglecting the interest upon money) is infinite. But calculations of expectations leave out of account the circumstance now under consideration, which reverses the whole thing. However, I must not be understood as saying that insurance is on this account unsound, more than other kinds of business. All human affairs rest upon probabilities, and the same thing is true everywhere. If man were immortal he could be perfectly sure of seeing the day when everything in which he had trusted should betray his trust and, in short, of coming eventually to hopeless misery. He would break down at last as every good fortune, as every dynasty, as every civilization does. In place of this we have death.

From “The Doctrine of Chances.” In 1870 Peirce proposed the idea of pragmatism—that for any statement to be meaningful, it must have practical application. A friend of William James and a teacher to John Dewey, he was removed from his academic position at Johns Hopkins for living openly with his mistress. In 1891 he retired to his Pennsylvania farm, spending his remaining days on the edge of penury. “The theory of probabilities,” wrote Peirce, “is simply the science of logic quantitatively treated.”

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