It should be noted that this duration is considerably longe… - William Feller

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It should be noted that this duration is considerably longer than we naively expect. If two players with 500 dollars each toss a coin until one is ruined, the average duration of the game is 250,000 trials. If a gambler has only one dollar and his adversary has 1000, the average duration is 1000 trials.

William Feller

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About William Feller

William "Vilim" Feller (July 7, 1906 – January 14, 1970), born Vilibald Srećko Feller, was a Croatian-American mathematician specializing in probability theory. Feller was one of the greatest probabilists of the twentieth century, who is remembered for his championing of probability theory as a branch of mathematical analysis in Sweden and the United States.

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Native Name: Vilibald Srećko Feller

Alternative Names: Vilim Feller

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Richard von Mises Richard Arnold Epstein William Poundstone Ivars Peterson Leonard Mlodinow

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It is seen that continued shuffling may reasonably be expected to produce perfect "randomness" and to eliminate all traces of the original order. It should be noted, however, that the number of operations required for this purpose is extremely large.

In stochastic processes the future is not uniquely determined, but we have at least probability relations enabling us to make predictions.

Physical irreversibility manifests itself in the fact that, whenever the system is in a state far removed from equilibrium, it is much more likely to move toward equilibrium, than in the opposite direction.

It should be noted that this duration is considerably longer than we naively expect. If two players with 500 dollars each toss a coin until one is ru… - William Feller

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