“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

Source: An Introduction To Probability Theory And Its Applications (Third Edition), Chapter XIV, Random Walk And Ruin Problems, p. 349.

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William Feller30
Croatian-American mathematician 1906–1970

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