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The probability distribution of the duration of the game in the classical ruin problem
Edi Karni
Journal:

Journal of Applied Probability / Volume 14 / Issue 2 / June 1977

Published online by Cambridge University Press:

14 July 2016, pp. 416-420

Print publication:

June 1977
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This paper develops simple expressions for the exact probability distribution of the duration of the game, and the probability distribution of the duration of the game conditional upon its termination with the gambler's ruin, in the classical ruin problem.

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The probability distribution of the duration of the game in the classical ruin problem