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THE MULTIPLE-PLAYER ANTE ONE GAME

Published online by Cambridge University Press:  17 May 2011

Sheldon M. Ross
Sheldon M. Ross
Affiliation:
Department of Industrial and System Engineering, University of Southern California, Los Angeles, CA 90089 E-mail: [email protected]
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Abstract

Consider a group of players playing a sequence of games. There are k players, having arbitrary initial fortunes. Each game consists of each remaining player putting 1 in a pot, which is then won (with equal probability) by one of them. Players whose fortunes drop to 0 are eliminated. Let T(i) be the number of games played by i, and let T=max iT(i). For the case k=3, martingale stopping theory can be used to derive E[T] and E[T(i)]. When k>3, we obtain upper bounds on E[T] and, in the case in which all players have the same initial fortune, on E[T(i)]. Efficient simulation methods for estimating E[T] and E[T(i)] are discussed.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 25 , Issue 3 , July 2011 , pp. 343 - 353
Copyright
Copyright © Cambridge University Press 2011

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References

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