Probability in the Engineering and Informational Sciences

Table of Contents - 2011 - Volume 25, Issue 03  

Research Article

THE MULTIPLE-PLAYER ANTE ONE GAME

Sheldon M. Ross

a1 Department of Industrial and System Engineering, University of Southern California, Los Angeles, CA 90089 E-mail: smross@usc.edu

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 i T(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.

(Online publication May 17 2011)