Mark Broadie

An application of Markov chain analysis to the game of squash

Coauthor(s): Dev Joneja.


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If the score in a squash game is tied late in the game, one player has a choice of how many additional points (from a prespecified set of possibilities) are to be played to determine the winner. This paper constructs a Markov chain model of the situation and solves for the optimal strategy. Expressions for the optimal strategy are obtained with a symbolic algebra computer package. Results are given for both international and American scoring systems. The model and analysis are very suitable for educational purposes. The resulting Markov chain is small enough that it can be easily presented in a classroom setting, yet the model is sufficiently complex that algebraic manipulation is nearly hopeless. The final results illustrate the power of the combination of mathematical and computer modeling applied to a problem of practical interest.

Posted here is a working paper version of this article. For the published version, please see Decision Sciences.

Source: Decision Sciences
Exact Citation:
Broadie, Mark, and Dev Joneja. "An application of Markov chain analysis to the game of squash." Decision Sciences 24, no. 5 (1993): 1023-1035.
Volume: 24
Number: 5
Pages: 1023-1035
Date: 1993