An Application of Markov Chain Analysis to the Game of Squash*

Authors


  • *

    We would like to thank Will Carlin, 1989 winner of the U.S. National Soft Ball Championship, for suggesting this problem and for his helpful comments.

  • Mark Broadie is an Associate Professor in the Graduate School of Business at Columbia University. He received his Ph.D. in operations research from Stanford University. His current research interests are in portfolio management, option pricing, and term structure modeling. He also plays an occasional game of squash.

  • Dev Joneja is an Associate Professor in the Graduate School of Business at Columbia University. He received his Ph.D. in operations research from Cornell University. His current research interests are in production and operations management, inventory control, and logistics. His work has been published in a number of journals including OR Letters and Operations Research.

ABSTRACT

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.

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