AN APPLICATION OF MARKOV-CHAIN ANALYSIS TO THE GAME OF SQUASH

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 po ssibilities) are to be played to determine the winner. This paper cons tructs a Markov chain model of the situation and solves for the optima l strategy. Expressions for the optimal strategy ate obtained with a s ymbolic algebra computer package. Results ate given for both internati onal and American scoring systems. The model and analysis ate very sui table for educational purposes. The resulting Markov chain is small en ough that it can be easily presented in a classroom setting, yet the m odel is sufficiently complex that algebraic manipulation is neatly hop eless. The final results illustrate the power of the combination of ma thematical and computer modeling applied to a problem of practical int erest.