An Application of Markov Chain Analysis to the Game of Squash*
构建壁球比赛平局时的马尔可夫链模型，用符号计算软件求解最优加赛策略，结果适用于国际和美国两种计分制，适合教学演示。
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.