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An Application of Markov Chain Analysis to the Game of Squash *
Author(s) -
Broadie Mark,
Joneja Dev
Publication year - 1993
Publication title -
decision sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.238
H-Index - 108
eISSN - 1540-5915
pISSN - 0011-7315
DOI - 10.1111/j.1540-5915.1993.tb00501.x
Subject(s) - markov chain , computer science , set (abstract data type) , mathematical optimization , squash , symbolic computation , theoretical computer science , mathematical economics , machine learning , mathematics , programming language , mathematical analysis , archaeology , history
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.