# Tennis with Markov

by Roman Wong (Washington and Jefferson College) and Megan Zigarovich (Washington and Jefferson College)

College Mathematics Journal
January, 2007

Subject classification(s): Statistics and Probability | Probability
Applicable Course(s): 3.8 Linear/Matrix Algebra | 6.1 Probability & Statistics

In the game of tennis, if the probability that player $$A$$ wins a point against player $$B$$ is a constant value $$p$$, then the probability that $$A$$ will win a game from deuce is $$p^2/(1 - 2p + 2p^2)$$.  This result has been obtained in a variety of ways, and the authors use a formal Markov chain approach to derive it.

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Capsule Course Topic(s):
Linear Algebra | Application: Markov
Probability | Stochastic Processes, Discrete Markov Chains