Racquetball as a Stochastic Process

Racquetball, volleyball, squash, and badminton are games in which one player (or team) serves, points are won only when serving, and the winner of a rally serves the next one. Generally, winning a point enhances the probability of winning the next point, since the opponent is at the disadvantage of having to win back the serve before having a chance to score. This scoring feature tends to make game scores lopsided in favor of the stronger player. Probabilistic aspects of these games have been considered by ApSimon [1951, 19571, Hsi and Burych 119711, Marcus [19851, Strauss and Arnold [1987], and Simmons [19891. We summarize the Markov model approach, note some results known for games to a fixed score, and extend those results to games in which the winner must win by at least two points.