On Scoring in Games

Abstract

The purpose of this paper is to consider the question: if p is the probability that a player P will win a given rally against a player Q, what is the probability that P will win a given game? The answer, of course, depends upon the method of scoring; and the methods considered here will be those used in squash and, for comparison table tennis.In table tennis P earns a point each time that he wins a rally. But in squash he must serve the rally that he wins in order to gain a point; and he relinquishes the service when he loses a rally that he serves.

A Statistical Investigation of Squash

“…The expected duration results were in agreement with those of Watson (1970) and Clarke and Norman (1979), each of whom used a two-dimensional approach. However, the advantage of the three-dimensional approach is that it allows for the expected number of handouts to be calculated and the importance of all the states to be evaluated.…”