On the length of winning a tennis game using random walks
Abstract
This article is a follow-up to a previous Gazette article that examined the length of a winning tennis game, as studied by Cooper and Kennedy [2021. Expected length and probability of winning a tennis game. Math. Gaz. 105(564): 490–500. doi:10.1017/mag.2021.117]. Let X denote a random variable representing the length of a tennis game under standard rules. Using random walks, we present simple expressions for the probability distribution P(X=k), the expectation E(X), and the variance Var(X). In addition, we derive the expected values of the maximum and minimum lengths across n games, together with asymptotic approximations for these quantities.
Fields of Study & Subjects
Probability and Statistical Research
Sports Analytics and Performance
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- The Mathematical Gazette
- Volume
- 110
- Issue
- 577
- Pages
- 74–87
- Publication date
- 2 January 2026
- Language
- EN