Optimal challenges in tennis

The use of technology in sport to assist umpires has been gradually introduced into several sports. This has now been extended to allow players to call upon technology to arbitrate when they disagree with the umpire's decision. Both tennis and cricket now allow the players to challenge a doubtful decision, which is reversed if the evidence shows it to be incorrect. However, the number of challenges is limited, and players must balance any possible immediate gain with the loss of a future right to challenge. With similar challenge rules expected to be introduced in other sports, this situation has been a motivation to consider challenges more widely. We use Dynamic Programming to investigate the optimal challenge strategy and obtain some general rules. In a traditional set of tennis, players should be more aggressive in challenging in the latter stages of the games and sets, and when their opponent is ahead. Optimal challenge strategy can increase a player's chance of winning an otherwise even five‐set match to 59%.