Using Game Theory to Optimize Performance in a Best-of-N Set Match

This paper analyzes the situation in a best-of-N set match, where both players/teams are given the opportunity to increase their probability of winning a set (increase in effort) on one particular set. To gain insight to the problem, a best-of-3 set match (as typically used in tennis) is analyzed. Using game theory to obtain an optimal solution, the results indicate that both players should use a mixed strategy, by applying their increase in effort at each set with a probability of one third. A conjecture is devised to obtain an optimal solution for a best-of-N set match. Some applications are given to the theoretical results, which could be used by coaches and players to optimize performance.