Expected length and probability of winning a tennis game

The game of tennis has provided mathematicians with many interesting problems. In [1], the problem of finding the probability that a certain player wins a tennis tournament was studied. Gale [2] determined the best serving strategy in tennis. First, we assume Alice and Bob play a game of tennis using the standard (or Deuce/Ad) scoring system, without a tiebreaker, and that Alice serves the game. We also assume that the probability that Alice wins any point she serves is. Stewart [3] proved that the probability that Alice wins is 'Equation Presented'. © 2021 The Mathematical Association.