Some Remarks on Strategy in Playing Tennis

摘要

The paper shows how the probability of winning a game, a set and a match, depend on the probability of winning a ball (from one's own and from the opponent's serve). The conditions are given under which the usual serve strategy (strong-weak) is optimal. It is also shown that a game is 'strategy-less in the sense that if the player has k( = 1, 2 or 3) balls which he can play with increased probability of winning, then all strategies of placing these balls during the game are equivalent. Finally, it is shown that the last property does not carry over to the case of optimal strategy in a match. (Author)