The previous post is incorrect, the minimum would be 1 shot. Why? because both players could in theory double fault every game to get to a tie break. Both players would than continue to double fault until 5-6. Than the person who serves first would be 5-6 down. The other person would than have to get an ace or service winner to win the set with only one shot going in!
One stroke would be enough. Imagine a set where each player double faults (and spectacularly miss the ball also), then all it would take is one stroke in the tie breaker to gain a point against more double faulting.
Purely theoritically, if the opposing party were to make double-faults on each serve, and you would Ace every single serve you make, it would be:
Twelve.
6 games to win the set, each party gets 3 games to serve, 4 ace's/double-faults to win the game.
4 ace's every game that you serve = 4 shots in each of the 3 games you serve.
4 double-faults every game the opposing party serves = 0 shots in 3 games.
Adds up to 4 * 3 shots = 12 shots in 6 games = set win.
4, since 1 game is 4 points. You would have to ace the serve on every single one, and it has to be you who's serving.
Six
12
No Minimum Height! :)
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