[screwperman]

She was leading 4-1 and serving at 40-30, meaning that she was one point from winning the game

Eh, what?

[DTrejo]

Tennis has very strange scoring. It's complicated to explain, but here goes:

The first person to get 6 games wins the set.*

The first person to win 4 rallies in a game wins that game.*

During a game, if you have one point your score is "15," two points is "30" and three points is "40." When you get four points or win by two, then you win the game.

*One must win by two.

[screwperman]

Oh, what a debacle! Even after being such a devout tennis buff, I have confused "game" with "match". Or maybe I just can't read :(.

[DTrejo]

If you win 2 out of 3 of the sets then you win the match! (assuming you're playing a regular match)