Service box 1
Points
A game is built from points. Win your first and the score is 15. Win a second and it is 30, a third and it is 40. Win a fourth point while your opponent has 30 or fewer and you win the game. Zero is called love. The server's score is always called first, so "thirty-fifteen" means the server has two points and the receiver has one.
The jump from 30 to 40 is just a quirk. The scoring is a tally with names, not arithmetic. Four points make a game, and the numbers are labels.