As a result of temporary magical powers, you have made it to the Wimbledon finals and are playing Roger Federer for all the marbles. However, your powers cannot last the whole match. What score do you want it to be when they disappear, to maximize your chances of hanging on for a win?
It sounds obvious that you should ask to be ahead two sets to love (it takes 3 out of 5 sets to win
the men’s), and in the third set, ahead 5-0 in games and 40-love in the sixth game. (Probably you
want to be serving, but if your serve is like mine, you might prefer Roger to be serving the sixth
game down 0-40 so that you can pray for a double fault.)
Not so fast! These solutions give you essentially 3 chances to get lucky and win, but you can
get six chances—with three services by you and three by Roger. You still want to be up two sets
to none, but let the game score be 6-6 in the third set and 6-0—in your favor, of course—in the
tiebreaker.
A man was looking through a window on the 6th floor, opened it, thought for a minute then jumped, passing through the open window, but he was not injured. How was this possible?