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Now that we have solved birthday paradox problem an easy one for you. For those of you who understand the game of tennis it will be more fun...this problem was posted by Peter Winkler (math professor at Dartmouth University) in his math puzzles collection

Winning Wimbledon

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?
Yes the correct answer is to be two sets up and tiebreak at 6-6 in the third one with 6-0 score then you have more chances (6) to win the match than if you are just up 40-0 in the final game
Wouldn’t it be better to tiebreak the 1st set then get as close to winning the 2nd set as possible so that even if you lose the 2nd set you still have a chance to win the 3rd?
No because then you would have to win many more points if you are playing for the whole set and if you are in the last set (by the way Wimbledon is 3 out 5 sets but it doesn't matter) and up 6-0 in the tiebreak you just need to win 1 out of 6 points to win the match. The probability of winning 1 out of 6 is higher (even assuming you always only have 0.1% chance of winning any single point from Federer).