Picking the Larger of Two Cards


I got this problem from Rustan Leino, who was told it by Roger Wattenhofer.

I solved it and wrote up my solution.


Someone picks, at their will, two cards from a deck of cards. The cards have different numbers, so one is higher than the other. (In other words, the person picks two distinct numbers in the inclusive range 1 through 13.) The cards are placed face-down on a table in front of you. You get to choose one of the cards and turn it face-up. Now, you'll select one of the two cards (one of which you can see the face of, the other one of which you can't). If you select the highest card, you win. Design a card-selection strategy for which your chance of winning is strictly greater than 50%.

Solution     Reveal