A host randomly selects two consecutive positive integers (e.g. 26 and 27). There are two contestants, A and B. The host randomly puts one of the integers on A's forehead, and the other on B's (so that A knows B's integer, but not his own).
The host asks A, "Do you know your own integer?" If A says no, the host asks B, "Do you know your own integer?" If B says no, the host asks A, "Do you know your own integer?" again, and repeats this process until one of the contestants correctly determines his own integer, thereby winning the game.
Who wins the game?
(Keep in mind that this is a high-risk game; if you decide to take a 50-50 chance and lose, you lose everything.)
Also, if you already know the solution, don't spoil it!