What happens if you play your favorite two-player game, such as connect four or chess, but instead of alternating moves you bid against your opponent for the right to move? The bidding works like this---suppose you and your opponent both start with one hundred chips. If you bid ten for the first move, and your opponent bids twelve, then your opponent gives you twelve chips and makes the first move. Now you have one hundred and twelve chips, your opponent has eighty-eight, and you bid for the second move. The goal is simply to win the game; chips have no value when the game is over. The basic theory of such games is simple and elegant, with a surprising relation to random-turn games, in which the right to move is determined by a coin flip.

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