Games have a complex, and seemingly paradoxical structure: they are both competitive and cooperative, and the competitive element is required for the cooperative element to work out. They are mechanisms for transforming competition into cooperation. Several contemporary philosophers of sport have located the primary mechanism of conversion in the mental attitudes of the players. I argue that these views cannot capture the phenomenological complexity of game-play, nor the difficulty and moral complexity of achieving cooperation through game-play. In this paper, I present a different account of the relationship between competition and cooperation. My view is a distributed view of the conversion: success depends on a large number of features. First, the players must achieve the right motivational state: playing for the sake of the struggle, rather than to win. Second, successful transformation depends on a large number of extra-mental features, including good game design, and social and institutional features.