# Zermelo's theorem (game theory)

## In board games that cannot end in a draw, one of the two players has a winning strategy / From Wikipedia, the free encyclopedia

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In game theory, **Zermelo's theorem** is a theorem about finite two-person games of perfect information in which the players move alternately and in which chance does not affect the decision making process. It says that if the game cannot end in a draw, then one of the two players must have a winning strategy (i.e. can force a win). An alternate statement is that for a game meeting all of these conditions except the condition that a draw is now possible, then either the first-player can force a win, or the second-player can force a win, or both players can at least force a draw.^{[1]}
The theorem is named after Ernst Zermelo, a German mathematician and logician, who proved the theorem for the example game of chess in 1913.