In any finite two-player game of perfect information with no possibility of a draw, one of the two players has a winning strategy; allowing draws, at least one player has a strategy guaranteeing at least a draw. Proved by Ernst Zermelo for chess-like games, it is the founding determinacy result of combinatorial game theory.
Facts
StatementZermelo's theorem states that in any finite two-player game of perfect information with alternating moves and no element of chance, if the game cannot end in a draw then one of the two players must have a winning strategy that forces a win. 1 Connections
In Branch
Named After
Derived from the theorem's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
Sources
1. Zermelo's Theorem (Game Theory) (Wikipedia)
Wikimedia FoundationIntroductionQuote, Introduction
The theorem is named after Ernst Zermelo, a German mathematician and logician, who proved the theorem for the example game of chess in 1913.
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