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Combinatorial Game Theory (History)Combinatorial game theory arose first in relation to the game of nim, which can be solved completely. Nim is an impartial game for two players, and subject to the normal play condition (a player who cannot move loses) the Sprague–Grundy theorem was proved in the 1930s. The theorem shows that all impartial game are equivalent to heaps in nim, thus showing that major unifications are possible in games considered at a combinatorial level (in which detailed strategies matter, not just pay-offs). The theory introduced in the 1960s of partizan games extended the impartial theory, by relaxing the condition that a play available to one player be available to both. It was pioneered by Elwyn R. Berlekamp, John H. Conway and Richard K. Guy in their book Winning Ways for your Mathematical Plays. Some of the inspiration (for the use in particular of disjoint sums of games) was based on Conway's observation of the play in go endgames. His book On Numbers and Games, which introduces the concept of surreal number and its generalization to games, was published ahead of Winning Ways, though based in part on the same collaboration.
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