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 is now normally played with the ending condition that the player unable to play loses. The theory of impartial games subject to that condition (the Sprague-Grundy theory) was worked out in the 1930s. It reduces games to Nim positions, 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 the authors Berlekamp, Conway and Guy ofWinning Ways for your Mathematical Plays, published after quite some delay in book form. Some of the inspiration (for the use in particular of disjoint sums of games) was based on observations of Conway of the play in Go endgames. His book On Numbers and Games introducing a general conception of number was published ahead of Winning Ways, though based in part on the same collaboration.

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