In combinatorial game theory, the zero game is the game where neither player has any legal options. Therefore, under the normal play convention, the first player automatically loses, and it is a second-player win. The zero game has a Sprague–Grundy value of zero. The combinatorial notation of the zero game is: { | }.[1]
A zero game should be contrasted with the star game {0|0}, which is a first-player win since either player must (if first to move in the game) move to a zero game, and therefore win.[1]
- ^ a b Conway, J. H. (1976), On numbers and games, Academic Press, p. 72.
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