Zero game

Not to be confused with Zero-sum game.
This article is about combinatorial game theory. For the novel entitled "The Zero Game", see Brad Meltzer.

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]

  1. ^ a b Conway, J. H. (1976), On numbers and games, Academic Press, p. 72.