Fuzzy game

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In combinatorial game theory, a fuzzy game is a game which is incomparable with zero game: it is not greater than 0, which would be a win for Left; nor less than 0 which would be a win for Right; nor equal to 0 which would be a win for the second player to move. It is therefore a first-player win.

[edit] Examples

One example is the fuzzy game {0|0}, which is a first-player win, since whoever moves first can move to a second player win, namely the zero game. An example of a fuzzy game would be a normal game of Nim where only one heap remained where that heap includes more than one object.

Another example is the fuzzy game {1|-1}. Left could move to 1, which is a win for Left, while Right could move to -1, which is a win for Right; again this is a first-player win.

No fuzzy game can be a surreal number.

[edit] See also