Fuzzy game

In combinatorial game theory, a fuzzy game is a game which is incomparable with 0: 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.

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 would be a normal game of Nim where only one object remained.

Another example of a fuzzy game would be {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.