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.
Prerequisites
For the uninitiated or non-technical reader there are several other articles that will help you understand the language and concepts used here. Make sure you have an understanding of the Nim article, then move to zero game, then star (game). For further understanding check the "see also" section of this article.
Definitions
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 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 (as explained in the surreal number article).
See also
- surreal number the introduction to "Constructing Surreal Numbers" then section 5. Games