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.

• nim
• zero game
• star (game)

Nim is a two-player game in which players take turns removing objects from heaps, one or more objects at a time but only from a single heap. ... In combinatorial game theory, the zero game is the game where neither player has any legal options. ... Star, written as * or *1, is the value given to the combinatorial game {0 | 0}, where zero is the zero game. ...

Definitions

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. This article may be too technical for most readers to understand. ... In combinatorial game theory, the zero game is the game where neither player has any legal options. ...

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. In combinatorial game theory, the zero game is the game where neither player has any legal options. ... Nim is a two-player game in which players take turns removing objects from heaps, one or more objects at a time but only from a single heap. ...

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). In mathematics, the surreal numbers are a field containing the real numbers as well as infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number, and therefore the surreals are algebraically similar to superreal numbers and hyperreal numbers. ...

See Also

• surreal number the introduction to "Constructing Surreal Numbers" then section 5. Games