In combinatorial game theory, a nimber is a nonnegative integer associated with certain game positions. The nimber of a position is also sometimes called the nim-value or the Sprague-Grundy number of that position (or game).

Most of the games that are commonly thought of as nimbers, are impartial games, meaning that both players have essentially the same moves, so that the only advantage is conferred by whose turn it is. For example, chess, go, othello/reversi and checkers are not impartial because the two sides (white and black or red and black) have very different options in most game postions.

Technically, the two sides can have different moves as long as they are essentially the same under a semi-complicated equivalence but in most easy examples, such as Nim or Green Hackenbush, the two sides have exactly the same moves from each postion.

It turns out (this is not trivial) that every finite impartial game is equivalent to a single Nim-heap of some size. The nimber of a game is the size of the heap to which that game is equivalent.

An impartial game has nim-value zero if and only if there is a winning strategy for the player whose turn it is not. A game with nim-value one is also called star. Games with nim-values two, three, and so on, are called star two, star three, and so on.

Many partizan games (the complement of impartial games) have some positions with low nimber values. Domineering and chess, for instance, have positions of value star and star two.

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