In
combinatorial game theory, the
Sprague–Grundy theorem states that every
impartial game under the
normal play convention is equivalent to a
nimber. The
Grundy value or
nim-value of an impartial game is then defined as the unique nimber that the game is equivalent to. In the case of a game whose positions (or summands of positions) are indexed by the natural numbers (for example the possible heap sizes in nim-like games), the sequence of nimbers for successive heap sizes is called the
nim-sequence of the game.