Sprague-Grundy theorem

The Sprague-Grundy theory of games is a theory of certain classes of games called impartial games, developed by R. P. Sprague and P. M. Grundy. It was originally developed for the game of nim.

It has been developed further by E. R. Berlekamp, John Horton Conway and others, and these developments are presented in the books Winning Ways for your Mathematical Plays and On Numbers and Games.