Winning Ways for your Mathematical Plays [SEP] publisher
Winning Ways for your Mathematical Plays
Winning Ways for your Mathematical Plays (Academic Press, 1982) by Elwyn R. Berlekamp, John H. Conway, and Richard K. Guy is a compendium of information on mathematical games. It was first published in 1982 in two volumes.
The first volume introduces combinatorial game theory and its foundation in the surreal numbers; partizan and impartial games; Sprague–Grundy theory and misère games. The second volume applies the theorems of the first volume to many games, including nim, sprouts, dots
0|∗}.
Up is strictly positive (↑  0), but is infinitesimal. Up is defined in "Winning Ways for your Mathematical Plays".
Overview Down.
"Down", written as ↓, is a position in combinatorial game theory. In standard notation, ↓ = {∗|0}.
Down is strictly negative (↓ < 0), but is infinitesimal. Down is defined in Winning Ways for your Mathematical Plays.
Overview "Hot" games.
Consider the game {1|−1}.