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. Elwyn Ralph Berlekamp is professor of mathematics at University of California, Berkeley. ... John Horton Conway (born December 26, 1937, Liverpool, England) is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. ... Richard Kenneth Guy (born 1916) is a Professor Emeritus in the Department of Mathematics at the University of Calgary. ... Mathematical games include many topics which are a part of recreational mathematics, but can also cover topics such as the mathematics of games, and playing games with mathematics. ... 1982 (MCMLXXXII) was a common year starting on Friday of the Gregorian calendar. ...

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 and boxes, Sylver coinage, philosopher's football, fox and geese. A final section on puzzles analyzes the Soma cube, Rubik's Cube, peg solitaire, and Conway's game of life. Combinatorial game theory (CGT) is a mathematical theory that only studies two-player games which have a position which the players take turns changing in defined ways or moves to achieve a defined winning condition. ... 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 similiar to superreal numbers and hyperreal numbers. ... In combinatorial game theory, a game is partisan or partizan if it is not impartial. ... In combinatorial game theory, an impartial game is a game in which the allowable moves depend only on the position and not on which of the two players is currently moving, and where the payoffs are symmetric. ... In combinatorial game theory, the Sprague–Grundy theorem states that every impartial game is equivalent to a nimber. ... A misère version of a game is a game that is played according to its conventional rules, except that it is played to lose; that is, the winner is the one who loses according to the normal game rules. ... Nim is a two-player mathematical game of strategy in which players take turns removing objects from distinct heaps. ... Sprouts is a pencil-and-paper game with interesting mathematical properties. ... Dots and Boxes (also known as Boxes, Squares, Square-it, Dots and Dashes, Dots, or, simply, the Dot Game) is a pencil and paper game for two players (or sometimes, more than two). ... Sylver Coinage is a mathematical game for two players, invented by John H. Conway. ... Phutball (short for philosophers football) is a two-player board game described in Elwyn Berlekamp, John Conway, and Richard Guys Winning Ways for your Mathematical Plays. ... Fox and Geese Fox and geese is a board game where one player is the fox and tries to eat the geese, and the other is the geese and attempts to trap the fox. ... The pieces of a Soma cube (with extra coloring) The same puzzle, assembled into a cube The Soma cube is a solid dissection puzzle created by Piet Hein during a lecture on quantum mechanics by Werner Heisenberg. ... Rubiks Cube in scrambled state Rubiks Cube in solved state Rubiks Cube is a mechanical puzzle invented in 1974 by the Hungarian sculptor and professor of architecture ErnÅ‘ Rubik. ... English peg solitaire board European peg solitaire board Peg Solitaire is a board game for one player involving movement of pegs on a board with holes. ... Gospers Glider Gun creating gliders. The Game of Life is a cellular automaton devised by the British mathematician John Horton Conway in 1970. ...

A republication of the work by A K Peters splits the content into four volumes.

Editions

• 1st edition (Academic Press, 1982): ISBN 0-12-091101-9, ISBN 0-12-091102-7.
• 2nd edition (A K Peters Ltd., 2001–4): ISBN 1-56881-130-6, ISBN 1-56881-142-X, ISBN 1-56881-143-8, ISBN 1-56881-144-6.

External link

• Descriptions of games from the book