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 and boxes, Sylver coinage, philosopher's phutball, fox and geese.
A final section on puzzles analyzes the Soma cube, Rubik's Cube, peg solitaire, and Conway's Game of Life.
A republication of the work by A K Peters split the content into four volumes.
Editions
1st edition, New York: Academic Press, 2 vols., 1982; vol. 1, hardback: , paperback: ; vol. 2, hardback: , paperback: .
2nd edition, Wellesley, Massachusetts: A. K. Peters Ltd., 4 vols., 2001–2004; vol. 1: ; vol. 2: ; vol. 3: ; vol. 4: .
Games mentioned in the book
This is a partial list of the games mentioned in the book.
Note: Misere games not included
Hackenbush
Blue-Red Hackenbush
Blue-Red-Green Hackenbush (Introduced as Hackenbush Hotchpotch in the book)
Childish Hackenbush
Ski-Jumps
Toads-and-Frogs
Cutcake
Maundy Cake
(2nd Unnamed Cutcake variant by Dean Hickerson)
Hotcake
Coolcakes
Baked Alaska
Eatcake
Turn-and-Eatcake
Col
Snort
Nim (Green Hackenbush)
Prim
Dim
Lasker's Nim
Seating Couples
Northcott's Game (Poker-Nim)
The White Knight
Wyt Queens (Wythoff's Game)
Kayles
Double Kayles
Quadruple Kayles
Dawson's Chess
Dawson's Kayles
Treblecross
Grundy's Game
Mrs. Grundy
Domineering
No Highway
De Bono's L-Game
Snakes-and-Ladders (Adders-and-Ladders)
Jelly Bean Game
Dividing Rulers
See also
On Numbers and Games by John H. Conway, one of the three coauthors of Winning Ways
