Winning Ways for your Mathematical Plays

Winning Ways
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.wikipedia
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Richard K. Guy

Richard GuyGuyGuy, R. K.
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.
He is best known for co-authorship (with John Conway and Elwyn Berlekamp) of Winning Ways for your Mathematical Plays and authorship of Unsolved Problems in Number Theory.

John Horton Conway

John H. ConwayJohn ConwayConway
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. *On Numbers and Games by John H. Conway, one of the three coauthors of Winning Ways
This he developed with Elwyn Berlekamp and Richard Guy, and with them also co-authored the book Winning Ways for your Mathematical Plays.

Combinatorial game theory

combinatorial gamecombinatorial gamescombinatorial
The first volume introduces combinatorial game theory and its foundation in the surreal numbers; partizan and impartial games; Sprague–Grundy theory and misère games.
Their results were published in their book Winning Ways for your Mathematical Plays in 1982.

Sylver coinage

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.
Winning Ways for Your Mathematical Plays.

Elwyn Berlekamp

Elwyn R. BerlekampBerlekampE. R. Berlekamp
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.
Berlekamp teamed up with John Horton Conway and Richard K. Guy, two other close associates of Gardner, to co-author the book Winning Ways for your Mathematical Plays leading to his recognition as one of the founders of combinatorial game theory.

Sprouts (game)

SproutsSprout'' (game)
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.
Winning Ways for your Mathematical Plays reports that the 6-spot normal game was proved to be a win for the second player by Denis Mollison, with a hand-made analysis of 47 pages.

Soma cube

pieces composed of cubes
A final section on puzzles analyzes the Soma cube, Rubik's Cube, peg solitaire, and Conway's Game of Life.
The Soma cube was analyzed in detail by John Horton Conway in the September 1958 Mathematical Games column in Scientific American, and the book Winning Ways for your Mathematical Plays also contains a detailed analysis of the Soma cube problem.

Sprague–Grundy theorem

nim-valueSprague–Grundy theorynim-sequence
The first volume introduces combinatorial game theory and its foundation in the surreal numbers; partizan and impartial games; Sprague–Grundy theory and misère games.

Phutball

Philosopher's footballPhilosophers' Football
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.
Phutball (short for Philosopher's Football) is a two-player abstract strategy board game described in Elwyn Berlekamp, John Horton Conway, and Richard K. Guy's Winning Ways for your Mathematical Plays.

Nim

Last Onenim heap sizenim heap sizes
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.

Fox games

Fox and GeeseFox and HoundsFox & Geese
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.
Perfect play will result in a "hounds" victory, even if the fox is allowed to choose any starting square and to pass his turn once during the game, as demonstrated in Winning Ways.

Hackenbush

Blue-Red-Green Hackenbush
Hackenbush has often been used as an example game for demonstrating the definitions and concepts in combinatorial game theory, beginning with its use in the books On Numbers and Games and Winning Ways for your Mathematical Plays by some of the founders of the field.

Snakes and Ladders

Chutes and LaddersChutes & Laddersboard game
In the book Winning Ways the authors propose a variant which they call Adders-and-Ladders and which, unlike the original game, involves skill.

Toads and Frogs

Toads-and-Frogs
This mathematical game was used as an introductory game in the book Winning Ways for your Mathematical Plays.

On Numbers and Games

(Conway, 1976)John Horton Conway's book
*On Numbers and Games by John H. Conway, one of the three coauthors of Winning Ways
* Winning Ways for your Mathematical Plays

Mathematical game

Mathematical Gamesgamesmathematical
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.

Surreal number

surreal numbers(surreal) numbersurcomplex number
The first volume introduces combinatorial game theory and its foundation in the surreal numbers; partizan and impartial games; Sprague–Grundy theory and misère games.

Partisan game

partisanPartizan gamepartizan
The first volume introduces combinatorial game theory and its foundation in the surreal numbers; partizan and impartial games; Sprague–Grundy theory and misère games.

Impartial game

impartialimpartial games
The first volume introduces combinatorial game theory and its foundation in the surreal numbers; partizan and impartial games; Sprague–Grundy theory and misère games.

Dots and Boxes

Dotsdots-and-boxesStar Link
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.

Rubik's Cube

Rubik’s cube3x3x3Magic Cube
A final section on puzzles analyzes the Soma cube, Rubik's Cube, peg solitaire, and Conway's Game of Life.

Peg solitaire

Hi-Q (game)Peggedsolitaire
A final section on puzzles analyzes the Soma cube, Rubik's Cube, peg solitaire, and Conway's Game of Life.

Conway's Game of Life

Game of LifeConway's LifeConway’s Game of Life
A final section on puzzles analyzes the Soma cube, Rubik's Cube, peg solitaire, and Conway's Game of Life.

Academic Press

AcademicAcademic Press IncElsevier Academic Press