Winning Ways for your Mathematical Plays
Encyclopedia
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 game
s; Sprague–Grundy theory and misère game
s. 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
.
A republication of the work by A K Peters splits the content into four volumes.
Note: Misere games not included
Richard K. Guy
Richard Kenneth Guy is a British mathematician, Professor Emeritus in the Department of Mathematics at the University of Calgary....
is a compendium of information on mathematical games. It was first published in 1982 in two volumes.
The first volume introduces combinatorial game theory
Combinatorial game theory
Combinatorial game theory is a branch of applied mathematics and theoretical computer science that studies sequential games with perfect information, that is, two-player games which have a position in which the players take turns changing in defined ways or moves to achieve a defined winning...
and its foundation in the surreal numbers; partizan and impartial game
Impartial game
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...
s; Sprague–Grundy theory and misère game
Misère game
Misere or misère is a bid in various card games, and the player who bids misere undertakes to win no tricks or as few as possible, usually at no trump, in the round to be played...
s. The second volume applies the theorems of the first volume to many games, including nim
Nim
Nim is a mathematical game of strategy in which two players take turns removing objects from distinct heaps. On each turn, a player must remove at least one object, and may remove any number of objects provided they all come from the same heap....
, sprouts
Sprouts (game)
Sprouts is a pencil-and-paper game with interesting mathematical properties. It was invented by mathematicians John Horton Conway and Michael S. Paterson at Cambridge University in 1967.- Rules :...
, dots and boxes
Dots and Boxes
Dots and Boxes is a pencil and paper game for two players first published in 1889 by Édouard Lucas.Starting with an empty grid of dots, players take turns, adding a single...
, Sylver coinage
Sylver coinage
Sylver Coinage is a mathematical game for two players, invented by John H. Conway. It is discussed in chapter 18 ofWinning Ways for Your Mathematical Plays...
, philosopher's football, fox and geese. A final section on puzzles analyzes the Soma cube
Soma cube
The Soma cube is a solid dissection puzzle invented by Piet Hein in 1933 during a lecture on quantum mechanics conducted by Werner Heisenberg. Seven pieces made out of unit cubes must be assembled into a 3x3x3 cube...
, Rubik's Cube
Rubik's Cube
Rubik's Cube is a 3-D mechanical puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik.Originally called the "Magic Cube", the puzzle was licensed by Rubik to be sold by Ideal Toy Corp. in 1980 and won the German Game of the Year special award for Best Puzzle that...
, peg solitaire
Peg solitaire
Peg solitaire is a board game for one player involving movement of pegs on a board with holes. Some sets use marbles in a board with indentations. The game is known simply as Solitaire in the United Kingdom where the card games are called Patience...
, and Conway's game of life
Conway's Game of Life
The Game of Life, also known simply as 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, New YorkNew York CityNew York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and...
: Academic PressAcademic PressAcademic Press is an academic book publisher. Originally independent, it was acquired by Harcourt, Brace & World in 1969. Reed Elsevier bought Harcourt in 2000, and Academic Press is now an imprint of Elsevier....
, 2 vols., 1982; vol. 1, hardback: ISBN 0-12-091150-7, paperback: ISBN 0-12-091101-9; vol. 2, hardback: ISBN 0-12-091152-3, paperback: ISBN 0-12-091102-7. - 2nd edition, WellesleyWellesley, MassachusettsWellesley is a town in Norfolk County, Massachusetts, United States. It is part of Greater Boston. The population was 27,982 at the time of the 2010 census.It is best known as the home of Wellesley College and Babson College...
, MassachusettsMassachusettsThe Commonwealth of Massachusetts is a state in the New England region of the northeastern United States of America. It is bordered by Rhode Island and Connecticut to the south, New York to the west, and Vermont and New Hampshire to the north; at its east lies the Atlantic Ocean. As of the 2010...
: A. K. Peters Ltd., 4 vols., 2001–2004; vol. 1: ISBN 1-56881-130-6; vol. 2: ISBN 1-56881-142-X; vol. 3: ISBN 1-56881-143-8; vol. 4: ISBN 1-56881-144-6.
Games mentioned in the book
This is a partial list of the games mentioned in the book.Note: Misere games not included
- HackenbushHackenbushHackenbush is a two-player mathematical game that may be played on any configuration of colored line segments connected to one another by their endpoints and to the ground...
- Blue-Red Hackenbush
- Blue-Red-Green Hackenbush (Introduced as Hackenbush Hotchpotch in the book)
- Childish Hackenbush
- Ski-Jumps
- Toads-and-FrogsToads and frogs (game)The combinatorial game Toads and Frogs is a partisan game invented by Richard Guy. This mathematical game was used as an introductory game in the book Winning Ways for your Mathematical Plays....
- Cutcake
- Maundy Cake
- (2nd Unnamed Cutcake variant by Dean Hickerson)
- Hotcake
- Coolcakes
- Baked Alaska
- Eatcake
- Turn-and_Eatcake
- Col
- Snort
- NimNimNim is a mathematical game of strategy in which two players take turns removing objects from distinct heaps. On each turn, a player must remove at least one object, and may remove any number of objects provided they all come from the same heap....
(Green Hackenbush)- Prim
- Dim
- Lasker's Nim
- Seating Couples
- Northcott's Game (Poker-Nim)
- The White Knight
- Wyt Queens (Wythoff's GameWythoff's gameWythoff's game is a two-player mathematical game of strategy, played with two piles of counters. Players take turns removing counters from one or both piles; in the latter case, the numbers of counters removed from each pile must be equal...
) - Kayles
- Double Kayles
- Quadruple Kayles
- Dawson's Chess
- Dawson's Kayles
- Treblecross
- Grundy's GameGrundy's gameGrundy's game is a two-player mathematical game of strategy. The starting configuration is a single heap of objects, and the two players take turn splitting a single heap into two heaps of different sizes. The game ends when only heaps of size two and smaller remain, none of which can be split...
- Mrs. Grundy
- DomineeringDomineeringDomineering is a mathematical game played on a sheet of graph paper, with any set of designs traced out. For example, it can be played on a 6×6 square, a checkerboard, an entirely irregular polygon, or any combination thereof. Two players have a collection of dominoes which they place on the grid...
- No Highway
- De Bono's L-GameL gameThe L game is a simple strategic game invented by Edward de Bono.The L game is a two-player turn-based game played on a board of 4×4 squares. Each player has a 3×2 L-shaped piece, and there are two 1×1 neutral pieces. On each turn, a player first must move their L piece, and then...
- Snakes-and-LaddersSnakes and laddersSnakes and Ladders is an ancient Indian board game regarded today as a worldwide classic. It is played between two or more players on a game board having numbered, gridded squares. A number of "ladders" and "snakes" are pictured on the board, each connecting two specific board squares...
(Adders-and-Ladders) - Jelly Bean Game
- Dividing Rulers
See also
- On Numbers and GamesOn Numbers and GamesOn Numbers and Games is a mathematics book by John Horton Conway. The book is a serious mathematics book, written by a pre-eminent mathematician, and is directed at other mathematicians...
by John H. Conway, one of the three coauthors of Winning Ways