# Directory of Combinatorial Game Theory Resources

Combinatorial game theory is a branch of mathematics devoted to studying the optimal strategy in perfect-information games with two or more players (typical), one player (puzzles), or zero players (like Conway's Game of Life).

## Resources in This Category

• #### Aviezri Fraenkel

http://www.wisdom.weizmann.ac.il/~fraenkel
A comprehensive bibliography on combinatorial games; several papers about combinatorial games; and information about where to publish such results.

• #### David Eppstein - Combinatorial Game Theory

http://www.ics.uci.edu/~eppstein/cgt/
Many up-to-date links, and a short introduction.

• #### Dice Theorem

http://www.hermetic.ch/misc/dice/dice1.htm
How many ways are there of throwing n indistinguishable dice each with m faces?

• #### Elwyn Berlekamp - Combinatorial Game Theory

http://math.berkeley.edu/~berlek/cgt/index.html
Elwyn's research in the field, including several papers.

• #### Erik Demaine's Combinatorial Games

http://erikdemaine.org/games/
Research on pushing blocks, Clickomania, Phutball, and sliding coins. Survey paper on algorithmic combinatorial game theory.

• #### Fair Dice

http://www.mathpuzzle.com/Fairdice.htm
Includes a complete list of all possible Fair Dice, most of which are not cubes. Includes pictures.

• #### Introductory Combinatorial Game Theory

http://sps.nus.edu.sg/%7Elimchuwe/cgt/
Description and analysis of several impartial and partial (partisan) combinatorial games by Lim Chu Wee.

• #### Jeff Erickson - Mathematical Games, Toys, and Puzzles

http://compgeom.cs.uiuc.edu/~jeffe/mathgames.html
Links to several game theorists and actual games, plus a brief introduction. Also a couple of papers on game theory, about Toads and Frogs and Sowing Games.

• #### John Conway's Game of LIfe

http://psych.hanover.edu/JavaTest/Play/Life.html
A simple Java implementation of Conway's classic game of life.

• #### One-Dimensional Phutball

http://www.msri.org/publications/books/Book42/files/grossman.pdf
Solution of the case of a restricted version called Oddish Phutball by presenting an explicit strategy in terms of a potential function.

• #### Phutball Endgames are Hard

http://www.msri.org/publications/books/Book42/files/dephut.pdf
Mathematical paper by Erik Demaine, Martin Demaine and David Eppstein on solving the Philosopher's Football game.

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