Directory of Combinatorial Game Theory Resources

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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).

Subcategories

• Software

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.

Related Categories

• Home > Science > Social Sciences > Economics > Game Theory
• Home > Games > Paper and Pencil > Dots and Boxes
• Home > Games > Paper and Pencil > Sprouts

 

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