Great Math Board Game Software

By Xah Lee. Date: . Last updated:

This is my favorite category. The programs listed here are positional strategic board games involving no chance events or hidden information. Many of these games are extremely simple in rules yet defy mathematical analysis for a optimal strategy. Often mathematical theory of sorts can be derived or applied to them. My love of these games are not so much as playing them, but analyzing and figuring out algorithms about them.

There is a series of book on the general mathematical aspects of board games and puzzles: Winning Ways by E R Berlekamp, J H Conway, R K Guy. Buy at amazon

winning ways for your mathematical plays 1
Winning Ways Your Mathematical Plays volumn 1. Buy at amazon
winning ways for your mathematical plays 2
Winning Ways Your Mathematical Plays volumn 2. Buy at amazon
winning ways for your mathematical plays 3
Winning Ways Your Mathematical Plays volumn 3. Buy at amazon
winning ways for your mathematical plays 4
Winning Ways Your Mathematical Plays volumn 4. Buy at amazon
dots and boxes game
The Dots-and-boxes Game by Elwyn R Berlekamp, (2000). Buy at amazon

For rich info about board games, see Wikipedia: Solved board games.

Game of Go

go screenshot at

Go is a extremely complex game, particular difficult to program computer to play it.

You can play at

gnu go logo
GNU Go. OSX Mac Win Linux Java

There's a Mac OS X version called Goban with very good graphical interface at Mac

Computer go is extremely weak as of 2010. Any go hobbiest can beat any computers. But, in , Google AlphaGo changed this. See: Google AI AlphaGo vs Lee Sedol.

Here is perhaps the only book on programing go: Mathematical Go Buy at amazon by David Wolfe and Elwyn R Berlekamp, 1997.

Go Board Variations

game of go, board variation
Go played on 33344 tiling. Black to play. c2.5 or d3 are good moves. This particular tiling makes a good game, even though there are 5 liberties per node.

Freed Go by Lewey Geselowitz. It plays go on various 2D and 3D grids. Highly recommended. Win OSX

For more about go on different boards, see: Go Board Game on Hexagonal and Triangular Grids.

Game of Hex

Hex (board game) is a board game popularized by Martin Gardner's Scientific American in the 1960s. On a diamond shaped hexagonal board, two players alternatively place their pieces vying for a unbroken connection between opposite edges of the board.

Hexy by Vadim V Anshelevich.

As of , the best hex program is by Vadim V Anshelevich, available for Windows platform only, at the author's home page: The site includes his thesis. Win

Hex board up to 9x9 has been solved by Jing Yang.


Chinese Checkers

chinese checkers jump
Chinese checker. image source

Chinese checkers. Pieces move by jumping over other pieces. The goal is to be the first to arrive on the opposite side.

What is the origin of the name “Chinese checker”?

The game was invented in Germany in 1892 under the name "Stern-Halma" as a variation of the older American game Halma.

It was renamed “Chinese” in USA for marketing reasons.

chinese checkers opening
Chinese checkers best opening moves. [• Chinese checkers best opening moves By Cédric Jules. At , Accessed on 2014-12-06 ]


reversi board game
The game reversi.

Reversi is made popular by computer. Two player take turns placing disks of his color on a 8x8 square board. Opponent's pieces that lies between your pieces will be changed to your color. The winner is the one with most pieces on the board.

The champion of Reversi is no longer human. Program Logistello by professor 〔Michel Buro 〕 beat the current world champion Takeshi Murakami 6 to 0 in 1997 August.

Check out the reversi game server at . You can play with hundreds of human opponents around the world online. Really nice. Java


Ataxx screenshotAtaxx screenshot
Ataxx screenshot.

Ataxx is a arcade game in the early 1990s. The game is similar to reversi in that you flip over your opponent's pieces, but instead by sandwitching, you flip adjacent ones.

You can play the original arcade version of Ataxx on your personal computer by downloading MAME (basically, this program lets you play on your computer all early arcade video games up to about 1997.). Mac Win Linux


abalone board game
The initial positions of abalone.

Abalone is a game played on a hexagonal grid. The object of the game is to push your opponent's pieces off the board.


Five-in-a-row is a very popular game. Because the advantag of the first player, variosu rules has been designed to limit the first player's advantage. For more info, see: Gomoku.


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