Mathematical Rules of Go

Mathematical Rules of Go
by Jean-Claude Chetrit
WARNING: Discussions of the rules of Go are for people who not only know how to play Go very well, but also want to split hairs...

There are 4 rules in Mathematical Go. The last 3 should be familiar as they are frequently described in any precise set of rules. But the last sentence of the first rule is what makes Mathematical Go different and so much simpler than all the other sets of rules.

The Alternating Rule:
Two players, called Black and white, keep alternating moves till the end of the game. Black plays first. A move by a player begins by his placing a stone on an empty intersection of the go board. The first player who cannot put down a stone without breaking a rule loses the game.
The Rule of Capture:
After a stone is placed on the board, all enemy stones which have no liberties are removed. A player's move is not finished until this phase has been completed.
The Rule for Suicide:
Suicide is illegal. Precisely, after a stone has been played, and after the rule of capture has been applied to his enemy stones, if the stone has no liberty, then the move was illegal.
The SuperKo Rule:
A player is not allowed to place down a stone if, after the rule of capture has been applied, the resulting Board position has appeared previously in the game.

That's all, Folks!

Clarifications:

Please note that the words alive, dead, seki, eye, false eyes, territory, passing and counting have not been mentioned!
About The Rule of Capture: I did assume that the concept of liberty was understood, thereby saving myself the trouble of defining it. On the other hand, all the rules of Go agree on this (Japanese, Chinese, ING, AGA, etc...).

To make the super ko rule more precise, we can imagine that after each move, a snapshot of the goban is taken and archived. But, the archive's filing system will not accept the same snapshot twice.

The rules given above are equivalent not to the current chinese rules but to the OLD CHINESE rules: they penalized each separate group by 2 points. For more details, make sure you visit Robert Jasiek's Page on The Rules of Go.

Proof:

Intuitively, the game is played as usual; once Chinese rules players would pass, each Mathematical Go rules player starts playing in his/her territory; the player with the smallest territory will first get to a point where the only possible move is a suicide and therefore lose. Obviously, it is not necessary to go through this unless the game is very close.

For a serious proof, I refer you to the great book "Mathematical Go: Chilling Gets the Last Point", by Berlekamp and Wolf, available for $39.00. Another Warning: this is a great book if you're a serious mathematician, and a completely baffling one otherwise.

Last updated on December 8, 1998
Please send any comments to Jean-Claude Chetrit