Monday, March 27, 2006

Mathematical Go

I was taught to play go as a child, but it wasn't until a few years ago that I learned how complex the rules are, at least the ones used in tournaments. I had previously thought the rules were elegant and simple.

Actually, mathematicians have devised elegant and simple rules of go. [Broken? archived version] Unfortunately the mathematical rules are rarely used. Instead, there are several popular rule sets with different properties.

Luckily in most games the complicated cases never arise, but it is irritating to know that in general, the outcome of the game can depend on the legality of suicide, and in many cases it is unclear whether a group is live or dead if the mathematical rules are not followed. [Link broken; the FAQ can be found in the nextgo package.]

Evidently when the game was first invented, nobody thought about the messy corner cases. It seems as each one was discovered, an ad hoc solution was proposed, and over time these cumulative patches to the basic rules eroded the austere grace of the game.

As one might expect, starting afresh and approaching the game from a mathematician's point of view not only restores clarity and precision, but also yields unexpected results. For example, Berlekamp and Wolfe describe bizarre positions where highly nonintuitive moves are required to win. Even though such situations never occur in real play, studying them hints at the richness and depth of this ancient game. Unsurprisingly, it was a mathematician who first drew my attention to the flaws in traditional go rule sets!

I am not sure why the mathematical rules have not caught on. Are they too difficult to implement in a tournament? Is the grip of tradition is too strong? Or is it simply that most in the go world are unfamiliar with these recent developments?

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