Wednesday, November 20, 2002
      ( 9:02 AM ) Matt  

Go Boards Aren't Square

Yup, that's right. They are slightly longer than they are wide. Exactly what the ratio is varies, but it's fairly consistent. Charles Rich posted a survey of a few boards to rec.games.go. One common explanation is that since one sits at the side of the board and looks across it, perspective naturally makes it look shorter than it actually is. To correct for this, people started making the boards longer. But then, why are chess boards square?

I think it comes down to something more fundamental about Asian aesthetics. Japanese in particular do not like symmetry. For example, dinner plates are sold in sets of 3 or 5 because they don't like even numbers. Flower arrangements also never have an even number of flowers. If you want to impress your Japanese girlfriend, don't give her a dozen roses. Make sure it's either 11 or 13. Marco Scheurer posted an article on rec.games.go which elaborates on this hypothesis.

Another really cool fact about go is that the stones are too wide to fit horizontally across the board. A full size board is 19 intersections wide, but if you place 19 stones next to each other across the board, they don't fit! You have to shift them slightly out of line in the vertical direction for them to fit in the horizontal direction. The asymmetric board gives extra space in the vertical direction to allow for this.

A third fact about go is that the white stones are slightly larger than the black ones. People say that it's because the white stones are slightly harder to see against the light board, and therefor look smaller. They made them larger to compensate for this. To me this sounds a lot like the perspective explanation for the rectangular board, and I bet there is a better explanation. I can't find the article right now, but someone hypothesized that the difference in size was just due to a
manufacturing error, and a quick thinking sales person made up the bit about white looking smaller so that they wouldn't lose sales.

I've spent quite a while musing about what the 'ideal' length to width ratio of a go board is. Mostly, I'd like to know how they settled on the values they use now. What happens if the board is slightly more oblong, but had the same area? Would the stones not fit as well?

How tightly can you assume that stones played in a game of go will be? If you started playing stones horizontally across the board from an edge, placing them alternately above and below a straight line, you could pack them in much tighter than if you offset them randomly. In fact, by placing them far enough off center, you could pack them into a hexagonal pattern. This is the tightest packing possible for circles on a plane. How tightly packed can they be if placed randomly?

In Okonomigo I'd like to at least have an option for a more correct go board. The board would be slightly longer than it is wide, and the go stones would be slightly different sizes. The stones would be slightly randomized when placed, and stones would have to shift sometimes when new stones are played so that they don't overlap. It would be interesting to see how uneven the stones become with boards of various aspect ratios, and with stones of different sizes.

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