## Wednesday, October 18, 2006

### Three Dimensional Go

Although I said in my last post that Go is probably the one game that really needs no variants, naturally there exist variants for the game:

Variations on Go: Including other rules, other boards, other pieces, and ways to include a third or fourth player.

Other variants

And even more variants at Sensei.

Before looking at these pages, my first thought was 3-D Go. I honestly don't know why.

The biggest problem was also obvious to me: a simple cubic board would have too many locations that each have six liberties, making capturing a veritable nightmare. I played around with the idea of using Tetrahedrons to solve this (d4's), but it didn't really work out.

I then thought about trying the cubic board, but simply eliminate some of the lines so that most of the locations still have only four liberties. Something like this:

By eliminating all of the z-axis lines, aside from those on the edge of the board, you end up with some intersections with five liberties, most with four, and corners with three. Further elimination of some lines on the faces allow us to limit any location to having only four liberties. Using this system you should choose the optimal board dimensions to have the board make structural sense (unlike my example):

Actually, if you simply play only on the faces of the cube, you end up with a close approximation of a plain Go board, with no more than four liberties from any location. While that is a step "up" from a traditional Go board, it doesn't give me the real feel of three dimensions.

(A variant for this would be to play on three nested but completely separated cubes. This would be like playing three games of Go simultaneously on three different sized boards, where you can decide on which board to move each time it is your play. While a tad more confusing, it doesn't really add anything to the experience.

Another very strange variant would be to play several dozen games of Go simultaneously, where each plane represents a different game, and a single stone is placed simultaneously on three boards.)

I then went on-line to see what had been done with 3-D Go already. There is a three dimensional Go game on Sourceforge, but it simply uses the 5x5x5 cube shape.

A more interesting approach is Diamond Go, which uses a strange crytalline latice structure in such a way that a true Go experience is recreated in three dimensions. Each location has four, three, or two liberties.

Ishihama Yoshiaki also examines several variations on three dimensional boards that produce playable experiences similar to the two dimentional version, including some really funky board shapes.

Funky.