On Thu, Feb 22, 2007 at 08:11:59AM -0600, Matt Gokey wrote: > I'm not sure I agree with this. I hypothesize that 2d, 3d, 4d, torus, > or any other shape is completely irrelevant with regard to game play. > The only thing that matters is the graph topology. A corollary is that > on any board that is completely balanced at the beginning with identical > number of neighbors for all nodes, any 1st play is equivalent and > therefore optimal.
Well, I am not a mathematician, so I may misunderstand what you mean with the graph topology. All I wanted to say was that if you make a torus by joining the opposing edges of the board, you get a shape where straight lines come back to their starting points. If, instead, you twist it a bit, so that the upper edge meets the lower edge one line off, you get a shape where a straight line passes right by its starting point, and fills the whole board before hitting the starting point again. If your twist is greater than one, you get various different effects. I believe the 'twist' also has an effect on how ladders behave. And incidentally, how hard they will be to read (if they crash into the start of the ladder in 38 moves, or if takes 180 moves to meet the beginning a few points on its left)... No comments about the higher dimensions, 2 is quite enough for me ;-) -H -- Heikki Levanto "In Murphy We Turst" heikki (at) lsd (dot) dk _______________________________________________ computer-go mailing list computer-go@computer-go.org http://www.computer-go.org/mailman/listinfo/computer-go/
