Heikki Levanto wrote:
On Wed, Feb 21, 2007 at 07:55:15PM -0600, Matt Gokey wrote:
Whether it is a torus or not is irrelevant. The only thing that matters
from a go game play perspective is the graph topology. If all points
have 4 neighbors the actual physical shape or layout doesn't matter.
There can still be subtle differences. In a standard torus, a ladder
comes back to its starting point. If you twist the torus enough, it will
miss, and fill the whole board...
Hardly relevant to random players that don't understand ladders, but
anyway...
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.
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