[computer-go] Big board. Torus ?

[Matt Gokey]

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.