Re: [spoon-discuss] Robot Chess

[Zarpint Jeremy Cook <mcfoufou@xxxxxxxxx>]

On Thu, 25 Dec 2003, Daniel Lepage wrote:
> I toyed with this for a while with some friends, way back in high
> school; we reached the conclusion that in order for an n-dimensional
> game to be playable, the length of each side of the board had to be n+1
> - the first player can guarantee a win if the board is 2x2, 3x3x3,
> 4x4x4x4, or 5x5x5x5; but not in the case of 3x3, 4x4x4, 5x5x5x5, or
> 6x6x6x6x6.
>
> We built a hyperbolic board, too, but I don't know what happened to
> it...

Correct me if I'm wrong, but wouldn't that only change the metric on
the board, not the topology? Spherical, toroidal, kleinish, or projective
boards I could see.

Did you ever fractalize Tic-Tac-Toe, where to win a level N square you need
to win the level N+1 game inside it? Do you know who wins the n-dimensional,
size m, fractal level l game?


> > This 11 by 11 situation would have me treating loacation as a digital
> > sequence where only 1 bit can be altered in a single operation. I
> > wouldn't even attempt to think of it in terms of actual terrain.
>
> That's what I was thinking; I never really got the hang even of 5
> dimensional visualization, much less anything higher.

Then you're one up on me--how did you master visualizing a 4-dim. space?
I would really like to know how to do that.

Anyway, back to the Grid. The point I was making was that I think the
new system needs to be less probabilistic and more preprogrammed. Like
SkArcher said, a deterministic sealed grid seems much more interesting.

-- 
Zarpint            "All thy toiling only breeds new dreams, new dreams;
Jeremy Cook         there is no truth saving in thine own heart."
mcfoufou@xxxxxxxxx       --W.B. Yeats, The Song of the Happy Shepherd
grep -r kibo /     "Movements are the problem, not the answer to problems."
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