Re: New Game: Torus

On Feb 7, 5:45 pm, Bill Taylor <w.tay...@[EMAIL PROTECTED]
> wrote:
>
> Alas, the same can be said about your "Torus".
>
> It is a game I considered some while ago, but discarded
> on the ground that the two players had noticeably different
> goals, of unequal difficulty.
>

You're wrong.  The two goals are exactly equivalent.  When viewed in
3D form, they "appear" to be different.  One player is surrounding a
circular axis and the other a linear axis, but in the 2D form the game
clearly has equal goals.  The 2D form is isomorphic to the 3D form.
The 2D form can be morphed into a rhombus with the left side matched
to the right side and likewise for the top and bottom, if that makes
you feel any better about it.

> The E/W direction paths
> have a different (global & local) topology from the N/S paths.
> If one wants a game that's as symmetric as possible
> between the two players, this isn't it.
>

In your game, as in mine, one player has a possible goal of forming an
N-S loop and the other player a W-E loop.  So it's way beyond me how
you arrived at the conclusion that your game has equal goals and mine
doesn't.

>
> The NZ game remains the best attempt at full
> player equivalence, though.   IMHO.
>

NZ has full player equivalence and so does Torus.  I wouldn't release
an unequal goals game.