Borderless Goban

    Keywords: Variant

A borderless goban is a "double-round" rectangular grid unusual goban, which means, on whichever side you leave the board, you re-enter it at the opposite point. This geometry is also called toroidal, because it corresponds to the surface of a torus (donut shape).

More exactly, a borderless goban can be created by defining the two end points of each row (also, respectively, each column) to be adjacent. Thereby, all points have four neighbours each.

On such a board, any game position constitutes an infinite two-dimensional square crystal structure with period of e. g. 19 points, with the actual board being just an arbitrary 19x19 section of the grid. This 19x19 focus may be shifted by arbitrary steps to get other views onto the (same) game.


Properties

  • It's hard to get settled in the beginning, because with such a board no corners exist; every point is "in the middle of the board".
  • Of course, the board size doesn't have to be 19x19. Here you can see a borderless 9x9, for instance:
[Diagram]
Borderless 9x9  
[Diagram]
Focus shifted (3 steps to the right)  
[Diagram]
Another view (shifted again, up by 2 points)  


Just a little exercise:

[Diagram]
All groups alive? help  


The answer is Yes: if White doesn't connect. (Am I right? Some more conscious players, please check it again. I am a tired 9k (KGS) only. -- rubilia)

[Diagram]
Black plays and kills  

Black's groups are alive: the marked stones are live configurations.

If Black plays at B1, then White only has one eye, at c. If White plays at W1, then she lives with two false eyes at c and d. - JoelR


[Diagram]

19x19 example opening, 50 moves so far


[Diagram]

the same game, shifted view (A1 shifted to G5):


[2] If you're not used to borderless Go yet, you may like the doubled focus view:

[Diagram]

Redundant (18x18) view of the above 9x9


-- rubilia


Borderless Goban last edited by JoelR on May 4, 2009 - 08:18
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