Life In 19x19

hyperpape wrote:

Bill Spight wrote:Play on a torus is not the only way to approximate komi on an infinite board. For one thing it has no corners. What about an infinite board with four corners?

How does this work? Are points in different corners infinitely far away from each other.

Yes.

perceval wrote:

Bill Spight wrote:Play on a torus is not the only way to approximate komi on an infinite board. For one thing it has no corners. What about an infinite board with four corners?

The value of a limit may depend upon how the limit is approached.

Proper komi for the 6x6 seems to be 2 or 3. Proper komi for the 7x7 seems to be 9. Proper komi for the 8x8 seems to be about 6, and proper komi for the 9x9 seem to be about 7.

mm on a truly infinite board if locally you have an inferior result you can alway tenuki and play the mirror move on another corner: the corners will never interact so i gues the best play would be to miror the optimal pattern that you opponent is playing on your own corner for a draw

The claim that mirror go is a draw is unproven. When you say that the corners will never interact, you are saying that the game will never end. That does not mean that it will be a draw.

The cool thing about small board on a torus is that its playable

Indeed.

Bill Spight wrote:

hyperpape wrote:

Bill Spight wrote:Play on a torus is not the only way to approximate komi on an infinite board. For one thing it has no corners. What about an infinite board with four corners?

How does this work? Are points in different corners infinitely far away from each other.

Yes.

How many infinitely large sub-boards are there? 4? 5? Countably many?

Hilbert, get out of this body !!!

hyperpape wrote:How many infinitely large sub-boards are there? 4? 5? Countably many?

If the length/width of the board are countable, should be countably many.

Just to clarify, I meant infinitely large disjoint sub-boards.

Given that, I'm not quite sure how countably many sub-boards follow. You can have n corners (four seems natural, but I'm not sure if it's really necessary), each infinitely large. Then you can have zero, one or more central regions which don't ever meet the corners.

robinz wrote:... Go on a 9x9 torus ... degenerate into one enormous capturing race.
...

My experience proves this to be true.

hyperpape wrote:Just to clarify, I meant infinitely large disjoint sub-boards.

Given that, I'm not quite sure how countably many sub-boards follow. You can have n corners (four seems natural, but I'm not sure if it's really necessary), each infinitely large. Then you can have zero, one or more central regions which don't ever meet the corners.

If I'm understanding this correctly, it's still countable. The way I'm seeing this is

corner ... corner
. .
. .
. .
corner ... corner

Where the ... are all countable. In this case, it's still countable, as you can wellorder it by starting at the top left corner and then going left to right down the whole thing. This should have order type w^2+w, but don't trust my ordinal arithmetic.

Yes, I should've said "a countable infinity of sub-boards" (if Bill says we should have continuum-many, I'll cry). ...I should just stop posting. If this goes on much longer, I'll end up posting sentence fragments full of made up words.

The reason I'm wondering is that way too many options seem reasonable in some sense. You could have four corners by analogy with the ordinary go board. But beyond the analogy, I don't see why you need four. Then you could also have a center that's infinitely far from each of the corners. And you could have multiple centers too.

Imagine taking a stack of (thin!) 19x19 boards. On each one, cut a slit from tengen to the edge of the board. Doesn't matter how, as long as you do it the same on every board. Now, tape the left edge of the top board to the right edge of the bottom board. Repeat for the whole stack. What would you call this, a flat helical board or something?

Infinite board with just as many corners per area as 19x19!

Although, I'm thoroughly confused about how a stone played on tengen would work on such a board...

I Just wanted to play go on a doughnut
what have i started ?

my 2 cents on the infinite board notion:

To me "good" komi on a finite board is the score difference between the 2 sides after perfect play. You may disagree .

It is reasonable to believe that it converges to something if the board size grows toward infinity (but it might converge to different values for even and odd board for example, and for periodic boundary conditions vs open BC), but it does NOT mean that the value obtained has anything to do with play on a truly infinite board.


On a finite board you can count the number of legal postions, and theorically at least define perfect play for both side, and thus define an ideal komi (according to my definition of komi above) . on an infinite board i do not even see how you would define perfect play, hence every other question is moot iMHO
You cannot even exhaust all games of less than say x moves to try to reach a meaningful limit .
(By that i mean that if you consider a ruleset than gemerates an infinite number of legal games but a finite number of games of N moves or less you can at least try to define best play for games of length less than N moves and try to come to a limit by taking N to infinity . A toy example would be for example a game of go on an infinite board when W must alway plays at less than a fixed distance from an existing B stone: in that case the number of possible games of length less than N is finite even though the total number of games as N goes to infinity is infinite )

It makes my think of another toy game
contact go: you have to always play a contact move (except obvisously first B move), ie each move must be to the contact onf one your opponet stone or one of your own.
i guess computer would be real good at it a the number of plays would be reduced. in fact that is almost what they play with monte carlo go if i understood correclty as they have automatic reply to a number of set patterns on a 3x3 grid (is that correct ?)

Someone wanna try that on a 9x9 (periodic or not)?