9x9 with Periodic boundary conditions ?

perceval · Post by **perceval** » Tue May 10, 2011 5:46 am

i was thinking about trying a game (Malkovitch ?)
with Periodic Boundary conditon om the goban ie :
The shaded area is a repetition (periodic image by translation of 9 steps)of the central 9x9 non shaded one

Click Here To Show Diagram Code: [go]$$c $$ ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? $$ ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? $$ ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? $$ ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? $$ ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? $$ ? ? ? ? . . . . . . . . . ? ? ? ? ? $$ ? ? ? ? . . . . . . . . . ? ? ? ? ? $$ ? ? ? ? . . . . . . . . . ? ? ? ? ? $$ ? ? ? ? . . . . . . . . . ? ? ? ? ? $$ ? ? ? ? . . . . , . . . . ? ? ? ? ? $$ ? ? ? ? . . . . . . . . . ? ? ? ? ? $$ ? ? ? ? . . . . . . . . . ? ? ? ? ? $$ ? ? ? ? . . . . . . . . . ? ? ? ? ? $$ ? ? ? ? . . . . . . . . . ? ? ? ? ? $$ ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? $$ ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? $$ ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? $$ ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?[/go]

This idea comes from the post on komi on smaller boards http://www.lifein19x19.com/forum/viewtopic.php?f=11&t=3707 : with standard boards the komi varies wildly.

Now in physics, if you want to study a small sample of particules, you need to use periodic boundary condition to allow a better convergence towards thermodynamic limit (because you restore translational invariance which is a key property of infinite systems)
Thus the idea that finite sample with periodic boundary conditions are much closer to an infinite sample than finite sample with finite BC
(FWIW for various Heisenberg interaction simulating up to 36 (ie 6x6) spin 1/2 interacting and extrapolating the results to thermodynamic limit works very well far from critical points

i wonder how this translate in go ,hence this proposal:
couple examples:
when one plays a move it places a stone at all periodic image of this stone (easier than to mentally imagine the periodic BC).
with the board as displayed, all dame in the center 9x9 has 3 images by translation
ie start example:

Click Here To Show Diagram Code: [go]$$c sample PBC start $$ ? ? ? 4 ? ? ? ? 1 ? ? ? 4 ? ? ? ? 1 $$ ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? $$ ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? $$ ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? $$ ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? $$ ? ? ? 2 . . . . 3 . . . 2 ? ? ? ? 3 $$ ? ? 5 ? . . . . . . . 5 . ? ? ? ? ? $$ ? ? ? ? . . . . . . . . . ? ? ? ? ? $$ ? ? ? ? . . . . . . . . . ? ? ? ? ? $$ ? ? ? 4 . . . . 1 . . . 4 ? ? ? ? 1 $$ ? ? ? ? . . . . . . . . . ? ? ? ? ? $$ ? ? ? ? . . . . . . . . . ? ? ? ? ? $$ ? ? ? ? . . . . . . . . . ? ? ? ? ? $$ ? ? ? ? . . . . . . . . . ? ? ? ? ? $$ ? ? ? 2 ? ? ? ? 3 ? ? ? 2 ? ? ? ? ? $$ ? ? 5 ? ? ? ? ? ? ? ? 5 ? ? ? ? ? ? $$ ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? $$ ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?[/go]

a ladder example:

Click Here To Show Diagram Code: [go]$$c Ladder in PBC $$ ? ? ? ? ? ? O a W O ? ? ? ? ? O a X $$ ? ? ? ? ? O X X O ? ? ? ? ? O X X O $$ ? ? ? ? O X X O ? ? ? ? ? O X X O ? $$ ? ? ? O X X O ? ? ? ? ? O X X O ? ? $$ ? ? O X X O ? ? ? ? ? O X X O ? ? ? $$ ? O X X O . . . . . O X X O ? ? ? ? $$ O X X O . . . . . O X X O ? ? ? ? ? $$ X X O ? . . . . W X X O . ? ? ? ? W $$ X O ? ? . . . W B X O . . ? ? ? W B $$ W ? ? ? . . O a W W . . . ? ? O a W $$ ? ? ? ? . O X X O . . . . ? O X X O $$ ? ? ? ? O X X O . . . . . O X X O ? $$ ? ? ? O X X O . . . . . O X X O ? ? $$ ? ? O X X O . . . . . O X X O ? ? ? $$ ? O X X O ? ? ? ? ? O X X O ? ? ? ? $$ O X X O ? ? ? ? ? O X X O ? ? ? ? ? $$ X X O ? ? ? ? ? W X X O ? ? ? ? ? ? $$ X O ? ? ? ? ? W B X O ? ? ? ? ? W B[/go]

a fun property is that all joseki just disintegrate

who i up for a test of that ( iam 7-8 k) ?

i would like to try komi bidding, i think here the komi value should be low

[Edited diagrams]

robinz · Post by **robinz** » Tue May 10, 2011 5:55 am

I may have misunderstood, but isn't this just Go on played on a torus (ie. such that opposite edges are considered next to each other)? OK, you've got 4 copies of it, but that doesn't seem to have any effect on gameplay.

I've never actually played on a torus, although I have considered it. I think I just concluded that without any corners or edges it'd just be weird

perceval · Post by **perceval** » Tue May 10, 2011 6:14 am

robinz wrote:I may have misunderstood, but isn't this just Go on played on a torus (ie. such that opposite edges are considered next to each other)? OK, you've got 4 copies of it, but that doesn't seem to have any effect on gameplay.

I've never actually played on a torus, although I have considered it. I think I just concluded that without any corners or edges it'd just be weird

yes it is exaclty go played on a torus, and it will be weird obviously. i think a lot of people have thought of it, but i would like to try it now because i wonder what kind of komi would be proper

Tryphon · Post by **Tryphon** » Tue May 10, 2011 6:36 am

Best first move is obviously at tengen :mrgreen:

willemien · Post by **willemien** » Tue May 10, 2011 6:46 am

see also BasiliskGoServer

Tryphon wrote:Best first move is obviously at tengen

not sure about this, isn't everywhere you play tengen?

robinz · Post by **robinz** » Tue May 10, 2011 6:50 am

willemien wrote:
Tryphon wrote:Best first move is obviously at tengen

not sure about this, isn't everywhere you play tengen?

Yes, at least in the sense that all points are equivalent at the start of the game. I assume that Tryphon knew this, and was being humorous

Tryphon · Post by **Tryphon** » Tue May 10, 2011 6:56 am

robinz wrote:Yes, at least in the sense that all points are equivalent at the start of the game. I assume that Tryphon knew this, and was being humorous

I was trying to be, hence the smiley

I'm a math teacher and unable to resist to these kind of remark, sorry...

perceval · Post by **perceval** » Tue May 10, 2011 7:13 am

note that for the psychopath-inclined you do not have to have translation vector as (0,a) and (a,0) (here a=9),
you can take 2 vectors (a,b) and (c,d) for a total intersection of ad-bc. to keep things sane you can impose a 90 angle between vectors but that still leave
T1=(a,b) T2=(b,-a) for a^2+b2 intersections and a really weird geometry (not sure its still fun to play though because reading would be a nightmare)

topazg · Post by **topazg** » Tue May 10, 2011 7:16 am

I always like funky new ways of playing Go. I'll certainly follow one of these.

Shaddy · Post by **Shaddy** » Tue May 10, 2011 7:30 am

Funny, I was thinking about this the other day. I'll play a game, but only if it's 19x19, I don't like 9x9 too much.

robinz · Post by **robinz** » Tue May 10, 2011 7:39 am

I'm pretty sure I'd prefer 9x9 (if I choose to play one - I've not decided yet whether or not I want to), since it'd just be a bit of fun and turn-based 19x19 games tend to take months.

The other funky thing about playing Go on a 9x9 torus - well, I expect so, although this prediction remains to be tested in practice - is that, with no edges, it'll be so difficult to make eyes in such a relatively small space that the game will I think degenerate into one enormous capturing race.

Hey, this sounds a lot more fun now I've said that :lol:

BobC · Post by **BobC** » Tue May 10, 2011 7:50 am

Interesting idea but I don't think it makes the game hard enough...

How about having an attack on any group (or stone) being functionally dependent not on immediate contact but "local contact". A group can live or die dependent on the number of actual liberties whihc would be diminished by surrounding stones. If an attacking stone is close it reduces the number of liberties a group has. Liberties then become fractional...

Although painful to play in real life.. a computer could actually give a running account of liberties of each group... You could get situations where a large group (with many apparent free liberties) would die on exact placement of a stone somewhere distant from the actual group.. Some moves on the board become suicide - and you wouldn't even know it!!!

Bill Spight · Post by **Bill Spight** » Tue May 10, 2011 7:54 am

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.

hyperpape · Post by **hyperpape** » Tue May 10, 2011 8:23 am

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.

perceval · Post by **perceval** » Tue May 10, 2011 8:34 am

the reason to suggesting 9x9 is the representation of the torus as a repeated pattern, which should ease reading i am not sure it would be practical on a 19x19.
(i can't make a 38x38 board on the forum :sad:

)

BobC wrote:Interesting idea but I don't think it makes the game hard enough...

How about having an attack on any group (or stone) being functionally dependent not on immediate contact but "local contact". A group can live or die dependent on the number of actual liberties whihc would be diminished by surrounding stones. If an attacking stone is close it reduces the number of liberties a group has. Liberties then become fractional...

Although painful to play in real life.. a computer could actually give a running account of liberties of each group... You could get situations where a large group (with many apparent free liberties) would die on exact placement of a stone somewhere distant from the actual group.. Some moves on the board become suicide - and you wouldn't even know it!!!

true it won't b
e hard maybe.. but I am aiming to something playable

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

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9x9 with Periodic boundary conditions ?

9x9 with Periodic boundary conditions ?

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Re: 9x9 with Periodic boundary conditions ?

Re: 9x9 with Periodic boundary conditions ?

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Re: 9x9 with Periodic boundary conditions ?

Re: 9x9 with Periodic boundary conditions ?

Re: 9x9 with Periodic boundary conditions ?

Re: 9x9 with Periodic boundary conditions ?

Re: 9x9 with Periodic boundary conditions ?

Re: 9x9 with Periodic boundary conditions ?

Re: 9x9 with Periodic boundary conditions ?

Re: 9x9 with Periodic boundary conditions ?

Re: 9x9 with Periodic boundary conditions ?

Re: 9x9 with Periodic boundary conditions ?