Life In 19x19 :: Komi on smaller boards

It depends on the size. Here are some values from the top of my head. The last two are educated guesses. The 7x7 value is mostly regarded as correct, although it is not completely proven yet, as far as I know.

2x2: 0
3x3: 8
4x4: 1
5x5: 24
7x7: 9
9x9: 6
13x13: 8

On an infinite board, what is the value of a move?

Harleqin wrote:

Is there a theory out there somewhere suggesting convergence of komi to some value?

On an infinite board, what is the value of a move?

shapenaji wrote:

Harleqin wrote:

Is there a theory out there somewhere suggesting convergence of komi to some value?

On an infinite board, what is the value of a move?

I'd guess that the value of a move on an infinite "square" board is 0 since there is an infinite amount of potential territory and so whatever gain there might be from one move is 0 as a percentage. If there are also infinitely many stones of each color the game might never end. It's not clear that it makes sense to talk about go on an infinite board.

I don't think komi actually matters for amateurs.

When playing socially, I usually only count the score on the board (no komi).

In 19x19, lots and lots of pro play confirms 7 to be about right.

If we take theoretical komi to be the summed-up value of the influence around a stone, then komi is the value of the largest first move on the board.

emeraldemon wrote:

In 19x19, lots and lots of pro play confirms 7 to be about right.

Why? Isn't Black still winning significantly more than 50%? So the komi must be 6.5 or greater!

Current statistics for professional play with 6.5 komi show a winning percentage of about 50.5%.

HermanHiddema wrote:

Current statistics for professional play with 6.5 komi show a winning percentage of about 50.5%.

In which countries?

I think in China and Taiwan with 7.5 komi (equivalent) they also have Black above 50%.

Until dynamic komi and / or komi bidding are used, pro game statistics will remain too partial because playing style adapts to a given komi.

the statistcis strongly hint that 7 komi is correct

HermanHiddema wrote:

the statistcis strongly hint that 7 komi is correct

Rather they show that too few games are measured.

Author:	MarylandBill [ Thu Apr 21, 2011 8:07 pm ]
Post subject:	Komi on smaller boards
Hi, I am just curious, when you play on a smaller board, should the Komi be the same as it is on a full size board? Thanks, Bill

Author:	emeraldemon [ Thu Apr 21, 2011 8:12 pm ]
Post subject:	Re: Komi on smaller boards
Close enough. In 19x19, lots and lots of pro play confirms 7 to be about right. In smaller sizes there isn't nearly the volume of experience. This might help: http://senseis.xmp.net/?HandicapForSmallerBoardSizes

Author:	Harleqin [ Sat Apr 23, 2011 5:38 am ]
Post subject:	Re: Komi on smaller boards
It depends on the size. Here are some values from the top of my head. The last two are educated guesses. The 7x7 value is mostly regarded as correct, although it is not completely proven yet, as far as I know. 2x2: 0 3x3: 8 4x4: 1 5x5: 24 7x7: 9 9x9: 6 13x13: 8

Author:	shapenaji [ Sat Apr 23, 2011 5:56 am ]
Post subject:	Re: Komi on smaller boards
Harleqin wrote: It depends on the size. Here are some values from the top of my head. The last two are educated guesses. The 7x7 value is mostly regarded as correct, although it is not completely proven yet, as far as I know. 2x2: 0 3x3: 8 4x4: 1 5x5: 24 7x7: 9 9x9: 6 13x13: 8 Is there a theory out there somewhere suggesting convergence of komi to some value? On an infinite board, what is the value of a move?

Author:	mw42 [ Sat Apr 23, 2011 6:02 am ]
Post subject:	Re: Komi on smaller boards
shapenaji wrote: On an infinite board, what is the value of a move? 0.

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Komi on smaller boards http://www.lifein19x19.com/viewtopic.php?f=11&t=3707	Page 1 of 2

Author:	gowan [ Sat Apr 23, 2011 6:06 am ]
Post subject:	Re: Komi on smaller boards
shapenaji wrote: Harleqin wrote: It depends on the size. Here are some values from the top of my head. The last two are educated guesses. The 7x7 value is mostly regarded as correct, although it is not completely proven yet, as far as I know. 2x2: 0 3x3: 8 4x4: 1 5x5: 24 7x7: 9 9x9: 6 13x13: 8 Is there a theory out there somewhere suggesting convergence of komi to some value? On an infinite board, what is the value of a move? I'd guess that the value of a move on an infinite "square" board is 0 since there is an infinite amount of potential territory and so whatever gain there might be from one move is 0 as a percentage. If there are also infinitely many stones of each color the game might never end. It's not clear that it makes sense to talk about go on an infinite board.

Author:	topazg [ Sat Apr 23, 2011 6:34 am ]
Post subject:	Re: Komi on smaller boards
Harleqin wrote: 9x9: 6 13x13: 8 This is also what I heard (ok, actually 5.5 for 9x9, 7.5 for 13x13, and 6.5 for 19x19 - the 9x9 I know started from some professional opinion somewhere, but I can't remember who or when, and the 13x13 I have no idea about).

Author:	shapenaji [ Sat Apr 23, 2011 11:05 am ]
Post subject:	Re: Komi on smaller boards
gowan wrote: shapenaji wrote: Harleqin wrote: It depends on the size. Here are some values from the top of my head. The last two are educated guesses. The 7x7 value is mostly regarded as correct, although it is not completely proven yet, as far as I know. 2x2: 0 3x3: 8 4x4: 1 5x5: 24 7x7: 9 9x9: 6 13x13: 8 Is there a theory out there somewhere suggesting convergence of komi to some value? On an infinite board, what is the value of a move? I'd guess that the value of a move on an infinite "square" board is 0 since there is an infinite amount of potential territory and so whatever gain there might be from one move is 0 as a percentage. If there are also infinitely many stones of each color the game might never end. It's not clear that it makes sense to talk about go on an infinite board. Well, here's what I'm thinking, each move exerts a certain amount of influence around it, imagine each stone as a source of influence which drops off as a power-law or as an exponential. This influence reflects off sides of the board, leading to the strange nature of komi on small boards. (and in cases where the game is solved like on a 5x5, we have values of 24 for komi, which is silly, because this assumes perfect play, in which case it's not a game anyhow) If we take theoretical komi to be the summed-up value of the influence around a stone, then komi is the value of the largest first move on the board. If I assume influence is an inverse-squared law (Just a first approximation) (and assuming a continuous board, for the time being (just so I don't have to do the discrete math)) then a stone in the corner, (where I can assume the greatest reflection) will effectively generate the influence of 4 stones, by the method of images. the influence on the "real" portion of the board from these 4 stones, would then be: integral(from 0->inf,integral(from 0->inf, A/((x-xo)2+(y-yo)2)+A/((x-x1)2+(y-y1)2)+A/((x-x2)2+(y-y2)2)+A/((x-x3)2+(y-y3)2) We then call this sum for the board involved, Komi where A is a constant to be calibrated xo, yo are the x,y coordinates of the actual stone x1, y1 are the coordinates of image 1 x2, y2 are the coordinates of image 2 x3, y3 are the coordinates of image 3 (I'm currently a little busy, so I can't work this out just yet, but the logic here is that on a larger board, the number of places where you can get an advantage from reflection drops off. As the board size gets larger and larger, the fraction of territory where reflection is an issue drops to 0, so if we can use the value of A from a 19x19 board, using the above equation. Then we would just need to find the integral of A/(x2+y2) over all space, and that would be our convergent value of komi

Author:	shapenaji [ Sat Apr 23, 2011 11:08 am ]
Post subject:	Re: Komi on smaller boards
An interesting caveat here is that under this, tengen gets better and better as the board gets smaller, (since, theoretically, there are 4 images contributing, (even more if the influence drops off slowly) Also, I noticed a mistake above, a stone in the corner actually has 3 images, there's one on either side of the board, and then one behind the corner.

Author:	shapenaji [ Sat Apr 23, 2011 11:45 am ]
Post subject:	Re: Komi on smaller boards
1/r2 is wrong too, since that is clearly not integrable, 1/(1+r2) is a possibility Basically though, we want a quarter of the total potential of a quadrapole moment in the corner

Author:	xed_over [ Sat Apr 23, 2011 7:31 pm ]
Post subject:	Re: Komi on smaller boards
I don't think komi actually matters for amateurs. When playing socially, I usually only count the score on the board (no komi).

Author:	daniel_the_smith [ Sat Apr 23, 2011 7:38 pm ]
Post subject:	Re: Komi on smaller boards
xed_over wrote: I don't think komi actually matters for amateurs. When playing socially, I usually only count the score on the board (no komi). Eh, komi definitely makes a difference to me. Especially on a small board.

Author:	Shaddy [ Sat Apr 23, 2011 7:41 pm ]
Post subject:	Re: Komi on smaller boards
Komi has suddenly started mattering a lot more to me after 1-2d.

Author:	RobertJasiek [ Sat Apr 23, 2011 10:53 pm ]
Post subject:	Re: Komi on smaller boards
emeraldemon wrote: In 19x19, lots and lots of pro play confirms 7 to be about right. Why? Isn't Black still winning significantly more than 50%? So the komi must be 6.5 or greater!

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Author:	RobertJasiek [ Sat Apr 23, 2011 11:01 pm ]
Post subject:	Re: Komi on smaller boards
shapenaji wrote: If we take theoretical komi to be the summed-up value of the influence around a stone, then komi is the value of the largest first move on the board. As I am about to show for 19x19 in Joseki / Volume 2 / Strategy, the value of the first stone's sum of territory and territorial value of influence is about 8.8 points. Details will be in the book.

Author:	HermanHiddema [ Sun Apr 24, 2011 1:27 am ]
Post subject:	Re: Komi on smaller boards
RobertJasiek wrote: emeraldemon wrote: In 19x19, lots and lots of pro play confirms 7 to be about right. Why? Isn't Black still winning significantly more than 50%? So the komi must be 6.5 or greater! Since when is 7 no longer greater than 6.5? Current statistics for professional play with 6.5 komi show a winning percentage of about 50.5%. Previously, at 5.5 komi, this was around 53%.

Author:	RobertJasiek [ Sun Apr 24, 2011 1:37 am ]
Post subject:	Re: Komi on smaller boards
HermanHiddema wrote: Current statistics for professional play with 6.5 komi show a winning percentage of about 50.5%. In which countries? I think in China and Taiwan with 7.5 komi (equivalent) they also have Black above 50%. Until dynamic komi and / or komi bidding are used, pro game statistics will remain too partial because playing style adapts to a given komi.

Author:	HermanHiddema [ Sun Apr 24, 2011 2:06 am ]
Post subject:	Re: Komi on smaller boards
RobertJasiek wrote: HermanHiddema wrote: Current statistics for professional play with 6.5 komi show a winning percentage of about 50.5%. In which countries? Given that I'm speaking of professional play at 6.5 komi, I think it is pretty obvious I'm talking about Japan and Korea. Quote: I think in China and Taiwan with 7.5 komi (equivalent) they also have Black above 50%. In fact, according to SL's http://senseis.xmp.net/?Komi/Statistics, area scoring with a komi of 7.5 or 8 (Ing rules, so effectively 7.5) show a winning percentage of about 50.5% for White. If anyone has statistics over a larger sample size, please post them. Quote: Until dynamic komi and / or komi bidding are used, pro game statistics will remain too partial because playing style adapts to a given komi. At the moment, it is the best method we have, and the statistcis strongly hint that 7 komi is correct. We would only really have absolute certainty on the issue if we find perfect play, which we can pretty much rule out.

Author:	RobertJasiek [ Sun Apr 24, 2011 4:02 am ]
Post subject:	Re: Komi on smaller boards
HermanHiddema wrote: the statistcis strongly hint that 7 komi is correct Rather they show that too few games are measured.

Author:	Bill Spight [ Sun Apr 24, 2011 7:50 am ]
Post subject:	Re: Komi on smaller boards
RobertJasiek wrote: HermanHiddema wrote: the statistcis strongly hint that 7 komi is correct Rather they show that too few games are measured. I wouldn't say that. Statistics on games in Japan back when komi was 4.5 indicated a median board score of 7. Ing based his komi of 7.5 on statistics many years ago. Many, many, many games have been used for komi statistics. It is possible that, as pro play improves, komi will change. But the games which would indicate that have yet to be played.