Perfect komi on 7x7 Go, Japanese rules

lightvector · Post by **lightvector** » Tue Apr 21, 2020 10:22 pm

The only komi value I've ever heard anyone seriously claim as the fair komi for 7x7 is 9. Including in Japanese rules, at least according to this page: https://senseis.xmp.net/?7x7ArticleByJDavies

Today I loaded up a recent KataGo 30 block net on 7x7, a board size which it actually plays a tiny percent of games on in the current run. It's pretty quick to hit tens of thousands of playouts on such a small board from the opening position, and doesn't take all that long to hit hundreds of thousands, on the cloud GPU I used. Searching from the opening position, ~200k playouts, 32 threads:

Tromp-Taylor-like rules: KataGo clearly agrees with 9 komi.
8.5 komi: 95% winrate for Black
9.5 komi, 5% winrate for Black

Chinese-like rules: KataGo clearly agrees with 9 komi.
8.5 komi: 95% winrate for Black
9.5 komi, 5% winrate for Black

Japanese-like rules: KataGo thinks the correct komi is 8.
7.5 komi, 94% winrate for Black
8.5 komi: 11% winrate for Black

Woah. What is the magic sequence that White uses to gain an extra point? Let's explore at 8.5 komi to see how White supposedly wins!

Click Here To Show Diagram Code: [go]$$Bc First moves. $$ --------------------------------------- $$ | . . . . . . . | $$ | . . a . b . . | $$ | . . c 2 3 . . | $$ | . . 4 1 . . . | $$ | . . . 5 . . . | $$ | . . . . . . . | $$ | . . . . . . . | $$ ---------------------------------------[/go]

The Sensei's library article suggests white to continue at "a" or "b". KataGo dislikes "a" very rapidly and agrees it's losing for white (again, 8.5 komi). For "b" the first 200k or so playouts have the winrate fluctuate wildly all over the place, but eventually seems to converge on the move being also losing, 93% winrate for Black at 1 million playouts.

Instead, KataGo thinks that "c" for White wins.

Click Here To Show Diagram Code: [go]$$Bc Continuation $$ --------------------------------------- $$ | . . . . . . . | $$ | . . . . b . . | $$ | . . W O X . . | $$ | . . O X . . . | $$ | . . a X . . . | $$ | . . . . . . . | $$ | . . . . . . . | $$ ---------------------------------------[/go]

Black can try "a" or "b" but KataGo thinks neither works (white answers either of them by playing the other). The variations after Black "a" White "b" are numerous and I don't understand them. But I found a neat gem in how KataGo thinks White refutes Black "b". I'm guessing this might be what human players have all missed so far? Of course there's always a chance KataGo missing something here too.

Click Here To Show Diagram Code: [go]$$Bc Continuation with Black "b". $$ --------------------------------------- $$ | . . . . . . . | $$ | . . . . 1 . . | $$ | . . O O X . . | $$ | . . O X . . . | $$ | . . 2 X . . . | $$ | . 4 3 5 . . . | $$ | . . . . . . . | $$ ---------------------------------------[/go]

Now, what does White do next? Some simple things don't work.

If White blocks on the top, then Black hanes on the bottom:

Click Here To Show Diagram Code: [go]$$Wc Failure for White $$ --------------------------------------- $$ | . . . a b . . | $$ | . . . 1 X . . | $$ | . . O O X . . | $$ | . . O X . . . | $$ | . c O X . . . | $$ | . O X X . . . | $$ | . 2 . . . . . | $$ ---------------------------------------[/go]

Next if White protects against "c", then Black will take "a" and win easily by a comfortable margin, having gotten both big endgame moves. But if White tries to take the top first with "b", Black will ignore and play "c". If you work out the endgame, Black will win again by a comfortable margin. (It's not that hard of an endgame to work out).

And if White instead of blocking on the top at all plays on the bottom, then the monkey jump easily destroys too much territory and Black is comfortably winning. You can pretty much already count, more or less:

Click Here To Show Diagram Code: [go]$$Wc Failure for white $$ --------------------------------------- $$ | . 2 . . . S S | $$ | . . . . X S S | $$ | T T O O X S S | $$ | T T O X S S S | $$ | T T O X S S S | $$ | T O X X S S S | $$ | T 1 . . S S S | $$ ---------------------------------------[/go]

So, trusting KataGo is right and isn't missing something (always a chance for a blind spot), maybe we can try this as a nested puzzle if people enjoy trying to work it out.

White to play and win, 8.5 komi, Japanese rules.

Click Here To Show Diagram Code: [go]$$Wc White to play. $$ --------------------------------------- $$ | . . . . . . . | $$ | . . . . X . . | $$ | . . O O X . . | $$ | . . O X . . . | $$ | . . O X . . . | $$ | . O X X . . . | $$ | . . . . . . . | $$ ---------------------------------------[/go]

Initial spoiler/hint and two followup questions:

Partial spoiler + hints for question 1:

Partial spoiler + hints for question 2:

Magicwand · Post by **Magicwand** » Thu Apr 23, 2020 1:09 pm

7x7 has been solved already by brute force method by computer.

Uberdude · Post by **Uberdude** » Thu Apr 23, 2020 1:33 pm

I seem to recall an article in which Li Zhe 6p claimed to have solved 7x7, It wasn't through an exhaustive search (so not what I'd call solved), but he did look at a lot of variations, I wonder if these ones.

Here's extracts: viewtopic.php?p=224716#p224716, the link to original Chinese article is broken.

lightvector · Post by **lightvector** » Thu Apr 23, 2020 2:59 pm

Magicwand wrote:7x7 has been solved already by brute force method by computer.

Do you have a reference for this? For rigorous brute force methods, I was under the impression not even 6x6 has been fully exhaustively proven, although 6x6 has a good chance of being within reach if anyone wanted to spend the (massive) amount of compute power, it's just that I think nobody has yet. But for 7x7 the only thing I had heard of was "human" solutions, or maybe human + computer assistance for endgames or something like that.

Also, all the rigorous brute force methods I think have only used various kinds of area scoring rules? Japanese rules are a bit harder.

Uberdude wrote:I seem to recall an article in which Li Zhe 6p claimed to have solved 7x7, It wasn't through an exhaustive search (so not what I'd call solved), but he did look at a lot of variations, I wonder if these ones.

Here's extracts: viewtopic.php?p=224716#p224716, the link to original Chinese article is broken.

Hmm, is there any source remaining for the claimed solutions if the website is down? The excerpts posted there also omit any mention of the variation that KataGo is finding, starting on move 6. Also, given that it was a Chinese solution, perhaps the solution was also using Chinese rules? It's only on Japanese rules that this new variation (supposedly) becomes strictly superior.

lightvector · Post by **lightvector** » Thu Apr 23, 2020 3:07 pm

By the way, anyone up for taking a shot at what the main idea for what white is at least trying to accomplish in this variation, ignoring some of the messy details?

Especially after you see the first move, after that question 1 at least I think should be quite solvable. It's basically an a endgame tesuji puzzle.

alreadydone · Post by **alreadydone** » Thu Apr 23, 2020 11:24 pm

fyi, someone has recently made some videos in Chinese with the help of KataGo and with the feedback from Li Zhe himself:
https://b23.tv/BV1XT4y1G7St
https://b23.tv/BV1Ra4y1x7pi
https://b23.tv/BV19V411o7Xs
Additional videos with KataGo are found in https://space.bilibili.com/43473472

alreadydone · Post by **alreadydone** » Wed Apr 29, 2020 9:33 pm

I should've included a link to Li Zhe's article, which has been posted before on the leela-zero issues: https://github.com/leela-zero/leela-zer ... Li.Zhe.pdf
https://github.com/leela-zero/leela-zero/issues/1835

yoyoma · Post by **yoyoma** » Wed Apr 29, 2020 9:44 pm

I don't read Chinese, but I assume Li Zhe's article only covers Chinese rules?

KataGo agrees with the consensus for those rules, the question is what about for Japanese rules? Can someone find prior work on that? Or can someone refute KataGo's solution for Japanese rules?

I was too lazy to do it, but maybe someone can post a KataGo solution that illustrates the score difference between Japanese and Chinese rules?

bayu · Post by **bayu** » Thu Apr 30, 2020 2:10 am

edit: oops, I can't count to ten. My post doesn't make sense.

I believe the miraculous stuff already happens within Chinese rules: Without komi, the score difference between the players is usually odd, so it should not make a difference, whether komi 7.5 or 8.5 is used.

Since it does make a difference for katago, something mighty interesting seems to be there. And that something will most probably also explain the shift when using Japanese rules.

alreadydone · Post by **alreadydone** » Mon May 04, 2020 12:03 am

Li Zhe says that his analysis intends to distinguish between B+8 and B+9 (i.e. if black gets the last dame to achieve B+9, Li will count this as B+8, as in Japanese rules), although he will use the Chinese rules in case of seki. He reached the conclusion of B+9 in the article, but according to some comments in the aforementioned videos, he has admitted his omission of this variation and believes that B+8 should be correct.

Dragon · Post by **Dragon** » Tue May 19, 2020 1:56 pm

Magicwand wrote:7x7 has been solved already by brute force method by computer.

is there a link?

lightvector · Post by **lightvector** » Tue May 19, 2020 2:20 pm

As I mentioned above, I think not even 6x6 has been fully rigorously proven, so I think any claimed 7x7 solution is more like "all the human and computer effort invested so far hasn't found anything better, but there's always a chance we missed something" rather than "we know for sure and have proven it". I'd be doubtful that anyone has a true brute force 7x7 solution - maybe Magicwand was thinking of Li Zhe's work, which maybe did use computers a lot to help out analysis?

The latest word on rigorous proofs that I know of is still here, back in 2009, solving up to 5x6:
http://erikvanderwerf.tengen.nl/mxngo.html

It would be really cool to see more recent work, if someone knows of any. And if miraculously someone actually somehow brute-forced 7x7

I agree, a link to that would be cool too.

Anyways, for 7x7 it seems like it stands at B+9 for Chinese (due to Li Zhe and also earlier work by other human professionals and amateurs) and B+8 for Japanese (with KataGo's improvement), but still nobody can be sure if another improvement could be found in either case for either player. Fully rigorous solution is probably out of the question.

lightvector · Post by **lightvector** » Tue May 19, 2020 3:26 pm

By the way, this is maybe a bit overdue, but here's the solution to Question 1, the "easy" question, posed in the initial post.

Click Here To Show Diagram Code: [go]$$Wc First move. $$ --------------------------------------- $$ | . . . . . . . | $$ | . . . . X . . | $$ | . . O O X . . | $$ | . . O X 1 . . | $$ | . . O X . . . | $$ | . O X X . . . | $$ | . . . . . . . | $$ ---------------------------------------[/go]

What is the most basic meaning of this move, why does this cut help white?

Click Here To Show Diagram Code: [go]$$Wc If black simply captures it... $$ --------------------------------------- $$ | . . . . . . . | $$ | . . . . X . . | $$ | . . O O X . . | $$ | . . O X 1 2 . | $$ | . . O X 3 a . | $$ | . O X X . . . | $$ | . . b . . . . | $$ ---------------------------------------[/go]

Now if Black responds at "a", White "b" will become sente, giving White enough points. So of course Black plays the other way.

Click Here To Show Diagram Code: [go]$$Wc Continued... $$ --------------------------------------- $$ | . . . . . . . | $$ | . . . . X . . | $$ | . . O O X b . | $$ | . . O X O X . | $$ | . . O X O 5 . | $$ | . O X X 4 a . | $$ | . . . . . . . | $$ ---------------------------------------[/go]

We'll look at "a" and "b" here. Let's look at "a" first.

Click Here To Show Diagram Code: [go]$$Wc Variation a $$ --------------------------------------- $$ | . . . . . . . | $$ | . . . . X . . | $$ | . . O O X . . | $$ | . . O X O X . | $$ | . . O X O O . | $$ | . O X X X B . | $$ | . . . . . . . | $$ ---------------------------------------[/go]

Click Here To Show Diagram Code: [go]$$Wc Variation a $$ --------------------------------------- $$ | . . . . 3 . . | $$ | . . . 1 X . . | $$ | . . O O X . . | $$ | . 5 O X W B . | $$ | . 4 O X W W . | $$ | 6 O X X B B . | $$ | . 2 . . . . . | $$ ---------------------------------------[/go]

Earlier (in the first post in this thread) we saw that white's problem was that blocking at

didn't have a big enough followup. Black can get

, and

is gote, black can ignore it to play

and white loses more in the lower left than can be gained in the upper right. But that was before white cut and made the exchanges inside black's territory.

Because of the exchanges in black's territory, white can now cut here!

Click Here To Show Diagram Code: [go]$$Wc Variation a, key move (1 capture by black) $$ --------------------------------------- $$ | . . . . O . . | $$ | . . . O X . . | $$ | . . O O X 1 . | $$ | . O O X O X . | $$ | . X O X O O . | $$ | X . X X X X . | $$ | . X . . . . . | $$ ---------------------------------------[/go]

So the earlier probe helped, without it it would be like this, and obviously this wouldn't work:

Click Here To Show Diagram Code: [go]$$Wc Variation a, key move without the probe, doesn't work. (1 capture by black) $$ --------------------------------------- $$ | . . . . O . . | $$ | . . . O X 2 . | $$ | . . O O X 1 . | $$ | . O O X . . . | $$ | . X O X . . . | $$ | X . X X . . . | $$ | . X . . . . . | $$ ---------------------------------------[/go]

So we get:

Click Here To Show Diagram Code: [go]$$Wc Variation a continued (4 captures by black) $$ --------------------------------------- $$ | . . . . O . . | $$ | . 9 . O X 3 . | $$ | 7 . O O X 1 5 | $$ | 6 O O X 4 X . | $$ | 8 X O X . . 2 | $$ | X . X X X X . | $$ | . X . . . . . | $$ ---------------------------------------[/go]

Both sides have 10 points, with black having 4 captures, so black winning only by 4 before komi. With an 8.5 komi as posed in the problem, white wins massively. This is the fundamental meaning of white's probe - to make this sequence work.

Compare to without it:

Click Here To Show Diagram Code: [go]$$Wc Variation without the probe, white's best attempt (1 capture by black) $$ --------------------------------------- $$ | . . . . O 5 . | $$ | . 3 . O X 1 4 | $$ | 7 . O O X 2 . | $$ | 6 O O X . . . | $$ | 8 X O X . . . | $$ | X . X X . . . | $$ | . X . . . . . | $$ ---------------------------------------[/go]

White can only hane at

without the probe, and when black blocks, white has no eye in the upper right corner, so must make eyes with

. We finish the endgame and black has 16 points to white's 6, and one capture. So black wins by 11 here before komi. This is much worse for white than other lines, in fact starting all the way from move 6 from the very original empty board, white's third move in the game is unplayable unless white has this probe planned.

Let's go back and look at variation "b".

Click Here To Show Diagram Code: [go]$$Wc Variation b $$ --------------------------------------- $$ | . . . . . . . | $$ | . . . . X . . | $$ | . . O O X 6 . | $$ | . . O X O X . | $$ | . . O X O 5 . | $$ | . O X X X a . | $$ | . . . . . . . | $$ ---------------------------------------[/go]

Black might try to connect at

to prevent the future trouble in the upper right. White's behind in the liberty race with the probe cutting stones, so now how does white make good on the probe?

Turning here is the start. This isn't the only way, but it's the most stylish.

Click Here To Show Diagram Code: [go]$$Wc Black in trouble $$ --------------------------------------- $$ | . . . . . . . | $$ | . . . . X . . | $$ | . . O O X X . | $$ | . . O X O X . | $$ | . . O X O O . | $$ | . O X X X 1 . | $$ | . . . . . . . | $$ ---------------------------------------[/go]

Now, if black blocks directly:

Click Here To Show Diagram Code: [go]$$Wc Black resistance 1 fails $$ --------------------------------------- $$ | . . . . . . . | $$ | . . . c X . . | $$ | . . O O X X . | $$ | . . O X O X . | $$ | . . O X O O . | $$ | . O X X X 1 b | $$ | . 3 . . a 2 . | $$ ---------------------------------------[/go]

is sente here because it threatens a throw in at "a" for a connect-and-die. Black could make a desperation ko at "b" in response to "a", but black has no threats. So that means black must defend again and white also gets "c", an easy win by white.

Click Here To Show Diagram Code: [go]$$Wc Black resistance 2 fails $$ --------------------------------------- $$ | . . . . . . . | $$ | . . . . X . . | $$ | . . O O X X . | $$ | . . O X O X . | $$ | . . O X O O . | $$ | . O X X X 1 . | $$ | . 2 . . . 3 . | $$ ---------------------------------------[/go]

What if black goes the other way to get that endgame first? Then white descends at

!

And we get this well-known tesuji.

Click Here To Show Diagram Code: [go]$$Bc Tower squeeze $$ --------------------------------------- $$ | . . . . . . . | $$ | . . . . X . . | $$ | . . O O X X . | $$ | . . O X O X . | $$ | 3 1 O X O O . | $$ | 2 O X X X O . | $$ | 5 X . . 4 O . | $$ ---------------------------------------[/go]

Click Here To Show Diagram Code: [go]$$Wc Tower squeeze, :w7: captures at :b1: $$ --------------------------------------- $$ | . . . . . . . | $$ | . . 6 . X . . | $$ | . 4 O O X X . | $$ | . . O X O X . | $$ | X X O X O O . | $$ | 2 1 X X X O . | $$ | X X 5 3 O O . | $$ ---------------------------------------[/go]

And although black can get a bit of compensation on the top, black is losing too much.

Anyways, that's the "primary" meaning of white's probe, as I see it.

lightvector · Post by **lightvector** » Tue May 19, 2020 3:39 pm

As for question 2....

Life In 19x19

Perfect komi on 7x7 Go, Japanese rules

Perfect komi on 7x7 Go, Japanese rules

Re: Perfect komi on 7x7 Go, Japanese rules

Re: Perfect komi on 7x7 Go, Japanese rules

Re: Perfect komi on 7x7 Go, Japanese rules

Re: Perfect komi on 7x7 Go, Japanese rules

Re: Perfect komi on 7x7 Go, Japanese rules

Re: Perfect komi on 7x7 Go, Japanese rules

Re: Perfect komi on 7x7 Go, Japanese rules

Re: Perfect komi on 7x7 Go, Japanese rules

Re: Perfect komi on 7x7 Go, Japanese rules

Re: Perfect komi on 7x7 Go, Japanese rules

Re: Perfect komi on 7x7 Go, Japanese rules

Re: Perfect komi on 7x7 Go, Japanese rules

Re: Perfect komi on 7x7 Go, Japanese rules