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Perfect komi on 7x7 Go, Japanese rules http://www.lifein19x19.com/viewtopic.php?f=18&t=17413 |
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Author: | lightvector [ Tue Apr 21, 2020 10:22 pm ] |
Post subject: | Perfect komi on 7x7 Go, Japanese rules |
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! 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. 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. Now, what does White do next? Some simple things don't work. If White blocks on the top, then Black hanes on the bottom: 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: 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. Initial spoiler/hint and two followup questions: Partial spoiler + hints for question 1: Partial spoiler + hints for question 2: |
Author: | Magicwand [ Thu Apr 23, 2020 1:09 pm ] |
Post subject: | Re: Perfect komi on 7x7 Go, Japanese rules |
7x7 has been solved already by brute force method by computer. |
Author: | Uberdude [ Thu Apr 23, 2020 1:33 pm ] |
Post subject: | Re: Perfect komi on 7x7 Go, Japanese rules |
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: https://lifein19x19.com/viewtopic.php?p=224716#p224716, the link to original Chinese article is broken. |
Author: | lightvector [ Thu Apr 23, 2020 2:59 pm ] |
Post subject: | Re: Perfect komi on 7x7 Go, Japanese rules |
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: https://lifein19x19.com/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. |
Author: | lightvector [ Thu Apr 23, 2020 3:07 pm ] |
Post subject: | Re: Perfect komi on 7x7 Go, Japanese rules |
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. |
Author: | alreadydone [ Thu Apr 23, 2020 11:24 pm ] |
Post subject: | Re: Perfect komi on 7x7 Go, Japanese rules |
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 |
Author: | alreadydone [ Wed Apr 29, 2020 9:33 pm ] |
Post subject: | Re: Perfect komi on 7x7 Go, Japanese rules |
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 |
Author: | yoyoma [ Wed Apr 29, 2020 9:44 pm ] |
Post subject: | Re: Perfect komi on 7x7 Go, Japanese rules |
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? |
Author: | bayu [ Thu Apr 30, 2020 2:10 am ] |
Post subject: | Re: Perfect komi on 7x7 Go, Japanese rules |
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. |
Author: | alreadydone [ Mon May 04, 2020 12:03 am ] |
Post subject: | Re: Perfect komi on 7x7 Go, Japanese rules |
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. |
Author: | Dragon [ Tue May 19, 2020 1:56 pm ] |
Post subject: | Re: Perfect komi on 7x7 Go, Japanese rules |
Magicwand wrote: 7x7 has been solved already by brute force method by computer. is there a link? |
Author: | lightvector [ Tue May 19, 2020 2:20 pm ] |
Post subject: | Re: Perfect komi on 7x7 Go, Japanese rules |
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. |
Author: | lightvector [ Tue May 19, 2020 3:26 pm ] |
Post subject: | Re: Perfect komi on 7x7 Go, Japanese rules |
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. |
Author: | lightvector [ Tue May 19, 2020 3:39 pm ] |
Post subject: | Re: Perfect komi on 7x7 Go, Japanese rules |
As for question 2.... |
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