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 Post subject: Re: KataGo @ Igo Hatsuyoron 120
Post #41 Posted: Thu Dec 19, 2019 11:38 pm 
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lightvector wrote:
The thing is, some of white's gains on the left side costs white some turns or some liberties, but don't actually lose very much in the case that ultimately the semeai variation is chosen. If black spends those extra liberties pushing in the upper right, black improves the capture variation, but those moves *lose* points on the semeai variation.

So given that most of black's ability to balance white's gains comes at the cost of making one variation worse to improve the other, whereas some of white's gains just purely make one variation better without costing in the other, black starts to get squeezed in both variations.

Sorry, but this is not how the problem works!

Click Here To Show Diagram Code
[go]$$B
$$ ---------------------------------------------------------------------------------
$$ - . . . B O O . . . . O X X X O . O X . - . . . . X X W W . . O X X X O . O X . -
$$ - . . . B X O O X O O O X O X O . . O . - . . . . X O O . O O O X O X O . . O . -
$$ - . . . X O X O O . . O X O O O O O . . - . . . X . X X O . . O X O O O O O . . -
$$ - . X O , . X X X Q O O X . O O X O . . - . X O , X . X O . O O X O O O X O . . -
$$ - . . X X X X O O O . O X X . X X O O . - . . X X X X O O O . O X X O X X O O . -
$$ - X X X O O O . . . O . O X X X O O O O - X X X O O O . . . O . O X X X O O O O -
$$ - O O O O O X O O . . O O X . X O O X O - O O O O X X O O . . O O O O X . O X . -
$$ - O X X X X X O O O . O O O X X X X X X - O X X X . X . O O . O . O . X X X X X -
$$ - O X X X X X X O . . O O X X X X . . . - O X X X . X . O . . O O X X X X . . . -
$$ - O O O X X X O O . O O X X . . , . X X - O O O X . X O O . O O X X . . , . X X -
$$ - O O O O X O O O . O O X . . . X X X X - X . O O X . . O . O . X . . . X X X X -
$$ - X . O O X O X O . O . X . . X X X . . - . . O O X . . O . O . X . . X X X . . -
$$ - . . O O X X X O . O . X . . . X X X . - O O O X X . . O . O . X . . . X X X . -
$$ - O O O O O X . O . O X X X . . . X . . - O O O X O X . O . O O X X . . . X . . -
$$ - O O X O X X . O . O X O O X X X . . . - O O X . . X . O . O . O O X X X . . . -
$$ - O X X X X X . O . O O O O X O X . . X - O X X , X X . O . O O O O X . X . . X -
$$ - O X . . O X O O . . . O O O O X X . X - O X . . O X O O . . . O O O O X X . X -
$$ - O X X . X O . O O O O O O X X X X . X - O X X . X O . O O O O O O X . X X . X -
$$ - X X . . X O O O . . . . O X X X X . . - X X . . X O O O . . . . O X X X X . . -
$$ +-------------------------------------------------------------------------------+
$$ - . . . B O O . . . . O . . . O . O X . - . . . . X X W W . . O . . . O . O X . -
$$ - . . . B X O O X O O O . O . O . . O . - . . . . X O O . O O O . O . O . . O . -
$$ - . . . X O X O O . . O . O O O O O . . - . . . X . X X O . . O . O O O O O . . -
$$ - . X O , . X X X Q O O . O O O , O . . - . X O , X . X O . O O . O O O , O . . -
$$ - . . X X X X O O O . O . . O . . O O . - . . X X X X O O O . O . . O . . O O . -
$$ - X X X O O O X X X O O O . . . O O O O - X X X O O O X X X O . O . . . O . O O -
$$ - O O O O O X O O X X O O . O . O O . O - O O O O X X O O X X O O O O . O O . O -
$$ - O X X X X X O O O X O O O . . . . . . - O X X X . X . O O X O . O O . . . . . -
$$ - O X X X X X X O X X O O . . . . O O O - O X X X . X . O X X O O . . . . O O O -
$$ - O O O X X X O O X O O . . O O O O X . - O O O X . X O O X O O . . O O O O X . -
$$ - O O O O X O O O X O O . O O O X X X X - X X O O X . . O X O O . O O O . X X X -
$$ - X X O O X O X O X O O . O O X X X . . - . O O O X . . O X O O . O O X X X . . -
$$ - . O O O X X X O X O O . O O O X X X . - O O O X X . . O X O O . O O O X X X . -
$$ - O O O O O X . O X O . . . O O O X . . - O O O X O X . O X O O . . O O O X . . -
$$ - O O X O X X . O X O . O O X X X . . . - O O X . . X . O X O . O O X X X . . . -
$$ - O X X X X X . O X O O O O X . X . . X - O X X , X X . O X O O O O X . X . . X -
$$ - O X . . O X O O X X X X X X O X X . X - O X . . O X O O X X X X X X O X X . X -
$$ - O X X . X O . O O O O O O X . X X . X - O X X . X O . O O O O O O X . X X . X -
$$ - X X . . X O O O . . . . O X X X X . . - X X . . X O O O . . . . O X X X X . . -
$$ --------------------------------------------------------------------------------+[/go]

Only territorial gains and losses that are located OUTSITE the Main Semeai area (i.e. not in the immediate vicinity of White's large group on the left nor of Black's large group in the upper right) have an identical effect on both Main Variations (Capture and Semeai Variation).

White gained an absolute advantage of three points (B + 5 / B + 3 ==> B + 2 / Jigo).

Click Here To Show Diagram Code
[go]$$B
$$ ---------------------------------------------------------------------------------
$$ - . . . X O O . . . . O X X X O . O X . - . . . . X X O O . . O X X X O . O X . -
$$ - . . . X X O O X O O O X O X O . . O . - . . . . X O O . O O O X O X O . . O . -
$$ - . . . X O X O O . . O X O O O O O . . - . . . X . X X O . . O X O O O O O . . -
$$ - . X O , . X X X O O O X . O O X O . . - . X O , X . X O . O O X O O O X O . . -
$$ - . . X X X X O O O . O X X . X X O O . - . . X X X X O O O . O X X O X X O O . -
$$ - X X X O O O . . . O . O X X X O O O O - X X X O O O . . . O . O X X X O O O O -
$$ - O O O O O X O O . . O O X . X O O X O - O O O O X X O O . . O O O O X . O X . -
$$ - O X X X B X O O O . O Q O X X X X X X - O X X X . X . O O . O . O . X X X X X -
$$ - O X X X B X X O . . O O X X X X . . . - O X X X . X . O . . O O X X X X . . . -
$$ - O O O X B X O O . O O X X . . , . X X - O O O X . X O O . O O X X . . , . X X -
$$ - O O O O X O O O . O O X . . . X X X X - X . O O X . . O . O . X . . . X X X X -
$$ - X . O O X O X O . O . X . . X X X . . - . . O O X . . O . O . X . . X X X . . -
$$ - . . O O X X X O . O . X . . . X X X . - O O O X X . . O . O . X . . . X X X . -
$$ - O O O O O X . O . O X X X . . . X . . - O O O X O X . O . O O X X . . . X . . -
$$ - O O X O B X . O . O X O O X X X . . . - O O X . . X . O . O . O O X X X . . . -
$$ - O X X B B X . O . O O O O X O X . . X - O X X , X X . O . O O O O X . X . . X -
$$ - O X . . O X O O . . . O O O O X X . X - O X . . O X O O . . . O O O O X X . X -
$$ - O X X . X O . O O O O O O X X X X . X - O X X . X O . O O O O O O X . X X . X -
$$ - X X . . X O O O . . . . O X X X X . . - X X . . X O O O . . . . O X X X X . . -
$$ +-------------------------------------------------------------------------------+
$$ - . . . X O O . . . . O . . . O . O X . - . . . . X X O O . . O . . . O . O X . -
$$ - . . . X X O O X O O O . O . O . . O . - . . . . X O O . O O O . O . O . . O . -
$$ - . . . X O X O O . . O . O O O O O . . - . . . X . X X O . . O . O O O O O . . -
$$ - . X O , . X X X O O O . O O O , O . . - . X O , X . X O . O O . O O O , O . . -
$$ - . . X X X X O O O . O . . O . . O O . - . . X X X X O O O . O . . O . . O O . -
$$ - X X X O O O X X X O O O . . . O O O O - X X X O O O X X X O . O . . . O . O O -
$$ - O O O O O X O O X X O O . O . O O . O - O O O O X X O O X X O O O O . O O . O -
$$ - O X X X B X O O O X O Q O . . . . . . - O X X X . X . O O X O . O O . . . . . -
$$ - O X X X B X X O X X O O . . . . O O O - O X X X . X . O X X O O . . . . O O O -
$$ - O O O X B X O O X O O . . O O O O X . - O O O X . X O O X O O . . O O O O X . -
$$ - O O O O X O O O X O O . O O O X X X X - X X O O X . . O X O O . O O O . X X X -
$$ - X X O O X O X O X O O . O O X X X . . - . O O O X . . O X O O . O O X X X . . -
$$ - . O O O X X X O X O O . O O O X X X . - O O O X X . . O X O O . O O O X X X . -
$$ - O O O O O X . O X O . . . O O O X . . - O O O X O X . O X O O . . O O O X . . -
$$ - O O X O B X . O X O . O O X X X . . . - O O X . . X . O X O . O O X X X . . . -
$$ - O X X B B X . O X O O O O X . X . . X - O X X , X X . O X O O O O X . X . . X -
$$ - O X . . O X O O X X X X X X O X X . X - O X . . O X O O X X X X X X O X X . X -
$$ - O X X . X O . O O O O O O X . X X . X - O X X . X O . O O O O O O X . X X . X -
$$ - X X . . X O O O . . . . O X X X X . . - X X . . X O O O . . . . O X X X X . . -
$$ --------------------------------------------------------------------------------+[/go]

Opponent's territory can be also destroyed in an identical manner in both Main Variations IN the Main Semeai area, but these destructions are costly.
In principle, the destructor has to pay in LIBERTIES in the CAPTURE Variation, but in POINTS of territory in the SEMEAI Variation.

White gained a temporary advantage of another five points (B + 2 / Jigo ==> W + 3 / W + 5).

Click Here To Show Diagram Code
[go]$$B
$$ ---------------------------------------------------------------------------------
$$ - . . . X O O . . . . O X X X O . O X . - . . . . X X O O . . O X X X O . O X . -
$$ - . . . X X O O X O O O X O X O . . O . - . . . . X O O . O O O X O X O . . O . -
$$ - . . . X O X O O . . O X O O O O O . . - . . . X . X X O . . O X O O O O O . . -
$$ - . X O , . X X X O O O X . O O X O . . - . X O , X . X O . O O X O O O X O . . -
$$ - . . X X X X O O O . O X X . X X O O . - . . X X X X O O O . O X X O X X O O . -
$$ - X X X O O O . . . O . O X X X O O O O - X X X O O O . . . O . O X X X O O O O -
$$ - O O O O O X O O . . O O X . X O O X O - O O O O X X O O . . O O O @ X . O X . -
$$ - O X X X X X O O O . O O O X X X X X X - O X X X . X . O O . O . O . X X X X X -
$$ - O X X X X X X O . . O O X X X X . . . - O X X X . X . O . . O O X X X X . . . -
$$ - O O O X X X O O . O O X X . . , . X X - O O O X . X O O . O O X X . . , . X X -
$$ - O O O O X O O O . O O X . . . X X X X - X . O O X . . O . O . X . . . X X X X -
$$ - X . O O X O X O . O . X . . X X X . . - . . O O X . . O . O . X . . X X X . . -
$$ - . . O O X X X O . O . X . . . X X X . - O O O X X . . O . O . X . . . X X X . -
$$ - O O O O P X . O . O X X X . . . X . . - O O O X O X . O . O O X X . . . X . . -
$$ - O O X O X X . O . O # O O X X X . . . - O O X . . X . O . O . O O X X X . . . -
$$ - O X X X X X . O . O O O O X O X . . X - O X X , X X . O . O O O O X . X . . X -
$$ - O X . . O X O O . . . O O O O X X . X - O X . . O X O O . . . O O O O X X . X -
$$ - O X X . X O . O O O O O O X X X X . X - O X X . X O . O O O O O O X . X X . X -
$$ - X X . . X O O O . . . . O X X X X . . - X X . . X O O O . . . . O X X X X . . -
$$ +-------------------------------------------------------------------------------+
$$ - . . . X O O . . . . O . . . O . O X . - . . . . X X O O . . O . . . O . O X . -
$$ - . . . X X O O X O O O . O . O . . O . - . . . . X O O . O O O . O . O . . O . -
$$ - . . . X O X O O . . O . O O O O O . . - . . . X . X X O . . O . O O O O O . . -
$$ - . X O , . X X X O O O . O O O , O . . - . X O , X . X O . O O . O O O , O . . -
$$ - . . X X X X O O O . O . . O . . O O . - . . X X X X O O O . O . . O . . O O . -
$$ - X X X O O O X X X O W O . . . O W O O - X X X O O O X X X O . O . . . O . O O -
$$ - O O O O @ X O O X X O O . W . O O . O - O O O O X X O O X X O O P O . O O . O -
$$ - O X X X X X O O O X O O O . . . . . . - O X X X . X . O O X O . O P . . . . . -
$$ - O X X X X X X O X X O O . . . . O O O - O X X X . X . O X X O O . . . . O O O -
$$ - O O O X X X O O X O O . . O O O O X . - O O O X . X O O X O O . . O O O O X . -
$$ - O O O O X O O O X O O . O O O X X X X - X X O O X . . O X O O . O O O . X X X -
$$ - X X O O X O X O X O O . O O X X X . . - . O O O X . . O X O O . O O X X X . . -
$$ - . O O @ X X X O X O O . O O O X X X . - O O O X X . . O X O O . O O O X X X . -
$$ - O O O @ O X . O X O . . . O O O X . . - O O O X O X . O X O P . . O O O X . . -
$$ - O O X @ X X . O X O . O O X X X . . . - O O X . . X . O X O . O O X X X . . . -
$$ - O X X X X X . O X O O O O X . X . . X - O X X , X X . O X O O O O X . X . . X -
$$ - O X . . O X O O X X X X X X O X X . X - O X . . O X O O X X X X X X O X X . X -
$$ - O X X . X O . O O O O O O X . X X . X - O X X . X O . O O O O O O X . X X . X -
$$ - X X . . X O O O . . . . O X X X X . . - X X . . X O O O . . . . O X X X X . . -
$$ --------------------------------------------------------------------------------+[/go]

In the CAPTURE Variation, White's connection of her single stone at the left gained her two points.
However, she also lost liberties in the process, so Black is able to connect his single stone in the centre, as well as creating an eye (with White prisoner) in the top right, spending this won liberties for his own territorial gain.
In total, White lost two points from her temporary advantage (W + 3 ==> W + 1).

In the SEMEAI Variation, White spent four additional stones for destroying Black territory at the left, but Black added only three stones to his large group in the upper right.
Additionally, due to Black's eye, White has to occupy all cutting points around Black's large group, as well as Black's eye point, so losing another three points in the process.
In total, White lost five points from her temporary advantage (W + 5 ==> Jigo).

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 Post subject: Re: KataGo @ Igo Hatsuyoron 120
Post #42 Posted: Fri Dec 20, 2019 12:05 pm 
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Cassandra wrote:
A 50 per cent approach-move liberty

Did you ever wonder why the score difference between the Capture Variation and the Semeai Variation with KataGo's new ( & amateurish enhanced) solution is odd (W + 1 vs. Jigo), while this difference was even with Our Solution (B + 5 / B + 3), as well as decades ago?

...
With the Semeai Variation, however, due to Black's eye at O13 (and his connection at L6, and White's vanished eye in the centre at M12), White is able to approach at c AND d, only after connecting at the crossed board point before. This connection costs her one point of territory, but in the Semeai Variation only.


144 White's move should be in M11 instead of M12. its one point better for White in Semeai Variation.
so in both variations the result will be W + 1


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 Post subject: Re: KataGo @ Igo Hatsuyoron 120
Post #43 Posted: Fri Dec 20, 2019 1:40 pm 
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dany wrote:
144 White's move should be in M11 instead of M12. its one point better for White in Semeai Variation.
so in both variations the result will be W + 1.

Thanks a lot, dany. When thinking about the consequences of Joachim's tesuji of O14 (instead of O12), the Semeai Variation was not yet on our radar ...

Joachim will be very happy now, as he found different scores in both Main Variations a bit disappointing.

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 Post subject: Re: KataGo @ Igo Hatsuyoron 120
Post #44 Posted: Sat Jan 04, 2020 1:16 am 
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Online playing schedule: Little Golem, turn-based
This is maybe OT, but has anyone tested DNN-based bots (Leela Zero, KataGo, SAI, etc.) on the whole-board endgame problems (attached) in Appendix C of [BW94], including the 9-dan stumping problem [0] and many 9x9 problems? (LZ may be less appropriate due to fixed 7.5 komi.) Additional problems are found in:
http://library.msri.org/books/Book29/files/kim.pdf
http://library.msri.org/books/Book56/fi ... kamura.pdf (4.2. Whole board problems)
https://webdocs.cs.ualberta.ca/~mmuelle ... board.html
https://webdocs.cs.ualberta.ca/~mmuelle ... hesis.html (compressed pdf, A.3, modifications of [BW94] problems; Chapter 7 describes the program Explorer)
https://www.dumbo.ai.kyutech.ac.jp/~tei ... 1slide.pdf (Problems 3 and 4)

I wonder how these problems designed with mathematical theory differ from those from traditional Go practice. I think they likely also require specific training (like what lightvector did for Hatsuyoron 120) to solve. The search would need to be extremely wide and the number of variations/branches may be enormous due to lack of forced moves.
The attachments contain solutions to the [BW94] problems, but only the first moves. It's said in the paper [1] that "Our program Explorer uses this tool to play full board endgames. It plays a nontrivial class of endgame positions perfectly"; Explorer can be downloaded at [2] but only runs in Mac. Also, I can't find SGF files for the "Perfect Play" and "Node Rooms" collections (see [3]) in Mueller's Computer Go Test Collection [4]. Any idea?

[BW94] Berlekamp--Wolfe 1994, Mathematical Go: Chilling Gets the Last Point
[0] https://zhuanlan.zhihu.com/p/33860825 (in Chinese)
[1] https://webdocs.cs.ualberta.ca/~mmuelle ... dgames.pdf (Optimizations as described in 4. Local Move Generation are potentially necessary to solve the problems besides the AlphaZero/KataGo algorithms.)
[2] http://www.computer-go.info/db/oprog.php?a=Explorer or https://www.applefritter.com/node/13972
[3] https://webdocs.cs.ualberta.ca/~mmuelle ... endix.html
[4] https://webdocs.cs.ualberta.ca/~games/go/cgtc/


Attachments:
Mathematical Go solutions.pdf [215.82 KiB]
Downloaded 24 times
mathematical Go problems.pdf [1.2 MiB]
Downloaded 24 times

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 Post subject: Re: KataGo @ Igo Hatsuyoron 120
Post #45 Posted: Fri Jan 10, 2020 11:24 am 
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The Variation Tree of our website has been updated:

KataGo's New Move Suggestions

Please let me know if you find any issues ...

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The really most difficult Go problem ever: http://igohatsuyoron120.de/index.htm
Igo Hatsuyoron #120 (still unresolved by professionals, maybe solved by four amateurs)


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 Post subject: Re: KataGo @ Igo Hatsuyoron 120
Post #46 Posted: Sat Jan 11, 2020 12:27 am 
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alreadydone,

1) thank you for your links in your message body.

2) Your two attachments contain photo/scan copies of several pages of a book. IMO, the copies have more pages than can be expected to be fair use when spread publicly. Judging from experience here, I'd say, one or two pages of photo/scan copies would be ok. Note that citations (that is not: photo/scan copies) with proper credit would allow more pages if occurring in new printed media (that is not: wiki web pages).

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Post #47 Posted: Mon Jan 20, 2020 4:17 pm 
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Did you by any chance test the version trained on Igo Hatsuyoron against any other versions of Kata? I don't know that it's an important question, but it piqued my curiosity whether it learned anything generalizable, forgot something other versions knew, or was essentially unaffected by spending so much time on such an obscure scenario.

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 Post subject: Re: KataGo @ Igo Hatsuyoron 120
Post #48 Posted: Tue Jan 21, 2020 2:35 pm 
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new move

W+1

Click Here To Show Diagram Code
[go]$$Wc
$$ +---------------------------------------+
$$ | . . . X O . . . . . . . X X . . O X . |
$$ | . . . X X O O X O O . X O X O . . O . |
$$ | . . . X O X O O . . . X O O . O O . . |
$$ | . X O , . X X X O O . X . O O X . . . |
$$ | . . X X X X O O O . O X X . X X O O . |
$$ | . X . O O O X X X O . . X . X O . O . |
$$ | O O O O O X O O X X O O X O X . . X . |
$$ | O X . X . X O O O X O . . . X X X X X |
$$ | O X . X X X X O X X O . X X X X O O O |
$$ | O O O X . X O O X O O X X O O O O X . |
$$ | X . O O X 1 . O X O . X O O O . X X X |
$$ | . X O O X 2 3 O X O . X O O X X X O O |
$$ | X . O O X . . O X O . X O . O . X X O |
$$ | . O O O O X . O X O . X X O O O X O O |
$$ | O O X O X X . O X O X . O X X X O O O |
$$ | O X X X X X . O X O O O O X O X O O X |
$$ | O . . . O X O O X X X X X . O X X O X |
$$ | O . X . X O . O O O O O O X O X . O X |
$$ | . X . . X O O O . . . . O X X X . O . |
$$ +---------------------------------------+[/go]


Attachments:
igo120ko_var4.sgf [1.93 KiB]
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igo120ko_var3.sgf [2.09 KiB]
Downloaded 12 times
igo120ko_var1.sgf [2.08 KiB]
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 Post subject: Re: KataGo @ Igo Hatsuyoron 120
Post #49 Posted: Fri Jan 24, 2020 11:52 pm 
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Dear dany,

Thank you very much indeed for your very interesting suggestion.

To be honest, I have not checked your ko variations, because usually Black is unable to win any ko in this problem.
In my opinion (not yet crosschecked by Joachim), Black can (should) do without your ko, and still reaches a jigo (with your choice of setting the komi to zero).

To ease the evaluation of "your" position (and the variations thereafter), I have played all the other "unaffected" moves of the Main Semeai first, and reached the following state on the board:

Click Here To Show Diagram Code
[go]$$Bc
$$ +---------------------------------------+
$$ | . . . X O a . . . . O X X X O . O X . |
$$ | . . . X X O O X O O O X O X O . . O . |
$$ | . . . X O X O O . . w X O O O O O . . |
$$ | . X O , . X X X O O O X . O O X w . . |
$$ | . . X X X X O O O . O X X O X X O O . |
$$ | X X X O O O X X X O . O X X X O O O O |
$$ | O O O O O X O O X X O O X O X . . X . |
$$ | O X X X X X O O O X O . O . X X X X X |
$$ | O X X X X X X O X X O O X X X X O O O |
$$ | O O O X b X O O X O O X X O O O O X . |
$$ | O O O O X O . O X O O X O O O . X X X |
$$ | X . O O X . . O X O . X O O X X X O O |
$$ | . . O O X b . O X O . X O O O X X X O |
$$ | O O O O O X . O X O w X X O O O X O O |
$$ | O O X O X X . O X O X w O X X X O O O |
$$ | O X X X X X . O X O O O O X O X O O X |
$$ | O X . k O X O O X X X X X . O X X O X |
$$ | O c X . X O . O O O O O O X O X . O X |
$$ | . X . . X O O O . . . . O X X X . O . |
$$ +---------------------------------------+[/go]

Please be aware:
  • White will never capture with moves at any of the b-points at the left.
  • However, Black will have to connect at these points, if necessary, before White's main decision point (i.e. just before she captures the hanezeki's tail, or chooses the Semeai Variation).
  • Black will never play at any of the w-points at the right, after White's decision between the Capture and the Semeai Variation.
  • White will capture the hanezeki's tail, or choose to continue with the Semeai Variation, at the moment when Black's large group at the top right has only seven liberties left -- after a Black move.

Please find my variations in the attached SGF.

Main points of interest are:
  • Will White connect at a at the upper edge, or will Black capture White's single stone there?
  • Will White play the kikashi of W k & W c in the lower left corner, or will Black be able to defend at c?



Attachments:
danysKo.sgf [29.09 KiB]
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The really most difficult Go problem ever: http://igohatsuyoron120.de/index.htm
Igo Hatsuyoron #120 (still unresolved by professionals, maybe solved by four amateurs)
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 Post subject: Re: KataGo @ Igo Hatsuyoron 120
Post #50 Posted: Sat Jan 25, 2020 3:38 am 
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Dany kindly made me aware that I missed an important detail ...

Click Here To Show Diagram Code
[go]$$Wc
$$ +---------------------------------------+
$$ | . . . X O . . . . . . . X X . . O X . |
$$ | . . . X X O O X O O . X O X O . . O . |
$$ | . . . X O X O O . . . X O O . O O . . |
$$ | . X O , . X X X O O . X . O O X . . . |
$$ | . . X X X X O O O . O X X . X X O O . |
$$ | . X . O O O X X X O . . X . X O . O . |
$$ | O O O O O X O O X X O O X O X . . X . |
$$ | O X 6 X 7 X O O O X O . . . X X X X X |
$$ | O X 5 X X X X O X X O . X X X X O O O |
$$ | O O O X . X O O X O O X X O O O O X . |
$$ | X . O O X W 8 O X O . X O O O . X X X |
$$ | . X O O X B W O X O . X O O X X X O O |
$$ | X . O O X . . O X O . X O . O . X X O |
$$ | . O O O O X . O X O . X X O O O X O O |
$$ | O O X O X X . O X O X . O X X X O O O |
$$ | O X X X X X . O X O O O O X O X O O X |
$$ | O . . . O X O O X X X X X . O X X O X |
$$ | O 4 X . X O . O O O O O O X O X . O X |
$$ | . X . . X O O O . . . . O X X X . O . |
$$ +---------------------------------------+[/go]

After dany's creation of the ko shape in the centre, Black is unable to strive for a jigo (komi = 0) by definding his lower left corner with the move at 4.

Due to the shortage of liberties of Black's two stones at the left, Black is forced to start a ko fight with 8 that he cannot win.

With what we know now, the variation with Black's tenuki after KataGo's bad-shape move really ends with W + 1 (komi = 0) respectively W + 2 (komi = 1).

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The really most difficult Go problem ever: http://igohatsuyoron120.de/index.htm
Igo Hatsuyoron #120 (still unresolved by professionals, maybe solved by four amateurs)

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