KataGo @ Igo Hatsuyoron 120

Cassandra · #1

Apparently triggered by the report of my experiences with ZBaduk, I received an email from "lightvector", kindly asking for the SGFs of our variation tree to be used as training material for KataGo -- in exchange for hopefully (not at all guaranteed) some new insights into the problem for our further study.

This thread is intended to present those of KataGo's findings that affect the final score of the problem (according to our estimation).

Disclaimer:
Please be aware that these AIish findings -- similar to our amateurish enhancements of professional sequences -- are not yet crosschecked and "officially" validated by professinal Go players; therefore their status cannot be considered to be stable yet.
KataGo's work is a fascinating new kind of an "ongoing" analysis, it must not be understood as having found a new solution to the problem.
Please remember the tremendous efforts of Fujisawa Hideyuki and his study group, without which neither we nor any AI would ever have had the slightest chance to "find" a complete solution sequence to the most difficult problem ever created.

If lightvector likes (and has time) to contribute with the AI technical and processual side of the medal, he is happily invited to do so.

My postings will concentrate on the game of Go.

Cassandra · #2

Click Here To Show Diagram Code: [go]$$Wcm94 W 94 (KataGo's Atari) $$ +---------------------------------------+ $$ | . . . . . . . . . . . . X . . . O X . | $$ | . . . . . . . X O O . X O X O . . O . | $$ | . . . . . X . O . . . X O . . O O . . | $$ | . 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 . | $$ | O O O O . X O O X X O O . O X . . X . | $$ | O X . X . X . O O X O . . . X X X X X | $$ | O X . X . . . O X X O . X X X X O O O | $$ | X O O , . X . O X O O X X O O O O X . | $$ | X X ? O X . . O X O . X O O O . X X X | $$ | X . . O X . . O X O . X O O X X X O O | $$ | X X O 1 X . . O X O . X O O O X X X O | $$ | X O O X O X . O X O . X X O O O X O O | $$ | X O X . . X . O X O X . O X X X O O O | $$ | O X X , X . . O X O O O O X O X O O X | $$ | O . . . O X . O X X X X X . O X X O X | $$ | O . X . . . X O O O O O O X O X . O X | $$ | . X . . . . . O . . . . O X X X . O . | $$ +---------------------------------------+[/go]

For White's move 94 in Our Solution, KataGo suggested giving atari at Black's single stone below (with D7), instead of immediately giving atari at Black's nakade (with a move at C9).
KataGo's atari is typical for Inoue Dosetsu Inseki, because it can be played successfully at only one moment in time.

KataGo's findings will be shown at an equivalent moment in the course of Our Solution.
KataGo has several changes in the order of moves, because e.g. it does not have a solid understanding of what a "technical correct timing" of a forcing move is.

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Click Here To Show Diagram Code: [go]$$Bc Var B 95 (Mistake: Black is unable to capture) $$ +---------------------------------------+ $$ | . . . . . . . . . . . . X . . . O X . | $$ | . . . . . . . X O O . X O X O . . O . | $$ | . . . . . X . O . . . X O . . O O . . | $$ | . 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 . | $$ | O O O O . X O O X X O O . O X . . X . | $$ | O X . X . X . O O X O . . . X X X X X | $$ | O X . X . . . O X X O . X X X X O O O | $$ | X O O , . X . O X O O X X O O O O X . | $$ | X X . O X . . O X O . X O O O . X X X | $$ | X . . O X . . O X O . X O O X X X O O | $$ | X X O O X . . O X O . X O O O X X X O | $$ | X O O X O X . O X O . X X O O O X O O | $$ | X O X . 1 X . O X O X . O X X X O O O | $$ | O X X , X . . O X O O O O X O X O O X | $$ | O . . . O X . O X X X X X . O X X O X | $$ | O . X . . . X O O O O O O X O X . O X | $$ | . X . . . . . O . . . . O X X X . O . | $$ +---------------------------------------+[/go]

Just now, Black is unable to capture White's single stone with a move at 1.

Click Here To Show Diagram Code: [go]$$Bc Var B 95 (contd) $$ +---------------------------------------+ $$ | . . . . . . . . . . . . X . . . O X . | $$ | . . . . . . . X O O . X O X O . . O . | $$ | . . . . . X . O . . . X O . . O O . . | $$ | . 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 . | $$ | O O O O . X O O X X O O . O X . . X . | $$ | O X . X . X . O O X O . . . X X X X X | $$ | O X . X . . . O X X O . X X X X O O O | $$ | X O O , . X . O X O O X X O O O O X . | $$ | X X . O X . . O X O . X O O O . X X X | $$ | X 2 3 O X . . O X O . X O O X X X O O | $$ | X X O O X . . O X O . X O O O X X X O | $$ | X O O X . X . O X O . X X O O O X O O | $$ | X O X . X X . O X O X . O X X X O O O | $$ | O X X , X . . O X O O O O X O X O O X | $$ | O . . . O X . O X X X X X . O X X O X | $$ | O . X . . . X O O O O O O X O X . O X | $$ | . X . . . . . O . . . . O X X X . O . | $$ +---------------------------------------+[/go]

White throws-in at 2, forcing Black to capture at 3.

Click Here To Show Diagram Code: [go]$$Bc Var B 95 (contd II; White lives easily at the left) $$ +---------------------------------------+ $$ | . . . . . . . . . . . . X . . . O X . | $$ | . . . . . . . X O O . X O X O . . O . | $$ | . . . . . X . O . . . X O . . O O . . | $$ | . 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 . | $$ | O O O O . X O O X X O O . O X . . X . | $$ | O X . X . X . O O X O . . . X X X X X | $$ | O X . X . . . O X X O . X X X X O O O | $$ | X O O , . X . O X O O X X O O O O X . | $$ | X X 4 O X . . O X O . X O O O . X X X | $$ | X . X O X . . O X O . X O O X X X O O | $$ | X X O O X . . O X O . X O O O X X X O | $$ | X O O X . X . O X O . X X O O O X O O | $$ | X O X . X X . O X O X . O X X X O O O | $$ | O X X , X . . O X O O O O X O X O O X | $$ | O . . . O X . O X X X X X . O X X O X | $$ | O . X . . . X O O O O O O X O X . O X | $$ | . X . . . . . O . . . . O X X X . O . | $$ +---------------------------------------+[/go]

Finally, White 4 is a double-atari, securing life for White's large group at the left.
The entire right half of the board is White's territory now, so she wins the game by a large margin.

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Click Here To Show Diagram Code: [go]$$Wcm94 B 95 (Black's continuation) $$ +---------------------------------------+ $$ | . . . . . . . . . . . . X . . . O X . | $$ | . . . . . . . X O O . X O X O . . O . | $$ | . . . . . X . O . . . X O . . O O . . | $$ | . 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 . | $$ | O O O O . X O O X X O O . O X . . X . | $$ | O X . X . X . O O X O . . . X X X X X | $$ | O X . X . . . O X X O . X X X X O O O | $$ | X O O 2 . X . O X O O X X O O O O X . | $$ | X X 3 O X . . O X O . X O O O . X X X | $$ | X 4 . O X . . O X O . X O O X X X O O | $$ | X X O O X . . O X O . X O O O X X X O | $$ | X O O X O X . O X O . X X O O O X O O | $$ | X O X a b X . O X O X . O X X X O O O | $$ | O X X , X . . O X O O O O X O X O O X | $$ | O . . . O X . O X X X X X . O X X O X | $$ | O . X . . . X O O O O O O X O X . O X | $$ | . X . . . . . O . . . . O X X X . O . | $$ +---------------------------------------+[/go]

KataGo recommended to answer from above with Black 95, forcing White to connect at 96 (the throw-in at 97 is no longer possible).
This is also an atari at Black's oversized nakade, so Black has to complete the shape with 97.
Locally, White wants to capture at a, while Black wants to capture at b.

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Click Here To Show Diagram Code: [go]$$Wcm18 W 118 (White captures) $$ +---------------------------------------+ $$ | . . . . . # . @ . . . . X . . . O X . | $$ | . . . . X @ @ . O O . X O X O . . O . | $$ | . . . # . # # O . . . X O . . O O . . | $$ | . X O , # . # 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 . | $$ | O O O O . X O O X X O O . O X . . X . | $$ | O X . X . X . O O X O . . . X X X X X | $$ | O X . X . # . O X X O . X X X X O O O | $$ | X O O X . X @ O X O O X X O O O O X . | $$ | X X O O X . . O X O . X O O O . X X X | $$ | X X . O X . . O X O . X O O X X X O O | $$ | X X O O X . . O X O . X O O O X X X O | $$ | X O O X O X . O X O . X X O O O X O O | $$ | X O X 1 . X . O X O X . O X X X O O O | $$ | O X X , X # . O X O O O O X O X O O X | $$ | O . . . O X @ O X X X X X . O X X O X | $$ | O . X . # @ . O O O O O O X O X . O X | $$ | . X . . # @ @ O . . . . O X X X . O . | $$ +---------------------------------------+[/go]

Let's assume a "peaceful" continuation, following the course of the endgame of Our Solution in the left half of the board (marked stones).
Thereafter, White has sente to capture at 118.

Click Here To Show Diagram Code: [go]$$Wcm118 B 119 - W 124 $$ +---------------------------------------+ $$ | . . . . . X . O . . . . X . . . O X . | $$ | . . . . X O O . O O . X O X O . . O . | $$ | . . . X . X X O . . . X O . . O O . . | $$ | . X O , 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 . | $$ | O O O O . X O O X X O O 7 O X . . X . | $$ | O X . X . X . O O X O . . . X X X X X | $$ | O X . X . X . O X X O . X X X X O O O | $$ | X O O X . X O O X O O X X O O O O X . | $$ | X X O O X . . O X O . X O O O . X X X | $$ | X X . O X . . O X O . X O O X X X O O | $$ | X X O O X . . O X O . X O O O X X X O | $$ | X O O 5 O X . O X O 3 X X O O O X O O | $$ | X O X O 4 X . O X O X 6 O X X X O O O | $$ | O X X 2 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]

Black blocks at 119, whereafter both sides exchange the atari of 120 and 121.
White's connection at 122 costs her two liberties in the Main Semeai, so Black can also connect at 123, losing the same number of liberties for his large group in the upper right.

Click Here To Show Diagram Code: [go]$$Bc $$ +---------------------------------------+ $$ | . . . . . X . O . . . . X . . . O X . | $$ | . . . . X O O . O O . X O X O . . O . | $$ | . . . X . X X O . . . X O . . O O . . | $$ | . X O , 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 . | $$ | O O O O . X O O X X O O O O X . . X . | $$ | O X . X . X . O O X O . . . X X X X X | $$ | O X . X . X . O X X O . X X X X O O O | $$ | X O O X . X O O X O O X X O O O O X . | $$ | X X O O X . . O X O . X O O O . X X X | $$ | X X . O X . . O X O . X O O X X X O O | $$ | X X O O X . . O X O . X O O O X X X O | $$ | X O O O P X . O X O O X X O O O X O O | $$ | X O X P Z X . O X O Z X O X X X O O O | $$ | O X X Z 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]

White reduced Black's territory at the left, so she will prefer the Capture Variation, living with her group at the left (Black will also live in the upper right).
Compared to Our Solution, Black lost four points of territory at the left (crossed), while White did not get one point of territory at the right (crossed).

Click Here To Show Diagram Code: [go]$$Bc $$ +---------------------------------------+ $$ | . . . . . X . O . . . . X . . . O X . | $$ | . . . . X O O . O O . X O X O . . O . | $$ | . . . X . X X O . . . X O . . O O . . | $$ | . X O , 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 . | $$ | O O O O . X O O X X O O O O X . . X . | $$ | O X . X . X . O O X O . . . X X X X X | $$ | O X . X . X . O X X O . X X X X O O O | $$ | X O O X . X O O X O O X X O O O O X . | $$ | X X O O X . . O X O . X O O O . X X X | $$ | X X . O X . . O X O . X O O X X X O O | $$ | X X O O X . . O X O . X O O O X X X O | $$ | X O O P @ X . O X O O X X O O O X O O | $$ | X O X O X X . O X O # X O X X X O O O | $$ | 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]

Additionally, White caputured one Black stone at the left (crossed).
Both sided did not capture one opponent's stone each (squared).

In total, White gained FOUR points, so the final score of the Capture Variation is reduced from B + 5 to
B + 1.

The Semeai Variation is not affected, so its score remains
B + 3.

Final scores are our own calculation, using Japanese counting.
These might differ (usually by one point) from results given by KataGo, which uses Chinese counting.

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Click Here To Show Diagram Code: [go]$$Bcm13 B 113 (Black captures) $$ +---------------------------------------+ $$ | . . . . . # . O . . . . X . . . O X . | $$ | . . . . X @ @ . O O . X O X O . . O . | $$ | . . . # @ # # O . . . X O . . O O . . | $$ | . 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 . | $$ | O O O O . X O O X X O O . O X . . X . | $$ | O X . X . X . O O X O . . . X X X X X | $$ | O X . X . # . O X X O . X X X X O O O | $$ | X O O X . X @ O X O O X X O O O O X . | $$ | X X O O X . . O X O . X O O O . X X X | $$ | X X . O X . . O X O . X O O X X X O O | $$ | X X O O X . . O X O . X O O O X X X O | $$ | X O O X O X . O X O . X X O O O X O O | $$ | X O X . 1 X . O X O X . O X X X O O O | $$ | O X X , X . . O X O O O O X O X O O X | $$ | O . . . O X . O X X X X X . O X X O X | $$ | O . X . # @ X O O O O O O X O X . O X | $$ | . X . . # @ @ O . . . . O X X X . O . | $$ +---------------------------------------+[/go]

Black has to tenuki the "peaceful" endgame sequence of Our Solution to capture White's single stone, e.g. with 113 here.

Click Here To Show Diagram Code: [go]$$Bcm13 W 114 - ... $$ +---------------------------------------+ $$ | . . . . . X . O . . . . X . . . O X . | $$ | . . . . X O O . O O . X O X O . . O . | $$ | . . . X O X X O . . . X O . . O O . . | $$ | . X O , 5 4 . . . 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 . | $$ | O O O O . X O O X X O O . O X . . X . | $$ | O X . X . X . O O X O . . . X X X X X | $$ | O X . X . X . O X X O . X X X X O O O | $$ | X O O X . X O O X O O X X O O O O X . | $$ | X X O O X . . O X O . X O O O . X X X | $$ | X X . O X . . O X O . X O O X X X O O | $$ | X X O O X . . O X O . X O O O X X X O | $$ | X O O X . X . O X O . X X O O O X O O | $$ | X O X . X X . O X O X . O X X X O O O | $$ | O X X , X 3 . O X O O O O X O X O O X | $$ | O . . . O X 2 O X X X X X . O X X O X | $$ | O . X . X O X O O O O O O X O X . O X | $$ | . X . . X O O O . . . . O X X X . O . | $$ +---------------------------------------+[/go]

After the forcing exchange of White 114 for Black 115, the atari of White 116 starts a reduction of Black's territory in the upper left.

Click Here To Show Diagram Code: [go]$$Bcm13 ... - W 120 $$ +---------------------------------------+ $$ | . . . . . X . O . . . . X . . . O X . | $$ | . . . . X O O . O O . X O X O . . O . | $$ | . . . X 7 X X O . . . X O . . O O . . | $$ | . X O , X O 6 . . 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 . | $$ | O O O O . X O O X X O O 8 O X . . X . | $$ | O X . X . X . O O X O . . . X X X X X | $$ | O X . X . X . O X X O . X X X X O O O | $$ | X O O X . X O O X O O X X O O O O X . | $$ | X X O O X . . O X O . X O O O . X X X | $$ | X X . O X . . O X O . X O O X X X O O | $$ | X X O O X . . O X O . X O O O X X X O | $$ | X O O X . X . O X O . X X O O O X O O | $$ | X O X . X X . O X O X . O X X X O O O | $$ | O 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]

After Black's connection at 119, White continues with the Main Semeai by connecting at 120 at the right.

Click Here To Show Diagram Code: [go]$$Bc $$ +---------------------------------------+ $$ | . . . . . X . O . . . . X . . . O X . | $$ | . . . . X O O . O O . X O X O . . O . | $$ | . . . X Z X X O . . . X O . . O O . . | $$ | . X O , X P O T . 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 . | $$ | O O O O . X O O X X O O O O X . . X . | $$ | O X . X . X . O O X O . . . X X X X X | $$ | O X . X . X . O X X O . X X X X O O O | $$ | X O O X . X O O X O O X X O O O O X . | $$ | X X O O X . . O X O . X O O O . X X X | $$ | X X . O X . . O X O . X O O X X X O O | $$ | X X O O X . . O X O . X O O O X X X O | $$ | X O O X . X . O X O . X X O O O X O O | $$ | X O X . Z X . O X O X . O X X X O O O | $$ | O 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]

Gains and losses are located outside the Main Semeai, so these count for the Capture Variation, as well as for the Semeai Variation.
Black lost three points of territory (crossed).
White gained one point of territory in the upper left (triangled).

In total, White gained FOUR points, so the result of the Capture Variation is again reduced from B + 5 to
B + 1.

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Click Here To Show Diagram Code: [go]$$Bc $$ +---------------------------------------+ $$ | . . . . . X . O . . . . X . . . O X . | $$ | . . . . X O O . O O . X O X O . . O . | $$ | . . . X X X X O . . . X O . . O O . . | $$ | . X O , X O 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 . | $$ | O O O O . X O O X X O O O O X . . X . | $$ | O X . X . X . O O X O . . . X X X X X | $$ | O X . X . X . O X X O . X X X X O O O | $$ | X O O X . X O O X O O X X O O O O X . | $$ | X X O O X . . O X O . X O O O . X X X | $$ | X X . O X . . O X O . X O O X X X O O | $$ | X X O P X . . O X O . X O O O X X X O | $$ | X O O X . X . O X O . X X O O O X O O | $$ | X O X . X X . O X O X . O X X X O O O | $$ | O 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]

Does this imply that White will win the Semeai Variation (was B + 3)?
No. White has added a stone at the crossed point that will become captured in the Semeai Variation, giving Black an additional TWO points.

In total, the score of the Semeai Variation will be reduced from B + 3 to also
B + 1.

A Black win by ONE point might be considered to be an "ideal" result to this whole board problem.

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Have we reached the end of the story?
Unfortunately, no.
Because on another day ...

RobertJasiek · #3

Could you please very briefly summarise whether, and to what extent, KataGo has motivated you to improve your current solution? If so, what new, better moves or timings did it reveal?

Cassandra · #4

RobertJasiek wrote:

Could you please very briefly summarise whether, and to what extent, KataGo has motivated you to improve your current solution? If so, what new, better moves or timings did it reveal?

Dear Robert,

I am afraid that you will have to rein in your impatience still a bit.

If I ever intended to publish "all"** of KataGo's findings (** resulting from the current status of its analysis of the problem) at once at the beginning of this thread, I would not have used the three points "..." at the end of my previous posting ;-)

The above explained improvement of the final result by two points in White's favour was the first of KataGo's findings that had been reported to us. To amphasize it again: KataGo's surprising atari must not be played earlier than move 94 in Our Solution, and it cannot be played later as move 94 in Our Solution to the same effect.

It was very interesting for me to get to know some details about KataGo's learning process, especially that it seemed to concentrate on different elements of the problem at different times.
Our amateurish research followed the same principle. The order of elements under investigation was not the same as what KataGo did, and the relative amount of invested time per element was also very different, but KataGo's "behaviour" was familiar to me.
Probably lightvector will give you more details about what happened in the background.

lightvector · #5

Briefly, before I head to work:

As Cassandra observed in posting in the earlier thread about this problem, the Zero-trained bots do very poorly on this problem because of its highly unusual shapes (e.g. unlike anything that would be likely to occur in a normal game), as well as the tightly-balanced large capturing races.

However, I saw no obvious reason why this could not be addressed. Like other bots, KataGo is very strong at normal games because its selfplay training consists of playing normal games. If we want it to do well at Igo Hatsuyoron 120, why not have it conduct selfplay training from random positions from Igo Hatsuyoron 120 variations? Analogously, although humans would not be quite as bad as the current Zero bots, we would also not expect any human to achieve a solid understanding of such a problem without spending some focused study time on it. A bot's version of "study time" is self-play training. KataGo also learns very fast compared to other self-play trained bots, so in theory it should not take much time to do this training.

So in collaboration with Cassandra and others I trained KataGo specifically on this problem for 1 week starting from the strongest official network (and using the same 27 GPUs as before). It is far from clear if KataGo has reached an optimal understanding, but, at a minimum it now seems to understand clearly the main elements of the problem, independently re-confirms many human moves and variations, and has a small number of exciting new move suggestions that we are now trying to analyze.

Gomoto · #6

Lightvector, your hands-on approach and we can attitude is very refreshing. Kudos! :clap:

Cassandra · #7

Click Here To Show Diagram Code: [go]$$Wcm98 (White captures immediately) $$ +---------------------------------------+ $$ | . . . . . . . . . . . . X . . . O X . | $$ | . . . . . . . X O O . X O X O . . O . | $$ | . . . . . X . O . . . X O . . O O . . | $$ | . 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 . . | $$ | O O O O . X O O X X O O . O X . . X . | $$ | O X . X . X . O O X O . . . X X X X X | $$ | O X . X . . . O X X O . X X X X O O O | $$ | X O O X . X . O X O O X X O O O O X . | $$ | X X O O X . . O X O . X O O O . X X X | $$ | X X . O X . . O X O . X O O X X X O O | $$ | X X O O X . . O X O . X O O O X X X O | $$ | X O O X O X . O X O . X X O O O X O O | $$ | X O X 1 . X . O X O X . O X X X O O O | $$ | O X X , X . . O X O O O O X O X O O X | $$ | O . . . O X . O X X X X X . O X X O X | $$ | O . X . . . X O O O O O O X O X . O X | $$ | . X . . . . . O . . . . O X X X . O . | $$ +---------------------------------------+[/go]

In the meantime, KataGo has increased cleverness and confidence.

In order to simplify the position and to avoid Black variations, KataGo decided to capture Black's single stone immediately with 98.

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

Black would like to tenuki and to take the large endgame point in the upper left with 1.

White has a "simple" local refutation (she captures Black's nakade with 2), so -- for the moment -- we can neglect the problem that this tenuki loses a decisive move in the Main Semeai.

Click Here To Show Diagram Code: [go]$$Bc $$ +---------------------------------------+ $$ | . . . . . . . . . . . . X . . . O X . | $$ | . . . . . . X X O O . X O X O . . O . | $$ | . . . . . X . O . . . X O . . O O . . | $$ | . 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 . . | $$ | O O O O . X O O X X O O . O X . . X . | $$ | O X . X . X . O O X O . . . X X X X X | $$ | O X . X . . . O X X O . X X X X O O O | $$ | . O O X . X . O X O O X X O O O O X . | $$ | 3 . O O X . . O X O . X O O O . X X X | $$ | . . O O X . . O X O . X O O X X X O O | $$ | . . O O X . . O X O . X O O O X X X O | $$ | . O O . O X . O X O . X X O O O X O O | $$ | . O X O . X . O X O X . O X X X O O O | $$ | O X X 4 X . . O X O O O O X O X O O X | $$ | O 7 6 5 O X . O X X X X X . O X X O X | $$ | O . X . . . X O O O O O O X O X . O X | $$ | . X . . . . . O . . . . O X X X . O . | $$ +---------------------------------------+[/go]

As usual, Black 3 reduces White's group at the left to only one eye.

But White has the crosscut of 4 and 6 at her disposal. Even if Black caputures with 7, ...

Click Here To Show Diagram Code: [go]$$Bc $$ +---------------------------------------+ $$ | . . . . . . . . . . . . X . . . O X . | $$ | . . . . . . X X O O . X O X O . . O . | $$ | . . . . . X . O . . . X O . . O O . . | $$ | . 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 . . | $$ | O O O O . X O O X X O O . O X . . X . | $$ | O X . X . X . O O X O . . . X X X X X | $$ | O X . X . . . O X X O . X X X X O O O | $$ | . O O X . X . O X O O X X O O O O X . | $$ | X . O O X . . O X O . X O O O . X X X | $$ | . . O O X . . O X O . X O O X X X O O | $$ | . . O O X . . O X O . X O O O X X X O | $$ | . O O . O X . O X O . X X O O O X O O | $$ | . O X O . X . O X O X . O X X X O O O | $$ | O X X O X . . O X O O O O X O X O O X | $$ | O X 0 X O X . O X X X X X . O X X O X | $$ | O 8 X . 9 . X O O O O O O X O X . O X | $$ | . X . . . . . O . . . . O X X X . O . | $$ +---------------------------------------+[/go]

... he does not have an answer to the atari of White 8. Black 9 and White 10 are miai, so White lives at the left edge.

The right half of the board is White territory now, so Black loses by a very large margin.

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Click Here To Show Diagram Code: [go]$$Bc $$ +---------------------------------------+ $$ | . . . . . . . . . . 2 3 X . . . O X . | $$ | . . . . . . . X O O . X O X O . . O . | $$ | . . . . . X . O . . . X O . . O O . . | $$ | . X O , . . . . . O . X . O O X . . . | $$ | . . X X X X O O O . O X X c X X O O . | $$ | . X . O O O X X X O . . X . X O O . . | $$ | O O O O . X O O X X O O 4 O X . . X . | $$ | O X . X . X . O O X O . . . X X X X X | $$ | O X . X . . . O X X O . X X X X O O O | $$ | X O O X . X . O X O O X X O O O O X . | $$ | X X O O X . . O X O . X O O O . X X X | $$ | X X . O X . . O X O . X O O X X X O O | $$ | X X O O X . . O X O . X O O O X X X O | $$ | X O O . P X . O X O . X X O O O X O O | $$ | X O X P . X . O X O X . O X X X O O O | $$ | O X X a X . . O X O O O O X O X O O X | $$ | O . . . O X . O X X X X X . O X X O X | $$ | O . X . 1 b X O O O O O O X O X . O X | $$ | . X . . . . . O . . . . O X X X . O . | $$ +---------------------------------------+[/go]

Black 1 here indirectly defends against White's push at a, and also defends against White's endgame move at b, but is also a fatal mistake.

White continues with the Main Semeai and starts taking Black's liberties in the upper right with 2 and 4 (White's peep at 2 is necessary to prevent Michael Redmonds kikashi in the bamboo joint at Black c, gaining one additional liberty). Black will suffer from the Punishment Semeai, because he lost a decisive move by not taking a liberty of White's group at the left.
As a matter of course, White will not connect her marked stones.

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Click Here To Show Diagram Code: [go]$$Bcm99 $$ +---------------------------------------+ $$ | . . . . . . . . . . . . X . . . O X . | $$ | . . . . . 2 . X O O . X O X O . . O . | $$ | . . . . . X . O . . . X O . . O O . . | $$ | . 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 . . | $$ | O O O O . X O O X X O O . O X . . X . | $$ | O X . X . X . O O X O . . . X X X X X | $$ | O X . X . . . O X X O . X X X X O O O | $$ | X O O X . X . O X O O X X O O O O X . | $$ | X X O O X . . O X O . X O O O . X X X | $$ | X X . O X . . O X O . X O O X X X O O | $$ | X X O O X . . O X O . X O O O X X X O | $$ | X O O . O X . O X O . X X O O O X O O | $$ | X O X O . X . O X O X . O X X X O O O | $$ | O X X 1 X . . O X O O O O X O X O O X | $$ | O . . . O X . O X X X X X . O X X O X | $$ | O . X . . . X O O O O O O X O X . O X | $$ | . X . . . . . O . . . . O X X X . O . | $$ +---------------------------------------+[/go]

Black is forced to block at 99, whereafter White continues in the upper left with Yamada's tsuke 100.

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Have we reached the end of the story?
Unfortunately, no.
Because on the last days of training ...

Cassandra · #8

Click Here To Show Diagram Code: [go]$$Bcm81 B 81 (The guzumi -- A bad shape move) $$ +---------------------------------------+ $$ | . . . . . . . . . . . . X . . . O X . | $$ | . . . . . . . X O O . X O X O . . O . | $$ | . . . . . X . O . . . X O . . O O . . | $$ | . X O , . . . . . O . X . O O 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 . . . | $$ | . O O O . X O O X X O O . O X . . 1 . | $$ | O . . X . X . O O X O . . . X X X X X | $$ | . . . X . . . O X X O . X X X X O O O | $$ | X O O , . X . O X O O X X O O O O X . | $$ | X . . O X . . O X O . X O O O . X X X | $$ | X . . O X . . O X O . X O O X X X O O | $$ | X X . . X . . O X O . X O O O X X X O | $$ | . O O X O X . O X O . X X O O O X O O | $$ | . . X . . X . O X O X . O X X X O O O | $$ | O X X , X . . O X O O O O X O X O O X | $$ | . . . . O X . O X X X X X . O X X O X | $$ | O . X . . . X O O O O O O X O X . O X | $$ | . X . . . . . O . . . . O X X X . O . | $$ +---------------------------------------+[/go]

Black's guzumi in the upper right by far was one of the very last and hardest-to-learn moves that KataGo learned in this problem over the one week of training. But it was eventually learned, and KataGo now also agrees that "my" guzumi is a valid move.

Additionally, KataGo thinks that this guzumi could be even played at a later moment, but questions related to the timing of moves are not as significant as they should now be answered with priority.

Why did KataGo consider the guzumi so "late"?
Well, the territorial value of the guzumi is very small, compared to what else is at stake on the board.

During the training, KataGo was initally busy with understanding
-- the hanezeki, including the growth of the tail,
-- the nakade at the left edge (which surprisingly took a very long time), and
-- the Main Semeai, including Semeai Variation, Capture Variation, and Punishment Semeai.

Endgame analysis came last.

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Have we reached the end of the story?
Unfortunately, no.
Because earlier that training week ...

RobertJasiek · #9

"KataGo was initally busy with understanding
-- the hanezeki, including the growth of the tail,
-- the nakade at the left edge (which surprisingly took a very long time), and
-- the Main Semeai, including Semeai Variation, Capture Variation, and Punishment Semeai."

This might be a description of a human being trying to understand the position. How can you identify that it was KataGo's progress? Isn't it just your perception of what KataGo has done?

Cassandra · **#10**

RobertJasiek wrote:

This might be a description of a human being trying to understand the position. How can you identify that it was KataGo's progress? Isn't it just your perception of what KataGo has done?

This is what lightvector told us about what happened during KataGo's training.

"... busy with UNDERSTANDING" is my interpretation.
I suppose that lightvector's statements were related to which extent KataGo followed the course of a "correct" solution.
For example, KataGo did not consider to play my guzumi before the last (one or two) days of the training period.

I am sure that lightvector will be able to explain much better what happened on the technical level.

lightvector · **#11**

The neural network learned many things in parallel over the course of the week, but it was clear that different moves were "discovered" or general understanding of different aspects "converged" at different times of the week when interacting with KataGo to see its move suggestions. The number of variations in this problem is immense, so of course I am not able to manually analyze all variations to see what KataGo did or did not understand at each point in training, but anecdotally:

* Very early was mostly stamping out all the mistaken tendencies that Cassandra's earlier post showed LZ and KG are very liable to do (white blocking the hanezeki tail early, black skipping a move in gote) - this was pretty quick.

* The atari move on the left was preferred quite early, even before KataGo understood the nakade itself (one could find spots where the neural net would fail to suggest black to complete the nakade or to form it in the correct way, and white would simply live).

* The guzumi was fairly late - at least personally, only in the last 2 days or so did I notice KataGo suggesting that move strongly. It is of course possible that it learned the guzumi earlier in some other variations before this point and I didn't notice due to not playing those variations.

* A huge amount of time was "spent" learning variations like these: http://igohatsuyoron120.de/2015/0363.ht ... oachimsKo2 that lead to complexities like Joachim's ko semeai: http://igohatsuyoron120.de/2015/0937.htm#%C3%BCJKSB3 - for a long time in the middle of the week, KataGo appeared to consider this and some similar variations (different forcing moves exchanged or not) to be the "main line", before eventually learning some critical tesuji to refute them (including some tesuji in variations that are not covered anywhere on the above site as far as I can tell).

* Amusingly, for a time white believed so strongly that the ko-semeai variations worked for black (and therefore leading to a huge win by black) that white began to refuse to enter into the hanezeki at the beginning at all, instead choosing alternate ways of the fight in the first 10 moves that completely avoided this and let black kill some things/live easily, and then try to fight out the rest of the game as a "normal" game (often losing by 5-10 points). KataGo also had to teach itself to be more confident about the outcomes here too (e.g. winrate only 70% for black early on, until KataGo got more experience that playing a "normal" game would also have black win).

Cassandra · **#12**

In addition to lightvector's posting above, it may be useful to clarify that the order of topics was chosen for "pedagogical" reasons, as well as for increasing the tension for the public.

Hopefully you will understand that it did not make much sense for me to present the highlight of KataGo's suggestions in the very beginning of this thread.

Cassandra · **#13**

RobertJasiek wrote:

This might be a description of a human being trying to understand the position.

Dear Robert,

What do you mean by "to understand"?

Knowledge of the COMPLETE variation tree?
It may be possible to work through the COMPLETE variation tree of e.g. Carpenter's Square (including all its modifications). But this task will never be done for Igo Hatsuyoron 120.

I suppose that one can say that Fujisawa Hideyuki and his study group had a solid "understanding" of Igo Hatsuyoron 120. However, they knew (i.e. "understood"?) "only" a small section of the entire variation tree, and -- most important -- they missed to visit an important branch. Eventually Joachim explored this white spot on the globe.

Cheng Xiaoliu "understood" a larger section of the entire variation tree, but he deliberately truncated some of its branches, guided by wishful thinking.

We three amateurs "understood" a different shaped section of the entire variation tree, supported by the kind assistance of a few professionals, what resulted in changes of the final score in Black's favour.

Luckily, lightvector said "Challenge accepted!", and now we have someone (i.e. KataGo) who gives us suggestions that we are unable to refute, and which result in changes of the final score in White's favour.

Is KataGo's "understanding" complete / perfect? We do not know.

Would KataGo give us further suggestions after another week, or another month, of training? We cannot know. We do not even know whether an additional training makes sense at all.

All we know is that at any time there is a still unrefuted sequence that must be considered to be the state of the art of a "solution" to Igo Hatsuyoron 120. Is this sequence THE solution? We three amateurs did not claim that. And I am sure that lightvector will not do so either.

Cassandra · **#14**

Click Here To Show Diagram Code: [go]$$Wcm20 W 120 (Another bad shape move) $$ +---------------------------------------+ $$ | . . . . . # . @ . . . . X . . . O X . | $$ | . . . . X @ @ . O O . X O X O . . O . | $$ | . . . # . # # O . . . X O . . O O . . | $$ | . X O , # . # 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 . | $$ | O O O O 1 X O O X X O O . O X . . X . | $$ | O X . X . X . O O X O . . . X X X X X | $$ | O X . X . # . O X X O . X X X X O O O | $$ | X O O X . X @ O X O O X X O O O O X . | $$ | X X O O X . . O X O . X O O O . X X X | $$ | X X . O X . . O X O . X O O X X X O O | $$ | X X O O X M . O X O . X O O O X X X O | $$ | X O O . P X . O X O . X X O O O X O O | $$ | X O X O . X . O X O X . O X X X O O O | $$ | O X X X X # . O X O O O O X O X O O X | $$ | O . . . O X @ O X X X X X . O X X O X | $$ | O . X . # @ . O O O O O O X O X . O X | $$ | . X . . # @ @ O . . . . O X X X . O . | $$ +---------------------------------------+[/go]

After having "understood" the "big" core issues of the problem, KataGo concentrated on analysing the endgame.

After the completition of the endgame sequence of Our Solution (squared), White's bad shape move of 120 is a big surprise.

Black gets caught on the wrong foot, due to the (crossed) cutting point in his formation that resulted from White's earlier moves in the lower left quadrant of the board.

Click Here To Show Diagram Code: [go]$$Bcm21 B 121 - W 126 (Black's first option) $$ +---------------------------------------+ $$ | . . . . . X . O . . . . X . . . O X . | $$ | . . . . X O O . O O . X O X O . . O . | $$ | . . . X . X X O . 6 5 X O . . O O . . | $$ | . X O , 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 . | $$ | O O O O O X O O X X O O 4 O X . . X . | $$ | O X . X 2 X . O O X O . . . X X X X X | $$ | O X . X 3 X . O X X O . X X X X O O O | $$ | X O O X . X O O X O O X X O O O O X . | $$ | X X O O X 1 . O X O . X O O O . X X X | $$ | X X . O X . . O X O . X O O X X X O O | $$ | X X O O X . . O X O . X O O O X X X O | $$ | X O O . O X . O X O . X X O O O X O O | $$ | X O X O . X . O X O X . O X X X O O O | $$ | 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]

KataGo recommends Black's connection at 121.

White's push at 122 is blocked by Black 123, also gaining a move in the Main Semeai that continues with White 124.

Due White's loss of one liberty at the left, Black is able to reduce White's territory in the upper right a bit with e.g. 125, spending the just won liberty.

Click Here To Show Diagram Code: [go]$$Bc $$ +---------------------------------------+ $$ | . . . . . X . O . . . . X . . . O X . | $$ | . . . . X O O . O O . X O X O . . O . | $$ | . . . X . X X O . P X X O . . O O . . | $$ | . X O , 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 . | $$ | O O O O O X O O X X O O O O X . . X . | $$ | O X . X P X . O O X O . . . X X X X X | $$ | O X . X Z X . O X X O . X X X X O O O | $$ | X O O X . X O O X O O X X O O O O X . | $$ | X X O O X X . O X O . X O O O . X X X | $$ | X X . O X . . O X O . X O O X X X O O | $$ | X X O O X . . O X O . X O O O X X X O | $$ | X O O . O X . O X O . X X O O O X O O | $$ | X O X O . X . O X O X . O X X X O O O | $$ | 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]

At the left, White destroyed TWO points of Black territory (crossed) at the cost of only ONE liberty in the Main Semeai.

This means that Black cannot destroy more than ONLY ONE point of White territory (crossed) in the upper right.

In total, White gained ONE point, so the result of the Capture Variation is reduced from B + 1 to
Jigo.

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Click Here To Show Diagram Code: [go]$$Bcm21 B 121 - W 130 (Black's second option) $$ +---------------------------------------+ $$ | . . . . . X . O . . . . X . . . O X . | $$ | . . . . X O O . O O . X O X O . . O . | $$ | . . . X . X X O . 0 9 X O . . O O . . | $$ | . X O , 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 . | $$ | O O O O O X O O X X O O 8 O X . . X . | $$ | O X . X 1 X . O O X O . . . X X X X X | $$ | O X . X . X . O X X O . X X X X O O O | $$ | X O O X a X O O X O O X X O O O O X . | $$ | X X O O X 4 6 O X O . X O O O . X X X | $$ | X X . O X 2 5 O X O . X O O X X X O O | $$ | X X O O X 3 7 O X O . X O O O X X X O | $$ | X O O . O X . O X O . X X O O O X O O | $$ | X O X O . X . O X O X . O X X X O O O | $$ | 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]

So, what about Black blocking immediately at 121 here?

White 122 is tesuji, exploiting Black's weakness in the centre. Black is forced to connect his troops with 123.

White 124 enables a throw-in at a, and also threatens to realise some points of additional territory in the centre (with a move at 127).

Black 125 and 127 prevent this additional White gain, whereafter the continuation from White 128 to White 130 is the same as in the variation before.

Click Here To Show Diagram Code: [go]$$Bc $$ +---------------------------------------+ $$ | . . . . . X . O . . . . X . . . O X . | $$ | . . . . X O O . O O . X O X O . . O . | $$ | . . . X . X X O . P X X O . . O O . . | $$ | . X O , 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 . | $$ | O O O O O X O O X X O O O O X . . X . | $$ | O X . X Z X . O O X O . . . X X X X X | $$ | O X . X . X . O X X O . X X X X O O O | $$ | X O O X M X O O X O O X X O O O O X . | $$ | X X O O X O O O X O . X O O O . X X X | $$ | X X . O X O X O X O . X O O X X X O O | $$ | X X O O X X X O X O . X O O O X X X O | $$ | X O O . O X . O X O . X X O O O X O O | $$ | X O X O . X . O X O X . O X X X O O O | $$ | 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]

Again, Black lost TWO points of territory (crossed) at the left, and invested his gain of ONE liberty in the Main Semeai for the destruction of ONE point of White territory (crossed) at the top.

The game (Capture Variation) will end in
Jigo.

+ + + + + + + + + + + + + + + + + + + +
+ + + + + + + + + + + + + + + + + + + +

Have we reached the end of the story?
Unfortunately, no.
Because the most surprising is kept secret until the end ...

RobertJasiek · **#15**

With human understanding, I have meant nothing more spectacular than descriptions in human-digestable form (haneseki, nakade, semeai etc.). We know that AI thinks in terms of neural nets but we do not know whether they represent such human-like objects. Currently we can only perceive some impact of its generated moves and WE can perceive that as if there would be those human-like objects.

This reminds me of a recent American Go E-Journal, in which someone was said to have praised AI for its newly invented strategy. Its what?! I ask whether AI has ever invented any new go strategy, even if allow our perception to interpret combinations of AI moves as strategy. I do not recall any new strategy. Better strategy in particular positions than human strategy found within limited time - yes. But better does not mean new in a general sense. Quite contrarily, AI has rediscovered very much of human strategy and therefore confirmed its validity.

Bill Spight · **#16**

Brief note on understanding

Understanding is a fuzzy concept. Do computer players understand their plays? One test of human understanding is whether someone can give an explanation for something. Bots currently do not do that. However, another idea of understanding is to have relevant concepts. For instance a snapback is a certain type of play along with its possible followers in certain positions. The bots plainly understand snapbacks in that they find them and play them, not only making the initial play, but making the followups if necessary. Similarly, they understand nakade, because they make the plays, but I am not sure that their understanding is as good as that of an amateur dan players. My guess is that they do not count liberties, but rely upon reading.

BTW, many years ago psychologist Jerome Bruner showed that we can regard concepts and strategies as the same thing. Not that we have to, OC.

Cassandra · **#17**

Click Here To Show Diagram Code: [go]$$Wcm102 W 102 (KataGo's crosscut after Yamada's tsuke) $$ +---------------------------------------+ $$ | . . . . . . . . . . . . X . . . O X . | $$ | . . . . B W ? X O O . X O X O . . O . | $$ | . . . . 1 X . O . . . X O . . O O . . | $$ | . 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 . | $$ | O O O O . X O O X X O O . O X . . X . | $$ | O X . X . X . O O X O . . . X X X X X | $$ | O X . X . . . O X X O . X X X X O O O | $$ | X O O X . X . O X O O X X O O O O X . | $$ | X X O O X . . O X O . X O O O . X X X | $$ | X X . O X . . O X O . X O O X X X O O | $$ | X X O O X . . O X O . X O O O X X X O | $$ | X O O . O X . O X O . X X O O O X O O | $$ | X O X O . X . O X O X . O X X X O O O | $$ | O X X X X . . O X O O O O X O X O O X | $$ | O . . . O X . O X X X X X . O X X O X | $$ | O . X . . . X O O O O O O X O X . O X | $$ | . X . . . . . O . . . . O X X X . O . | $$ +---------------------------------------+[/go]

We were very surprised that KataGo preferred the crosscut of 102 (after Yamada's tsuke = marked stones) to drawing-back with a move at G18.

On the other hand, this move might be standard endgame repertoire that we amateurs were absolutely not aware of.

Click Here To Show Diagram Code: [go]$$Bcm101 (B 103 - B 107) $$ +---------------------------------------+ $$ | . . . 7 4 . . . . . . . X . . . O X . | $$ | . . . 5 X O 6 X O O . X O X O . . O . | $$ | . . . 3 O X . O . . . X O . . O O . . | $$ | . 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 . | $$ | O O O O . X O O X X O O . O X . . X . | $$ | O X . X . X . O O X O . . . X X X X X | $$ | O X . X . . . O X X O . X X X X O O O | $$ | X O O X . X . O X O O X X O O O O X . | $$ | X X O O X . . O X O . X O O O . X X X | $$ | X X . O X . . O X O . X O O X X X O O | $$ | X X O O X . . O X O . X O O O X X X O | $$ | X O O . O X . O X O . X X O O O X O O | $$ | X O X O . X . O X O X . O X X X O O O | $$ | O X X X X . . O X O O O O X O X O O X | $$ | O . . . O X . O X X X X X . O X X O X | $$ | O . X . . . X O O O O O O X O X . O X | $$ | . X . . . . . O . . . . O X X X . O . | $$ +---------------------------------------+[/go]

We will display KataGo's main variation only.

Perhaps there is someone in the honoured audience who wants to refute KataGo? We have not succeeded so far.
Please remember that this is a sheer endgame problem. It has nothing at all to do with the rest of the board (ko-fights excluded).

Click Here To Show Diagram Code: [go]$$Wcm108 (W 108 - B 117) $$ +---------------------------------------+ $$ | . . . X O . . . . . . . X . . . O X . | $$ | . . . X X O O X O O . X O X O . . O . | $$ | . . . X O X 9 O . . . X O . . O O . . | $$ | . X O , . 0 6 . . 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 . | $$ | O O O O . X O O X X O O . O X . . X . | $$ | O X . X . X . O O X O . . . X X X X X | $$ | O X . X . . . O X X O . X X X X O O O | $$ | X O O X . X . O X O O X X O O O O X . | $$ | X X O O X . . O X O . X O O O . X X X | $$ | X X . O X . . O X O . X O O X X X O O | $$ | X X O O X . . O X O . X O O O X X X O | $$ | X O O . O X . O X O . X X O O O X O O | $$ | X O X O . X . O X O X . O X X X O O O | $$ | O X X X X 8 . O X O O O O X O X O O X | $$ | O . . . O X 7 O X X X X X . O X X O X | $$ | O . X . 2 1 X O O O O O O X O X . O X | $$ | . X . . 4 3 5 O . . . . O X X X . O . | $$ +---------------------------------------+[/go]

The endgame continues on the lower edge with White's "usual" move at 108.

Click Here To Show Diagram Code: [go]$$Wcm118 (W 118 - B 123) $$ +---------------------------------------+ $$ | . . . X O . . . . . . . X X . . O X . | $$ | . . . 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 2 3 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 . | $$ | O O O O 1 X O O X X O O . O X . . X . | $$ | O X . X . X . O O X O . . . X X X X X | $$ | O X . X . . . O X X O . X X X X O O O | $$ | X O O X . X . O X O O X X O O O O X . | $$ | X X O O X 6 . O X O . X O O O . X X X | $$ | X X . O X . . O X O . X O O X X X O O | $$ | X X O O X . . O X O . X O O O X X X O | $$ | X O O 5 O X . O X O . X X O O O X O O | $$ | X O X O 4 X . O X O X . O X X X O O O | $$ | 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]

Eventually, White 118 is her bad-shape move in the left centre that costs Black one point.

Click Here To Show Diagram Code: [go]$$Wcm124 (W 124 - W 128) $$ +---------------------------------------+ $$ | . . . X O 3 . . . . . . X X . . O X . | $$ | . . . 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 4 5 . | $$ | . . X X X X O O O . O X X . X X O O . | $$ | . X . O O O X X X O . . X . X O . O . | $$ | O O O O O X O O X X O O . O X . . X . | $$ | O X . X 1 X . O O X O . . . X X X X X | $$ | O X . X 2 . . O X X O . X X X X O O O | $$ | X O O X . X . O X O O X X O O O O X . | $$ | X X O O X X . O X O . X O O O . X X X | $$ | X X . O X . . O X O . X O O X X X O O | $$ | X X O O X . . O X O . X O O O X X X O | $$ | X O O O O X . O X O . X X O O O X O O | $$ | X O X O X X . O X O X . O X X X O O O | $$ | 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]

For the sake of simplicity for calculation, let us assume these moves here, which might not necessarily be played in order.

White's connection at 126 is not related to the Main Semeai, so White loses a move therein. Therefore, Black is able to play an additional forcing move at the right, e.g. at 127.

Click Here To Show Diagram Code: [go]$$Bc (White's gains and losses) $$ +---------------------------------------+ $$ | . . . X O O T T . . . . X X . . O X . | $$ | . . . 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 P . | $$ | . . X X X X O O P . O X X . X X O O . | $$ | . X . O O O X X X O . . X . X O . O . | $$ | O O O O O X O O X X O O . O X . . X . | $$ | O X . X O X . O O X O . . . X X X X X | $$ | O X . X X . . O X X O . X X X X O O O | $$ | X O O X . X . O X O O X X O O O O X . | $$ | X X O O X X . O X O . X O O O . X X X | $$ | X X . O X . . O X O . X O O X X X O O | $$ | X X O O X . . O X O . X O O O X X X O | $$ | X O O O O X . O X O . X X O O O X O O | $$ | X O X O X X . O X O X . O X X X O O O | $$ | 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]

White lost two points of territory (crossed), one in the centre and one at the right.

On the upper edge, she gains two points of territory in return (triangled).

Click Here To Show Diagram Code: [go]$$Bc (Black's losses) $$ +---------------------------------------+ $$ | . . . Z O O . . . . . . X X . . O X . | $$ | . . . Z 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 O . | $$ | . . X X X X O O O . O X X . X X O O . | $$ | . X . O O O X X X O . . X . X O . O . | $$ | O O O O O X O O X X O O . O X . . X . | $$ | O X . X O X . O O X O . . . X X X X X | $$ | O X . X X . . O X X O . X X X X O O O | $$ | X O O X . X . O X O O X X O O O O X . | $$ | X X O O X X . O X O . X O O O . X X X | $$ | X X . O X . . O X O . X O O X X X O O | $$ | X X O O X . . O X O . X O O O X X X O | $$ | X O O O O X . O X O . X X O O O X O O | $$ | X O X O X X . O X O X . O X X X O O O | $$ | 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]

Black's additional loss of territory in the upper left corner is two points (crossed).

The final score is reduced by this margin. Instead of ending in jigo, now the game's result is
W + 2.

+ + + + + + + + + + + + + + + + + + + +
+ + + + + + + + + + + + + + + + + + + +

Have we reached the end of the story?
We do not have the slightest idea ...

lightvector · **#18**

A major caveat that Cassandra may have forgotten to mention: W+2 is a potentially misleading result to conclude, because KataGo uses area-scoring (i.e. Chinese-style scoring). What KataGo itself "believes" currently is NOT W+2 territory-scoring, but rather is W+1 area-scoring.

Assuming no surprising endgame details (i.e. being able to defer a final ko fight until after filling all dame, or finishing the game somehow with certain kinds of seki), W+1 area-scoring is equivalent to either W+1 territory-scoring OR W+2 territory-scoring.

Therefore, even if there are no larger mistakes (again, it's not totally certain that KataGo has analyzed everything correctly) it is easily possible that KataGo is having black play a line that is slack by 1 point by territory scoring, because such a line would still be exactly identical in score and just as "optimal" under area scoring.

Bill Spight · **#19**

lightvector wrote:

Therefore, even if there are no larger mistakes (again, it's not totally certain that KataGo has analyzed everything correctly) it is easily possible that KataGo is having black play a line that is slack by 1 point by territory scoring, because such a line would still be exactly identical in score and just as "optimal" under area scoring.

That is why Berlekamp's, Wolfe's, and my zero komi problems have White to play and win instead of Black. Normally, on the 19x19 jigo by territory scoring is a Black win by area scoring, so White has to win by both forms of scoring. It might be interesting to set up the problem with colors reversed and White to play, and see what KataGo says.

lightvector · **#20**

Bill, I think there would be no difference, the parity would come out the same way. :study:

In fact, the neural net is not even told the absolute color of the player. It's only told in terms of "my color" and "opponent color" and "number of komi points added/subtracted from my own color's perspective". So it literally can't tell the difference between color inversion if komi adjusted appropriately, or if komi = 0 in the first place.

(at least, if I'm not forgetting some detail of how I'm doing things)

KataGo @ Igo Hatsuyoron 120

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