:: Igo Hatsuyôron 120 (2021)

Variations of Our Solution (IIIb)

Tricking KataGo (Triple-Ko)

VAR (C) (A) (.2) (.2) (.2)

: ( 222gm)
Black follows the original sequence for another time.

Please note that this move is the third successive mistake, making it a bit unlikely for KataGo (2020) to encouner this position during the selfplay-training of the net with the frequency necessary for extensive analysis.

(Referenced by 222ds)


: (A 222go)
White has to capture the nakade latest now.

This invention, made by Joachim, significantly improves White's position on the left in preparation of the forthcoming ko fights in the upper left corner. In the further course of the filling of the nakade, White will connect all her partial groups at the left, and so get rid of some shortage of liberties that otherwise might hinder her in the fight to come soon.

If this move is played later, even by only one move, Black might take the opportunity to play tenuki.

During the later ko fights, capturing the nakade might not even be a valid ko threat.

The comparable position without the Guzumi Exchange (i.e. in the classical line of play) has been discussed earlier ( 222ds).

:
Black is bound to strictly follow the Main Semeai.

:
Now, the time is ripe for White's extension into Black's corner.


: ( B 222ha ;  C 222hc)
Capturing White's two stones at the top is mistakenly favoured by KataGo (2020), apparently due to some kind of wishful thinking in some of the ensuing subvariations.

Extending to , instead, would revert to the sequence below.

However, we found that it would be better for Black to give atari at White's single stone in his corner first, with a move at .
Please note that KataGo (2021i) found an improvement in the subsequent sequence below, resulting in the same final score as with choosing this atari.

Jumping to at the second line is another idea, but slightly worse than .

:
White continues her attack by blocking the corner.

:
Black's peep from above is his best response.

:
White's connection is forced.


: ( A 222hd ;  B 222he)
Black's solid connection at the top, securing a second eye there, was once favoured by KataGo (2020).

However, KataGo (2021i) found that immediately connecting his partial groups in the upper left corner with would be better.

A move at , instead, seems to have a stronger effect on White's centre group, while also securing Black's connection in the corner. However, as it will turn out, it is slightly worse than the alternative subvariation.


:
Black simply connects after White's atari.

He will be unable to fight - and win - the ko after giving counter-atari with .

:
White starts cutting Black's forces into two.

:
After White's connection with , Black blocks the corner from above.


(Referenced by 222gz)


: (122 222hg ; A 222hm ; B 222hs ; 123 222ia)
White's push into Black's corner from below is suggested by Joachim, and the main reasoning for having captured the nakade already. This push will initiate a ko fight in Black's upper left corner.
White does not lose a Main Semeai Liberty here (by Black's block with ), as her push creates an approach-move liberty for her left-hand group in the corner.

Alternatively, White might also start another ko fight in Black's upper left corner by playing the hane at .

White's peep at the upper edge is apparently underestimated by KataGo (2020). It will also ensure a large White win, and thereby give Black the opportunity to avoid a ko fight in the upper left corner.

White's connection at in the upper right is favoured by KataGo (2020) with komi for White and with small reverse komi for Black, but a grave mistake. With correct play of both sided, White will achieve a drawn game only.

KataGo's (2020) fondness for White's connection at at the left edge in the upper left corner - when the komi is set to 0 - is also triggered by wishful thinking. After this mistake, Black will win the game.

:
Black is forced to block.

Descending to , instead, would enable him to capture White's cutting stones, but at the cost of losing one tempo in the Main Semeai. He is alredy par with the Punishment Semeai Liberty Level, and so does not have this extra liberty to spend.

:
White creates the ko shape in the corner.

:
It is best for Black to start the ko fight immediately.

:
White's descent starts a series of White ko threats at the lower left edge of the board.
As , the subsequent ko threats in the lower left corner will threaten the life of Black's entire group at the left. Precondition for this very serious impact is Joachim's idea of capturing the nakade, which has taken place long before.

Please note that we will not adjust the colours of the boards' edges during the ko fights.

:
Black closes his corner by descending to the lower edge.

Alternatively, he might consider connecting at , instead. This choice result sin a change in the order of moves in this area (White then continues with ).

:
Black has an internal ko threat in the corner.


Ko: ; ;

:
White continues with her life-threatening ko threats in the lower left corner.

:
Sooner or later, Black will have to resort to this ko threat, threatening to reduce White's bottom group to only one eye.

Please note that Black is unable to use his kikashi in the hanezeki as ko threats, as this would hurt the liberty count of his large group in the upper right decisively.

: ( A 222ig)
Here, White answers Black's ko threat.

However, as we found out, it would be better for White to ignore Black's previous move, and to end the ko fight in the upper left corner by connecting with .
White will be unable to win the ensuing semeai with Black's large group at the right, but still benefit by a few points.

:
White's move turns the approach-move ko into a direct one.


Ko:

:
This is White's last ko threat in the lower left corner.

:
Please note that Black's throw-in does not hurt his prospects of success in the forthcoming semeai with White's centre group, as he would have to play it anyway.

:
White's cut threatens to capture Black's stones in the left centre.

:
Black has run out of valid ko threats, and so ends the ko fight by capturing in the corner.

:
Black's stones in the left centre are dead now.
These stones do not have sufficient liberties to win a semeai with White's large group at the left.

:
However, Black is able to attack White's centre group, which is still eyeless.

; :
These two moves are miai.

:
Black is able to gain a few points by connecting.

If he ignored White's atari, he would have a ko threat at at his disposal, but which he does not need here in this fight.

:
White continues with the endgame in the lower left corner, as Black's large group at the right has sufficient outside liberties left to survive the semeai.

She will have to capture the hanezeki's tail with , latest when her centre group is reduced to five shared liberties ().

Thereafter, White will win the final ko (, ) at the top.

White will win the game by 13 points.

Copyright © 2021 Thomas Redecker.

Design by Jan van Rongen, modified by Thomas Redecker.

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