(Referenced by 58ee)

: ( 58ai)
Black plays a hane from below.

We inserted this alternative move manually.
The following subvariations show and explain KataGo's erroneous continuations, which appeared in about half of various selfplay games. This series of games was held at the end of June 2021, with different numbers of playouts. A higher number of playouts was not to be equated with fewer mistakes.
It is very likely that later versions of KataGo's special network will avoid all of the paths that were found to be error-prone here.

It was hard work to identify KataGo's mistakes in these selfplay games.
But this opened a golden opportunity to explain several of the "hidden beauties" of the problem, which KataGo apparently had to learn anew, to be included in the 2021 update of the Igo Hatsuyôron 120 website.
To go over this concentrated compilation will be much easier than to fight your way through all the other scattered parts of the variation tree, which are somewhat covered with the dust of the past.
We endeavored to list each type of error only once.

However, while commenting the created diagrams, we had to realise that we had been susceptible (mainly guided by wishful thinking) to "false positives" in the first pass through the variation tree of the selfplay games, i.e. seemingly potential errors KataGo's, but which lost their property on closer analysis.
We decided not to delete these relevant subvariations to give you an idea of how easy it is to err when working with this problem.

: ( A 58aq ;  B 58ar ;  C 58bb ;  D 58dc ; E 58dr)
KataGo's "first instinct" is a grave mistake here.

We first encountered this move when browsing through KataGo's favourite moves, being in KataGo's "Analysis Mode".
This hiki seems quite attractive to KataGo, as ist was also often chosen in KataGo's selfplay games after one of the moves from B to E (not included in this presentation).

All other alternative options - except , which is another genuine mistake - would result in changes in the order of moves with Our Solution - in principle. But KataGo took the opportunity to make mistakes in about half of the selfplay games.

: (A 58eb)
Black gives atari at White's single stone in the corner.

In the series of selfplay games, KataGo often continued with the extension to , instead, which will result in a change in the order of moves.

:
White captures Black's stone in the lower left.

:
Black is forced to follow White on the path of the Main Semeai.

:
White interrupts the Main Semeai for a white, and inserts the wedge in the left centre.

:
White plays the final atari of the meanwhile inserted sequence in the left centre.

: (130 58ec)
White returns to the upper left corner. This kikashi benefits her by one point overall.

:
Black is forced to connect in the corner.

He must not capture at , instead.

:
Thereafter, White plays the crosscut at the top.

:
White strengthens her centre group in sente.

Continuing at in the upper left corner first, in order to connect at later, will not benefit White. The overall result of the game will not be affected, while White will lose massively in the Semeai Variation, due to Black's subsequent defense at .

:
It is best for Black to capture White's two stones in the lower left.

Black is par with the Punishment Semeai Liberty Level, so he does not have any other choice.

:
The sequence in the upper left corner continues with White's atari.

We present the ensuing sequence in the upper left corner continuously.

:
Black ends in gote.

:
White continues with the hasami-tsue of in the lower left corner, reducing Black's territory there.

:
Please remember that White's atari at the bottom might be gote.

: (146 58ed)
Black strengthens his position at the top by descending to .

The connection at is miai, due to White's earlier kikashi , . White will hane at .

Please refer to the previous subvariation to see why Black would better if White had missed that kikashi.

Black must not play any reduction.

White will block at after her decision point.

Capture Variation:

Compared to the superordinate variation, ...

• White's cumulated gain in the upper left corner is four points.
• Black's cumulated gain at the top is four points.
• Black's cumulated gain in the left centre is one point.
• Black captured White's two stones in the lower left, so gaining four points.
• White got an additional point of territory in the right centre.

In total, Black gained four points.

White + 2 => Black + 2

Semeai Variation:

Compared to the superordinate variation, ...

• White's cumulated gain in the upper left corner is four points.
• Black's cumulated gain at the top is four points.
• Black's cumulated gain in the left centre is one point.
• Black captured two White stones less at the left, so losing four points.
• White captured one Black stone less in the right centre, so losing one point.

In total, Black lost two points.

Black + 4 => Black + 2