After we had finished our work on the 2020 update of our website, we first analysed "Dany's Ko: Joachim's no-ko-threats", i.e. Joachim's discovery that White moves around Black's bamboo joint in the upper right are no valid ko-threats.

Afterwards, we took great care to confirm our assumption that the guzumi must be played at the latest before the Crosscut Sequence in the left centre, and must by no means be delayed as much as the original KataGo version (2019) had still assumed.
Now that White had occupied the guzumi point, Joachim developed many ideas for variations in the top left corner, all with the aim of capturing Yamada's tsuke. One of these variations ended with a triple-ko (resulting in the game becoming "no result"), which KataGo (2019) did not avoid. For this reason we called this chapter "Tricking KataGo (Triple-ko)".

In mid-December 2020, Friday9i provided us with a first version of the special network for Igo Hatsuyôron 120 that he had further developed / trained – KataGo (2020).

KataGo (2020) not only confirmed Joachim's assessment of "Dany's Ko: Joachim's no-ko-threats", but also found another, fourth, ko-threat for White in the upper left corner.

KataGo (2020) now basically played the guzumi "early", confirming our assumption in this regard.
In the case of the guzumi "delayed" by Black, however, this version was still vulnerable to "Tricking KataGo (Triple-ko)", which led to this position being given extended treatment during further training of the network.
In the case of the "classical" atari in the top left, KataGo (2020) found some improvements for White, but without caring – typical of its approach – about the absolute level of White's final score.

During our further work on "Tricking KataGo (Triple-ko)", with the tsuke of Yamada Shinji played, Joachim found various improvements for Black.
This was in particular the finding that White must capture the nakade "early" in order to decisively improve her position on the left and in particular to avoid shortage of liberties for her subgroups there. Further improvements for Black in the fight in the upper left corner were also later confirmed by KataGo (2121i).

In June, I started to analyse the main path of Our Solution with the then current new network.

If the Guzumi is played at the earliest possible moment, KataGo offers an alternative variation in which White does not answer this move locally, but instead stabilises her position at the bottom against the growth of the hanezeki's tail.
Subsequently, there is no longer a Main Semeai; the sequence looks much more like a "real" game. However, nothing changes in the final result; White also wins this alternative line by two points.

In the course of this analysis, I discovered that the crosscut after Yamada Shinji's tsuke could also be played the other way round, starting with an inward tsuke.
However, KataGo did not seem to have studied this sequence extensively during its training, which is understandable given its approach, as the original order of moves works best for White. About half of a series of self-play games contained erroneous continuations! A higher number of playouts was not to be equated with fewer mistakes.
It was hard work to identify KataGo's mistakes in these self-play games. I felt transported back to the early days of our work on Igo Hatsuyôron 120, when no programme support was available. This is because the assessments of KataGo as an artificial intelligence are not necessarily reliable when you are in a part of the variation tree that has not been sufficiently searched during the training of the special network.
KataGo (2021i) as of end of July performed incomparably better after these games had been added to the material for further training. However, even with this updated network, it was not possible to achieve 100% freedom from errors.
You will find the details in "Solution KataGo (2021i)".

Darkgrey = 6 Main Semeai Liberties:
Black has fallen below the Punishment Semeai Liberty Level. White will choose the Capture Variation, capturing not only the hanezeki's tail, but also Black's large group int he upper right.

Darkred = 7 Main Semeai Liberties:
Black is bound to follow the Main Semeai, as he must not lose a single tempo in the Main Semeai. Black can play outside the Main Semeai area, only if White did so just before.

Brown = 8 Main Semeai Liberties:
Under certain cirumstances (depending on the number of territory reducing moves Black has to play to get a satisfactory score in the Capture Variation), White must be careful to not lose a single tempo in the Main Semeai, and so might be restricted in her movements on the baord.

Pink = 9 Main Semeai Liberties:
Under certain circumstances (and still nine Main Semeai Liberties at White's decision point), White might fall prey to Joachim's Final Ko in the Semeai Variation.

Lightgrey = 10 or more Main Semeai Liberties:
Under certain circumstances (and still nine Main Semeai Liberties at White's decision point), White might fall prey to Joachim's Final Ko in the Semeai Variation.
If Black still has ten Main Semeai Liberties at White's decision point, Black's large group in the upper right will survive the Semeai Variation, resulting in White losing the game by a very large margin.

Lightbrown:
Capture Variation.

Darkbrown:
Semeai Variation.

Cyan:
Analysis mode. Special restrictions apply (e.g. a ban on giving atari at Black groups, or capturing Black groups that are in atari).

Golden:
The moves displayed on the board were either played by KataGo in a self-play game or favoured in "Analysis Mode".

Brown:
The moves shown on the board were chosen by human amateurs, partly based on KataGo's assessment.

KataGo's 2021 Solution