When we started to work with KataGo's new moves, we were so convinced these would commit White to the Capture Variation, that we had completely lost sight of the Semeai Variation for a while. However, the Semeai Variation is intrinsically tied to the Capture Variation, as is the White group on the left edge to the Black group in the top right.

Destroying opponent's potential territory that is located outside the Main Semeai area has an identical effect on both the Capture Variation and the Semeai Variation. This implies that this destruction can be got for free.

Opponent's potential territory can also be destroyed inside the Main Semeai area, but this kind of destruction is costly. In principle, the destructor has to pay in liberies in the Capture Variation, but in points of territory in the Semeai Variation. And, of course, liberties and points are also different sides of the same medal.

In the following diagrams we compare gains and losses between Our 2015 Solution and Cheng's classical 1988 solution (we preferred Cheng 1988 to Fujisawa 1982, because Cheng played through the Main Variations until the end) and between the new KataGo-assisted 2019 solution and Our 2015 Solution.

Legend:
A green square (//) marks an one-point gain for Black, a dark-green diamond (//) a two-point one.
Similarly, a red square (//) stands for an one-point gain for White, a dark-red diamond (//) for a two-point one.

Capture Variation only:

Cheng's Capture Variation ended with three points for Black.

The effect of Joachim's oki in the lower right corner is
– five points for White.

This gain destroyed the 20th century professional solutions of the problem.

Black + 3 => White + 2

Semeai Variation:

Cheng's Semeai Variation ended with a drawn game (jigo).

The effect of my second throw-in in the hanezeki is
– four points for Black.

Jigo => Black + 4

Capture Variation:

The effect of my second throw-in in the hanezeki is
– one point for Black.

White + 2 => White + 1

Please note that both Main Variations have improved for Black.

Semeai Variation:

The effect of my guzumi and Harry's hasami-tsuke in the top right corner is
– none.

Black + 4 => Black + 4

Capture Variation:

The effect of my guzumi and Harry's hasami-tsuke in the top right corner is
– seven points for Black.

This large gain stopped White from choosing the Capture Variation.

White + 1 => Black + 6

Please note that the Capture Variation has improved for Black without hurting the Semeai Variation.

Semeai Variation:

The effect of Yamada Shinji's tsuke in the top left corner is
– one point for White.

Black + 4 => Black + 3

Capture Variation:

The effect of Yamada Shinji's tsuke in the top left corner is
– one point for White.

Black + 6 => Black + 5

Please note that both Main Variations are affected equally, as the tsuke is played outside the Main Semeai area.

Semeai Variation:

The effect of KataGo's crosscut after Yamada Shinji's tsuke in the top left corner is
– three points for White.

Black + 3 => Jigo

Capture Variation:

The effect of KataGo's crosscut after Yamada Shinji's tsuke in the top left corner is
– three points for White.

Black + 5 => Black + 2

Please note that both Main Variations are affected equally, as the crosscut is played outside the Main Semeai area.

Semeai Variation:

KataGo's new atari (& capture & connection) and bad-shape move destroy some Black territory on the left side of the board equally in both Main Variations:
– six points for White.

Jigo => White + 6

However, White's (temporary) gains are located inside the Main Semeai area, so some compensation by Black has to be expected. In the Semeai Variation, White will have to pay on the left side.

Capture Variation:

KataGo's new atari (& capture & connection) and bad-shape move destroy some Black territory on the left side of the board equally in both Main Variations:
– six points for White.

Black + 2 => White + 4

However, White's (temporary) gains are located inside the Main Semeai area, so some compensation by Black has to be expected. In the Capture Variation, White will have to pay on the right side.

Semeai Variation:

The compensating effect of KataGo's territory reducing moves on the left side of the board is
– eight points for Black.

White + 6 => Black + 2

Please note that White's gains in the Capture Variation hurt the Semeai Variation.

Capture Variation:

An additional effect of KataGo's territory reducing moves on the left side of the board is
– two points for White.

White + 4 => White + 6

Semeai Variation:

An additional effect of KataGo's territory reducing moves on the right side of the board is
– three points for White.

Black + 2 => White + 1

Please note that this gain is due to Black's attempts to gain compensation on the right for his territorial loss on the left in the Capture Variation.

Capture Variation:

The compensating effect of KataGo's territory reducing moves on the right side of the board is
– five points for Black.

White + 6 => White + 1

Please note that Black's gains in the Capture Variation hurt the Semeai Variation.

In retrospect, it is striking that there are only moves on the right side of the board that cause Black to improve the final score of the problem.

And that moves that improve the result in White's favour can be found on the left side of the board only.

With one crucial exception: Joachim's oki in the lower right corner, after White has captured the hanezeki's tail in the Capture Variation.

I guess Inoue Dōsetsu Inseki would never have expected 20^th century professional Go players to miss this move in solving the problem.

Harry wondered to what extent the (seemingly) "simple" White push at would be preferable to the wedge at that had been recommended by Michael Redmond.

is a well known sacrifice tesuji that ensures Black a solid connection of his stones in the centre.

After , Black is solidly connected in the centre. Black lost one stone at , but became one point of Black territory, so Black got his connection for free.

Additionally, White lost her direct liberty at , and the point of is no longer an approach-move liberty, too.

As a result, White lost two moves in the Main Semeai. This loss enables Black to reduce White's territory in the upper right with two moves, and .

However, White did not sacrify her wedging stone at .

continues with occupying liberties in the Main Semeai. At the end of the game, White will connect the ko at .

Capture Variation:

Equally in both Main Variations, Black gained one point of territory in the centre, at the cost of one sacrificed stone. Additionally, he did not capture White's wedging stone, resulting in a net loss of one point for him at the left side of the board.

At the right, however, Black destroyed two points of White's territory.

In total, Black gained one point in the Capture Variation.

White + 1 => Jigo

Semeai Varation:

In the Semeai Variation, Black captured an additional White stone (the initially played one in the left centre) for a gain of two points.

At the right, however, White captured an additional two Black stones, which were played to reduce White's territory in the Capture Variation.

Here, it is White who gained one point in total. And so – to Black's surprise – she will choose the Semeai Variation, instead of the Capture Variation after her wedge in the centre.

White + 1 => White + 2

The above result means that Black must not compensate up to the maximum!

Black has to do without one of his potential territory destroying moves in the upper right, in order to keep the final scores of both Main Variations stable.

White + 1 => White + 1

In principle, White has the option to keep things "simple" by playing the "usual" connection at in the upper right.

After his kikashi of and , Black takes the miai point at the left with .

White must connect at in the upper left corner as early as possible. Otherwise, Black will capture at the same point to gain a small, but decisive advantage – please see the variation shown below.

This connection costs White a move in the Main Semeai, so Black is able to additionally destroy one point of White's territory in the centre, with a move at .

and might be played even later than shown here.

Capture Variation:

Equally in both Main Variations, Black gained three points of territory in the left centre. White, however, had not sacrificed her wedging stone there, so that a net gain of two points for Black results.

In the Capture Variation, Black did not capture White's single stone in the top right for an eye, which cost him two points.

In total, gains and losses compensate for each other; the final score of the Capture Variation remained unaffected.

White + 1 => White + 1

Please note that White's marked cutting point in the centre must not be counted as an approach-move liberty when calculating the Punishment Semeai Liberties of Black's large group in the upper right. This cutting point will vanish as soon as White captures the hanezeki's tail.

Semeai Variation:

In the Semeai Variation, Black did not capture KataGo's bad-shape stone in the left centre for a loss of two points.

In the right centre, in return, Black gained one point by destroying White's eye in this area.

In total, Black gained one point in the Semeai Variation, but to no effect on the outcome of the game, as White will choose the Capture Variation again. Nevertheless, this variation might be considered "technically" flawed, because the final scores of both Main Variations are not identical.

White + 1 => Jigo

White gives atari at Black's single stone in the lower right with , instead of connecting her single stone in atari at the upper edge.

Black immediately takes the opportunity to capture this stone with a move at , but which loses a move in the Main Semeai.

Please note that – in total – a difference of two moves in the Main Semeai results. In this variation here, it is Black, who loses one move, while it is White in the main line.

Losing two moves in the Main Semeai means that Black is unable to connect his marked stone in the lower right, as he has only one liberty left to spend.

Black uses this surplus liberty to destroy one point of White's territory in the centre with a move at .

Capture Variation:

Equally in both Main Variations, Black gained two points in the top left – compared to the main line. He captured one of White's stones, and White has one point of territory less.

In the lower right, however, White captured one Black stone, compensating for her loss in the upper left.

In total, the final score for the Capture Variation remains stable.

White + 1 => White + 1

Semeai Variation:

In the Semeai Variation, White captured one Black stone less in the lower right, losing two points in comparison with the main line.

In the upper right, White did not need to occupy all approach-move liberties to be able to capture Black's large group.

In total, Black gained three points in the Semeai-Variation, winning him the game. But – as a matter of course – White will choose the Capture Variation. Nevertheless, this variation might be considered "technically" flawed, because the final scores of both Main Variations are not identical, and additionally because Black wins one of both Main Variations.

Jigo => Black + 3