Referenced by ( 2022MainLine)

: ( 2039)
This tenuki, capturing White's single stone in the right centre, was a suggestion of Joachim Meinhardt.

Seen historically, it was originally played two moves earlier, before Black's kikashi , in the lower left.

We decided to present it in the current position, in order to simplify the presentation.

Liberties:

Black's move loses two tempi in the Main Semeai.

On the one hand, occupies an own liberty of Black's group in the upper right. On the other hand, Black has not occupied a liberty of White's group at the left side of the board.

However, White's captured stone provides Black's group with an eye now, so his group has got an additional approach-move liberty at , due to the earlier played Hasami-Tsuke Sequence. Thus, ...

Black has effectively "only" lost one Main Semeai Liberty.

Territory (in the Capture Variation):

Compared to the superordinate variation, ...

• Black captured White's single stone in the right centre, so gaining two points.
• Black destroyed one point of White's territory in that area.

In total, Black gained three points locally by capturing White's single stone.

However, losing one Main Semeai Liberty implies the loss of one point of territory in the Capture Variation. Thus, ...

Joachim's Tenuki has effectively gained two points for Black.

Let's return to the world of KataGo as of 2019 for the continuation ...

:
KataGo's Wedge in the left centre is a surprising new move, aiming at destroying Black's potential eye in the left centre.

Please note that Black's two stones at the left edge are now in danger of suffering from a shortage of liberties after , (preceeded by ff., as a matter of course)

Please also note that the overall shape of Black's large group at the left side of the board is much weaker than it seems at first sight.

:
Black must give atari from the outside.

:
White's atari from below aims at utilising Black's weakness of the cutting point below.

:
Black is forced to capture.

:
White gives atari for a second time.

She might even do without this move now, and play this kikashi of hers later in the game.

:
Again, Black is forced to connect.
, is still lurking around the corner.

: ( C 2039c; D 2039d)
White attaches at the centre of Black's three stones, losing one tempo in the Main Semeai.

Choosing the atekomi of (discovered by Sergei Danilov 4d - aka "dany"), instead, would provide White with a benefit of one point overall, but under territory scoring only.

KataGo's initial 2019 version, however, used Trump-Taylor-Rules, which are based on area scoring.
Under area scoring, final territory scoring results of "White + 1" and "White + 2" cannot be distinguished; thus - in KataGo's assessment - both alternative moves had the same value.
Quite apparently, KataGo then favoured to more "solid" / "straightforward" option.

For further details of our analysis at the time, please refer to the history of our investigations ...
513a

Later, in 2021, we found another, less complicated, way for White to win the game by two points overall: The combination of and in the lower left corner.
However, Black would be better in the Semeai Variation than with Dany's Atekomi.

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Black's connection is forced, and also loses a tempo in the Main Semeai.

:
White extends upwards, creating a false eye in Black's formation above.

This move also threatens to create two points of additional territory in the left centre with a move at .

White's last move created an additional approach-move liberty for her large group at the left.

Thus, it did not lose a tempo in the Main Semeai, despite being played outside the Main Semeai Area.

:
Black strengthens his formation in the lower left corner, also continuing with the Main Semeai.

:
White connects her single stone at the upper edge for a net gain of one point.
Her move secures two points of territory, but loses one tempo in the Main Semeai.

:
Black takes the miai point.
Black destroys two points of potential White territory, at the cost of one tempo in the Main Semeai, and so his net gain is also one point.

:
White continues with a wedge in the right centre, threatening to lead her encircled stone into the open.

:
Black secures the capture of White's single stone below by creating a shortage of liberties on White's side.

This move from above has been found by Joachim Meinhard, and keeps Black's liberty at .

Before Joachim's finding, we played this move at from below, separating White's stone directly from its allies in the centre of the board.

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White continues with the Main Semeai.

This move benefits White by one point in the Semeai Variation, compared to the immediate connection at (which Black must answer with ), and was found by Dany.

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Black plays 2/2 reductions.

Capture Variation:

Compared to the superordinate variation, ...

• White's cumulated gain at the upper edge is two points.
• White's cumulated gain in the left centre is one point.
• White got an additional point of territory in the upper right corner.
• Black's cumulated gain in the right centre is three points.
• Black connected his single stone in the lower left, so gaining two points.

In total, Black gained one point.

White + 2 => White + 1

Semeai Variation:

Compared to the superordinate variation, ...

• White's cumulated gain at the upper edge is two points.
• White's cumulated gain in the left centre is one point.
• Black destroyed one point of White's territory in the upper right corner.
• White captured one Black stone less there, so losing one point.
• White captured two Black stones more at the right, so gaining four points.

In total, Black lost five points.

Black + 4 => White + 1

2039