We present the classical sequence chosen by Fujisawa Hideyuki 9p for mutually occupying opponent's liberties in the final stage of the Main Semeai. We explain in great detail when Fujisawa Hideyuki played at worthless points although there were still valuable endgame points available.

As a consequence, Fujisawa Hideyuki had to occupy some remaining valuable points in the course of the hanezeki's dissolution, which may have led him to overlook Joachim's Rediscovered Oki.

Several years later, Cheng Xiaoliu 6p published his suggestion for the final endgame on the left side of the board, which Fujisawa Hideyuki had left in the dark.

As Joachim Meinhardt later discovered, however, he had made a one-point mistake in doing so.

Jérome Hubert 3d developed his own solution to resolve the eclipse, which ultimately enabled Joachim Meinhardt 4k to rediscover the crucial oki in the hanezeki.

We will discuss different variations of the following endgame to illustrate how difficult it is in Igo Hatsuyōron 120 to avoid one-point mistakes, even when there are no more serious complications to calculate at the very end of the game.

Referenced by ( 2042), ( 2042), ( 2042), ( 2042)

Let's go back to the dawn of time....

: ( 2022MainLine)
In the classical solution of Fujisawa Hideyuki 9p, the mutual occupation of opponent's liberties in the Main Semeai starts with this move.

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It is not compulsory to play this kikashi so early.

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This is the first time that Black occupies a valueless point although there are still valuable points available, so violating a fundamental endgame principle.
This kind of move could be judged as technical error.

In this respect, Black would have been better off defending his territory in the lower left corner with a move at e.g. .

For further details of our analysis at the time, please refer to the history of our investigations ...
783

: ( A 2041)
White occupies a valueless point, too.

Building on Jérôme Hubert's earlier findings on the correct order of White's (later) moves on the right side of the board, Joachim Meinhardt suggested playing at , instead, giving atari at Black's single stone in the lower right.

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Black occupies a worthless point for the second time.

Again, a move at (or at ) would have been preferable.

: ( A 2041)
White occupies a worthless point for the second time, too.

Jérôme Hubert played at , instead, intending to capture Black's single stone in the lower right before White's decision point.

Taking profit in the right centre already during the mutual occupation of opponent's liberties was the decisive difference from the "classical" sequence of Fujisawa Hideyuki that finally led Joachim Meinhardt to rediscover the decisive oki in the hanezeki.

For further details, please refer to section "Joachim's Rediscovered Oki in the Hanezeki" ( 2042)

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For the third time, White occupies a worthless point.

Again, it would have been technically better to give atari at .

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The final capture of the nakade before White's decision point.

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Black's oki into White's four-point eye is mandatory.

Thereafter, in the right centre will start the Semeai Variation of Fujisawa Hideyuki.

will start his Capture Variation.

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In this section, we will discuss Fujisawa Hideyuki's Capture Variation only, as it is better for White than his Semeai Variation, but which was presented first in Fujisawa Hideyuki's 1988 book.

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Black recaptures four White stones.

: ( A 2041)
White starts the occupation of Black's remaining liberties in the right centre.

Joachim's Rediscovered Oki would benefit White by two points even here in this line, but has not been played by Fujisawa Hideyuki (for what unknown reason ever).

For further details, please refer to section "Joachim's Rediscovered Oki in the Hanezeki" ( 2042)

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Meanwhile Black is busy taking White's corner group in the hanezeki off the board.

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Even now, it would have been better to take Black's single stone in the lower right off the board with and .

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Finally, Black captures White's corner group.

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Thereafter, Black attacks White's upper group in the hanezeki.

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White connects her four stones in atari, so gaining one point overall.

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White connects her two stones on the right edge.

In contrast to White's previous move, she could do without this connection (and play immediately, instead), since Black would then have to take her two stones off the board.
Nothing would change in the final result of the game.

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Fujisawa Hideyuki's sequence ends with this move.

In his commentary, he only mentions that the endgame on the left side will continue with , , but dispenses with all the details of the concrete sequence he had in mind.

As a matter of course, White will capture with in the lower right much later.

Fujisawa Hideyuki gives the final result of the game as a two-point win for Black.

Let's take a short detour to China ...

Referenced by ( 2022MainLine), ( 2037)

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In Cheng's 1988 book, this hane at the upper edge starts the continuation of the endgame at the left side of the board (after Fujisawa Hideyuki's , ), most of which had also been developed by Jérôme Hubert ( 2041).
Please note that Cheng applied Fujisawa Hideyuki's classical order of moves for occupying the liberties of Black's large group at the right.

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Black plays this kikashi ...

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... before protecting his cutting point.

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White has sente, and so can play this hasami-tsuke in the lower left, successfully reducing Black's corner territory.

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Cheng's Tenuki to the top gains one point overall, compared to Jérôme Hubert's Solid Connection with .

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Cheng's Bump in the left centre kills two birds with one stone:
On the one hand, this move forces Black to defend his territory in the left centre in gote. On the other hand, Black's potential for creating territory below is in ruins.

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Black is forced to connect.

White threatened to destroy three points of Black's territory in sente by playing at herself.

: ( A 2041)
Cheng's sequence ends with this block, securing territory at the top.

But he apparently overlooked White's atari at at the bottom, which would be one point better overall.

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The final sequence displayed here was added by us.
Black's push at the bottom is the last move of value on the board.

Capture Variation:

Black's territory:

• Upper left corner: 21 points.
• Left centre: 3 points.
• Lower left corner: 12 points.
• Hanezeki: 7 + 28 + 31 points = 66 points.

= 102 points of territory in total.

White's territory:

• Nakade Area: 21 points.
• Bottom: 6 points.
• Hanezeki: 3 points.
• Hanezeki's tail: 39 points.
• Top and right centre: 10 points.
• Upper right corner: 19 points.

= 98 points of territory in total on the board.

Black wins the game by three points.

Let's enter the world of amateurs for some corrections ...

: ( 2041)
White gives atari at the bottom.

This move, apparently overlooked by Cheng, will benefit her by one point overall.

: (170 2041a)
Black connects immediately here.

It would not affect the outcome, if he pushed with at the top, instead.

Capture Variation:

Compared to the superordinate variation, ...

• White got an additional point of territory at the bottom.

White gained one point.

Black + 3 => Black + 2

2041

Let's go back in the history of amateur investigations ...

Referenced by ( 2022MainLine)

: ( 2041)
White gives atari at Black's single stone in the lower right.

This move starts Jérôme Hubert's continuation of the Main Semeai and the later endgame on the left side of the board.

Please note that he had also played once at a worthless point with just before.

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White captures Black's single stone in the lower right before her decision point.

This is the second move that differs from Fujisawa Hideyuki's sequence.

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White captures Black's four stones at the left edge.

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Black's oki is mandatory.

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White captures the hanezeki's tail, choosing the Capture Variation.

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Black recaptures.

: ( A 2041)
Jérôme Hubert continues with taking territory in the right centre, in sente, as Fujisawa Hideyuki did.

He also missed Joachim's Rediscoverd Oki at , which would be better for White.

For further details, please refer to section "Joachim's Rediscovered Oki in the Hanezeki" ( 2042)

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Black if forced to start the capture of White's corner group in the hanezeki.

He is unable to play the large endgame move of in the upper left, as White would capture his large group at the right.

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White secures one point of territory in the right centre.

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Jérôme Hubert wanted to enforce Black taking all of her hanezeki groups of the board unnecessarily, which Black would have to do anyway.

White already got all the profit in the right centre, and so could happily start the endgame on the left side of the board with , instead.

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Another (unnecessary) White kikashi at the right.

Referenced by ( 2041)

, :
Now, Jérôme Hubert starts the endgame on the left side, starting with the two moves that Fujisawa Hideyuki had mentioned.

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Black ends in gote at the top.

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White reduces Black's territory in the lower left corner, starting with this hasami-tsuke.

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Jérôme Hubert solidly connects his single stone in atari, so ending in gote in the lower left.

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White's atari at Black's three stones is an unnecessary kikashi.

Even if Black was able to play at himself, he would not get additional territory in this area.
would be also an atari, and Black would have to connect at , or to capture with in the corner to the same effect.

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Jérôme Hubert plays this peep in order to force Black defending his territory in the upper left centre with .

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Due to Jérôme Hubert's Solid Connection , White is able to force at the top.

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White gives atari at Black's single stone outside the hanezeki.

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Finally, White destroys Black's potential point of territory in the left centre (e.g. , , , , ).

Capture Variation:

Compared to Cheng's original Capture Variation, ...

• White got an additional point of territory at the top.
• White destroyed one point of Black's territory in the upper left corner.
• White did not capture Black's stone in the lower left, so losing two points.
• White got an additional point of territory at the bottom.

In total, White gained one point.

Black + 3 => Black + 2

This is the same final score as was given by Fujisawa Hideyuki.

Please note that Jérôme Hubert gave his result as "Black + 1", which, however, is an obvious mistake.

2041

After a short detour to the dawn of time again in the world of amateurs ...

: ( 2041)
This is the position after Black recaptured in the hanezeki, with Fujisawa Hideyuki's original liberty occupying moves at the top ().

Even without Jérôme Hubert's correct sequence for occupying Black's liberties at the right, Joachim's Rediscoverd Oki has any additional territorial effect, as will be shown below.

In this respect, it remains a mystery that neither Fujisawa Hideyuki nor Cheng (in his 1988 book) used this move during the dissolving of the hanezeki.

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Black has to take White's corner group a liberty.

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White cuts-off Black's single stone on the outside of the hanezeki, in sente.

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Again, Black is forced to occupy a White liberty in the corner.

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White captures Black's three stones in the corner.

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Black's oki is mandatory.

: ( A 2041c)
White captures Black's single stone, in sente again.

However, as we discovered later, White could do even better by doing without this (unnecessary) kikashi, but by starting the endgame with in the upper left just now.

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The endgame at the left side of the board (after Fujisawa Hideyuki's initial moves) follows the suggestion of Jérôme Hubert again.

: (156 2041b)
Jérôme Hubert's Solid Connection.

Cheng's Tenuki to at the top would not make a difference here in this line.

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Black ends in gote in the upper left.

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White continues with her kikashi in the right centre.

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Black connects, so destroying two points of White's territory.

You will easily realise that White would have gained by occupying this point much earlier.

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Black is able to destroy a third point of White's territory in the upper right centre, as White lost one move in the lower right corner too many.

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White peeps in the upper left centre.

Cheng's Bump would not make a difference here, as there is no valuable point left on the board.

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White's final move in the left centre, destroying Black's hopes for some points of territory there.

Capture Variation:

Compared to the superordinate variation, ...

• White got an additional point of territory at the top.
• White destroyed one point of Black's territory in the upper left corner.
• White did not capture Black's stone in the lower left, so losing two points.
• White got an additional point of territory at the bottom.
• White captured one Black stone at the bottom, so gaining one point.
• White destroyed an additional three points of Black's territory in the lower right.
• Black destroyed one point of White's territory in the right centre.
• White did not capture Black's stone in the lower right, so losing two points.

In total, White gained two points.

Black + 3 => Black + 1

This is one point better than the (supposed) sequence of Fujisawa Hideyuki.

2041

After a short detour to the dawn of time again in the world of amateurs ...

: ( 2041)
This is the position after Black recaptured in the hanezeki, with Jérôme Huberts proposal for the order of moves during the occupation of Black's Main Semeai Liberties ( instead of and played by Fujisawa Hideyuki).

White plays Joachim's Rediscovered Oki in the hanezeki.

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The continuation in the lower right corner follows a well-known path.

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White interrupts the dissolving of the hanezeki and starts the endgame with Fujisawa Hideyuki's Atari.

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The further endgame on the left side of the board follows Jérôme Hubert's suggestions.

: (154 2041e)
Jérôme Hubert's Solid Connection in the lower left.

Here in this variation, Cheng's Tenuki to at the top does not favour Black.

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White returns to the right side of the board.

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However, Black is able to destroy White's potential point of territory in the upper right centre. His large group has sufficient Main Semeai Liberties left.

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Cheng's Bump at , instead, would not make a difference, too, as White would have no use for her sente.

Capture Variation:

Compared to the superordinate variation, ...

• White captured one Black stone at the bottom, so gaining one point.
• White destroyed three points of Black's territory in the lower right.
• Black destroyed one point of White's territory in the right centre.

In total, White gained three points.

Black + 2 => White + 1

2041

After a short detour to the dawn of time again in the world of amateurs ...

: ( 2041)
This is the position after Black recaptured in the hanezeki, with Joachim Meinhardt's adjustment ( instead of played by Fujisawa Hideyuki) of Jérôme Hubert's proposal ( instead of and played by Fujisawa Hideyuki) for the order of moves during the occupation of Black's Main Semeai Liberties.

As before, White plays Joachim's Rediscovered Oki in the hanezeki.

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Black has to take White's corner group a liberty.

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White cuts-off Black's single stone on the outside of the hanezeki, in sente.

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Again, Black is forced to occupy a White liberty in the corner.

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White captures Black's three stones in the corner.

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Black's oki is mandatory.

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The endgame at the left side of the board (after Fujisawa Hideyuki's initial moves) follows the suggestion of Jérôme Hubert.

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Black ends in gote at the top.

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White continues with the hasami-tsuke of , aiming at the reduction of Black's conner territory in the lower left.

: ( 154 2041i)
We will study Jérôme Hubert's Solid Connection first.

As we will see below, Cheng's later Bump in the upper left centre will turn this connection into a mistake.

It would be better for Black to play tenuki here, in order to defend his territory in the upper left corner with a move at .

: ( A 2041f; 159 2041g)
Jérôme Hubert's Peep in the upper left centre loses one point overall here, as also a move at in the upper right centre.

White must play Cheng's Bump , instead.

: (159 2041h)
White destroys Black's potential territory in the right centre.

A move at would be equivalent.

Capture Variation:

Compared to the previous subvariation, there is no difference.

White + 1 => White + 1

2041

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