Igo Hatsuyōron 120 lives decisively from a very special, extended hanezeki. We will explain its individual components and their effects here in this section.

As usual in a hanezeki, neither player may make the first move without suffering a significant disadvantage.

An analysis of the surrounding positions ultimately ends with the conclusion that Black's large group in the upper right as well as White's group at the left edge are the decisive weak points that bring the dissolving of the Hanezeki back into the game.

We will show that the additional temporary seki is required as a buffer in the Main Semeai as well as for the regulation of the score difference.

At the very end, we present the Yōshin Teiki, another collection of problems by Inoue Dōsetsu Inseki, which may have represented an essential predecessor to his Igo Hatsuyōron.

Let's enter the analysis room ...

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We will utilise the board position after Black's move in the Crosscut Sequence, which rescued Black's single stone above, for the detailed explanation of the very special features of Igo Hatsuyōron 120's (extended) hanezeki in the lower right corner.

We decided to call the entire formation in the lower right quarter of the board - including Black's meandering group in the centre - "hanezeki", in order to simplify the verbal reference to it.

Strictly speaking, this compound of Black and White groups is a hanezeki extended by a simple seki, where the "hane" as the outer lying component is a tail of 20 stones.

The marked groups in this diagram form the true hanezeki in the corner.

The marked groups in this diagram form an additional seki on the right side.

The importance of this additional seki for the functionality of Igo Hatsuyōron 120 will become clear below.
The problem would not really work without.

Let's first discuss the hanezeki's tail ...

For most of the game, neither side wants to play , as that would be a serious mistake, as we will see below.

You can certainly imagine that such a move, with which 20 Black stones are either captured or supposedly saved, seems so extremely attractive to "normally-trained" AI - having never encountered a hanezeki it its life - that it wants to play it consistently.
This is one of the reasons why Igo Hatsuyōron 120 is far beyond the reach of any "normally-trained" AI.

The length of the tail with 20 pieces is no coincidence.
If it were only 19 stones (provided that this reduction would be possible without influencing the rest of the board), Black would win the game (under the adjusted assumption of no komi), not White.

We explain the dissolving of the hanezeki by White first.

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White captures the hanezeki's tail.

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Black recaptures four White stones.

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White's oki prevents Black from creating a two-eyed group.

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Black attackes White's group in the corner.

Connecting with would be a grave mistake.
White would answer with and Black would suffer from a serious shortage of liberties.

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White tries to capture Black's group.

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Black gives atari in the corner.

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White captures Black's three stones at the right edge.

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Black's oki is mandatory.

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White captures Black's single stone to the left, erasing her own shortage of liberties of the two stones to the right.

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Black wins the semeai by one move.

In a simplified view of the initial position, 23 Black but 34 White stones die.

Consequently, White would only be able to resolve the hanezeki if she won sufficient compensation for her big loss in it elsewhere on the board.

Black's dissolving of the hanezeki suffers from a comparable mechanism.

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Black connects the hanezeki's tail.

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White's oki is mandatory.

After this, Black is helpless, because his connected hanezeki group suffers from a severe shortage of liberties.

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But White is able to take Black's group off the board.

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White erases her own shortage of liberties in the corner by capturing Black's three stones.

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Black's oki is mandatory, as far as this semeai is concerned.

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White wins the semeai by one move.

In a simplified view of the initial position, 3 White but 35 Black stones die.

Consequently, Black would only be able to resolve the hanezeki if he killed any of White's groups that surround the hanezeki's tail.
Only in this case can he hope to kill White's group in the corner.

Let's now analyse the wider surroundings of the hanezeki ...

We start with Black's large group in the upper right.

Black's group cannot achieve independent life on its own.
Capturing any of White's stones is gote for Black, so he can only capture one of these for an eye, but not both.

Black's only hope is the collapse of the entire hanezeki.

White's upper right corner is alive as it stands.

There is no way to reduce White's formation to only one eye.

White's centre group (and at the top) is also alive as it stands.

In the current position, Black does not have any chance of killing this group, as and are miai.

Even otherwise, if Black got to occupy both of these points (; ), it would turn out that Black's large group (also one-eyed then) would have at least one liberty too few.

For further details, please refer to section "Joachim's Hiki at the Upper Edge (Joachim's Ko-Semeai #1)" ( 2034).

White's group in the additional seki at the right side is safe - for the time being.

Black cannot give atari at e.g. , as White would capture with .

In order to be able to attack this group successfully at all, the prior dissolving of the true hanezeki in the corner would be a mandatory prerequisite.

However, Black cannot give atari at White's corner group just now, due to his shortage of liberties.

If he played and , White would capture with .

It follows that Black must force White to capture the hanezeki's tail with .

However, as we have seen above, it is associated with a great disadvantage for White to play this move.
Consequently, she will only do so to save one of her groups involved in the atari at the tail of hanezeki.

As is already explained above, Black cannot hope on attacking White's centre group, as the points of and at the top are miai for creating an independently alive group.

Black could reduce White's bottom group to only one eye with a move at or at .

However, it is White's turn in this position.

Black could also reduce White's group at the left to only one eye with a move at .

But it is White's turn in this position again.

However, bringing these groups to independent life is gote for White in each case. Consequently, she can only succeed for one of them, because the rules forbid her to move twice in a row.

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It is correct for White to create a living shape for her bottom group.

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Black plays the last move of the Crosscut Sequence in the left centre, closing the hole in the encirclement of his upper left corner.

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White attacks Black's five stones at the left edge, so preventing Black from capturing her left-hand group easily.

This move starts the Nakade Sequence at the left side of the board.
Black will continue with , successfully keeping White's group down to only one eye.

Across the board, the Main Semeai will effectively develop between White's group on the left edge and the Black's large group in the upper right, buffered by the hanezeki.

As we now know, White's seemingly already captured stone will play a decisive role in this semeai, too.

Let's now determine the buffer effect of the hanezeki with regard to the Capture Variation of the Main Semeai, ...

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White captures the hanezeki's tail.

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Black recaptures White's four stones.

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White starts the occupation of Black's liberties in the upper right.

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Black returns the favour in the lower right.

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The mutual occupation of opponent's liberties continues.

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In the case of success, Black will capture White's upper group in the hanezeki by this move.

The hanezeki delays the Main Semeai in the Capture Variation by six moves / liberties.

Capture Variation of the Main Semeai:

However, if White were unable to effectively capture Black's large group in the upper right, because this group has at least seven liberties, ...

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... she would play Joachim's Rediscoverd Oki, destroying Black's potential territory in this area.

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White's cut is sente.

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Black's oki is mandatory.

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There is nothing valuable left that White could do in the lower right, so she should start the endgame on the left side of the board (latest now).

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Before the end of the game, Black will have to take both of White's groups in the hanezeki off the board.

Let's now determine the condition under which Black can successfully connect the hanezeki's tail ...

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Black connects the hanezeki's tail.

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White's oki is mandatory.

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Black starts the occupation of the liberties of White's left-hand group.

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White continues in the hanezeki.

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Black's connected hanezeki group will survive the semeai, if his move at at the latest is an atari that threatens to capture White's group at the left.
In this case, he will be able to capture at next.

Otherwise, his connected hanezeki group will be taken off the board by .

But here in the very specific environment of Igo Hatsuyōron 120, ...

... White would achieve independent life for her hanezeki group in the lower right corner, so gaining a large game-deciding benefit there.

Please remember that Black's large group in the upper right cannot get more than only one eye, and so would be dead here, as would be Black's group in the temporary seki.

As a result - with regard to the Main Semeai - Black can connect the hanezeki's tail, only if White's group at the left has a maximum of four liberties (i.e. would be her last liberty), enabling Black to play the oki into White's three-point eye in the lower right corner.

This also implies that White's left-hand group has four liberties at the moment of White's decision point.

As a matter of course, White would not have wasted her moves in the hanezeki under these circumstances.

Semeai Variation of the Main Semeai:

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If it were favourable for White, she would not capture the hanezeki's tail, but occupy a liberty of Black's large group in the upper right instead.
This starts the Semeai Variation of the Main Semeai.

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Black can do nothing but connect the tail of the hanezeki.

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White's oki is mandatory.

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Black is forced to reduce the liberties of White's left-hand group to only one.

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In the meantime, White continues with the occupation of Black's liberties in the upper right.

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Now the time has come to approach White's corner group in the hanezeki.

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Black's oki is mandatory.

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Usually, this move will take Black's large group off the board.

But let's continue for some moves, in order to achieve an additional insight into the problem.

If Black has a maximum of two surplus liberties (= 9 Main Semeai Liberties in total) then White will still capture his large group in the upper right in the Semeai Variation.

Black needed at least three surplus liberties (= 10 Main Semeai Liberties in total) for large group in the upper right to also survive the Semeai Variation.

This means that a gain of individual liberties for Black's large group in the upper right remains without any effect in the Semeai Variation.

This is also an effect of the additional temporary seki , on the right edge.

Finally, we will explain the territorial effect of the additional seki at the right side of the board ...

This diagram shows the board position at White's decision point; / is the additional temporary seki.

Please note that White's groups and Black's group in the lower right corner will be captured in both Main Variations.

Semeai Variation:

Roughly calculated, the captures of White's large group at the left side and of Black's large group in the upper right compensate for each other.

White will lose 32 stones and Black will lose 34, which is about the same.

Capture Variation:

Roughly calculated, the captures of Black's tail of the hanezeki and of White's group in the temporary seki at the right compensate for each other.

Black will lose 20 stones and White will lose 18, which is about the same.

Conclusion:

The temporary seki is needed for delaying the Main Semeai, as well as for adjusting the score between both Main Variations.

Only this design allows two almost equivalent Main Variations.

Let's now take a closing look back to the time before the Big Bang ...

Yōshin Teiki (要津定規, "Principles to Follow at Important Points") is a classic tsumego collection, written by Inoue Dosetsu Inseki in 1708. It was laid out in six volumes, encompassing over 1,500 problems, but the majority of the work has been lost. Each volume was ordered in a clear fashion from easy to hard, apparently with the intention to be used as a study course of lessons.

The two volumes which survived are the section on nakade, numbering 107 problems, and the section on seki, numbering 28 problems, for a total of 135 problems. The first problems of each section are accessible for a single-digit kyu player, while the last ones are at the high amateur dan level.

These surviving problems have been compiled by John Fairbairn in his book Today We Have a Splendid Feast, The Meijin Inseki's Yoshin Teiki by Inoue Inseki Meijin, which is accessible as a SmartGoBook.

There would certainly have been other mosaic stones to be found in the complete problem collection, with the help of which Igo Hatsuyōron 120 would have been better understood from the outset.

Problem 60 (at left) addresses a nine-stone Nakade, Problem 121 (at right) a "simple" Hanezeki.

Problem 60:

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White cuts at the lower left edge, also giving atari at Black's single stone.

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White threatened to connect along the left edge, so Black has to connect.

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Thereafter, White rescues her single stone in atari.
Please note the strange-looking row of six stones at the edge.

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Black's connection provides his cut-off upper stones with additional liberties.

His three stones at the left edge were in danger of becoming captured by White, starting with an atari at the same point.

Problem 121:

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Black plays hane at the right edge.

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White blocks by giving atari at Black's just played stone.

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Black occupies a crucial liberty of White's corner group.

Problem 60:

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White is forced to give atari at Black's two stones below.

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White's strange-looking move is tesuji.

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Black's connection erases his shortage of liberties.

White threatened to capture his stones in a series of atari, starting with .

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White creates a familiar lump shape.

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Capturing the nine-stone nakade will not result in life for Black's group.

Problem 121:
Neither side wants to play at , as they would lose the ensuing semeai in the corner.

The position has become a seki.

Problem 60:

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White's peep at the first row threatens to cut at , so massively reducing the size of Black's eye shape.

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Black connects.

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White occupies the vital point.

Thereafter, and are miai.

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White keeps Black's group down to only one eye.

If Black's group ever gets involved in an "external" semeai (assuming that parts of White's encirclement could be cut off), Black must play or in due time to prevent White from building an eye for herself at the inside.

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