(Referenced by 77; 91; 128; 133; 136; 140; 152; 190; 250; 363; 380; 390; 396; 399; 818; 825; 834; 1133)

: ( 219)

As shown in another sub-variation of our solution ( 555), Black cannot prevent White's large endgame in the upper left, with a move at 77, later. So what about trying it now, without having played the guzumi, just before the Crosscut Sequence is completed?

We also re-investigated the consequences of Black's move at . The results of our analysis of Joachim's second idea can be found later ( 363). These semeai are not simple at all, so we give them sufficient room for explanations. Here we can admire another example of Dōsetsu's genius. If Black had only one more liberty, he would win; whereas both of these attempts fail, and Black has to play the guzumi.

In 2014, we finished our theoretical analysis, whether Black could successfully use the three kikashi in the top left corner (; which have been played here already) as ko-threats, when he keeps them in reserve. Following our final conclusion ( 873), these potential three ko-threats cannot be counted independently on their own, so these will have no effect on the outcome of the game.

An exemplary application case can also be found earlier in this book ( 83).

: (A 236; B 237)

White follows the usual path, ensuring that her group on the left side cannot be captured by Black.

She will not succeed if, instead, she immediately tries to bring her group on the upper edge to life, with a move at .

If White wanted to pre-empt Black from forcing her to start the forthcoming ko-semeai on the right side "early", she would have to insert the kikashi in the top left corner first, starting with the atari of - this will stop Black from taking that point later ( 257). However, Black's shape in the upper left will become solidified unnecessarily, providing White with some problems in finding a smooth way through the forthcoming ko-fight.

In the middle of 2013, when analysing the consequences of Michael Redmond's kikashi in the bamboo joint (; 838), we suddenly recognized that we previously had missed the correct moment to play this move, as a starting point to create a larger eye for Black in the upper right. We now know that one valid option for Black is to play the kikashi before the Crosscut Sequence, what is the topic of another sub-variation (71 (); 390).

Another valid moment will arise later, when White's group on the upper edge is reduced to only one eye. We have adjusted the previous structure of this section, according to our newer findings, because we wanted to give the reader the opportunity to obtain a clear, and thorough, understanding of this complicated ko-fight.

: (A 243; B 255; C 257)

However, after , Black can no longer follow our solution's normal path, with a move at , since White, on the left side, has the marked stone already in place. Black here hopes to succeed through ko, in a semeai with White's group at top.

By playing at , instead, Black might also achieve a ko. However, Black gains a small territorial advantage here by the immediate capture of White's stone, should White reject the ko offer.

Black could also play the kikashi of Michael Redmond 9p in the bamboo joint now. As we found in 2014, Black could enforce an "early" ko-semeai thereafter. After Black's kikashi, White will no longer be able to win the sub-variation unconditionally. However, the endgame will become extremely close, so we are still unsure, whether this kikashi might be better technically than the block in the centre.

: (A 270; B 283; C 284)

For a very long period of time, we were quite sure that White could win unconditionally by pushing immediately with , aiming at a reduction of Black's corner territory in the upper left. An extremely close endgame was involved, in which White was ahead by only the smallest margin possible. Recently (end of 2014) however, Joachim came across with a surprising refutation of our assumption.

White can neither avoid the ko with moves at , or . Then Black will play at 80, and get an extra liberty (the "guzumi effect"), winning him the Semeai Variation. But choosing the Capture Variation (by taking the hanezeki's tail) is no valid option for White either, because she will not get enough points on the left side, to win.

(Referenced by 251)

: (A 285, B 286)

Black must now create, and fight, the ko. He will lose if he tries to do without, e.g. continuing with a move at .

It is also too late now to close the top left corner, with a move at , simultaneously attacking White's group on the left edge.

: (A 287)

White must prevent two eyes for Black now. We think that White would no longer be slightly ahead territorially, if she captured Black's five-stone-group on the left-hand edge, instead, so letting Black's group in the top right live. The window of opportunity for this option has closed.

Detailed explanations about this very special semeai here can be found in a separate chapter ( 937). More theoretical explanations about this type of semeai between two opposing groups with one eye each, and an external ko, can be found in a later chapter ( 1133).

: (86 292)

This throw-in creates another false eye for White, so Black gains one move, compared to the exchange of , .

(A 295)

Black must play here now to stop White playing at 85 on her own.

: (A 296; B 297; C 301)

Black must prevent two eyes for White. He plays from the left, so White has no chance to get a larger eye.

If Black plays more solidly at , to strengthen his shape on the upper edge, White will get two eyes after .

Cutting immediately at , instead, is more severe, but will not help Black either.

will allow White to build a larger eye, again leading to a ko-fight.

We did not find any other sequence, with which we were able further to reduce White's liberties in this area in the centre of the upper edge.

: (89 309)

White's block to the left is sufficient to win the "late" ko-semeai here. As we found in 2014, a move at 89, instead, would lead to an equivalent result.

Quite surprisingly, White does not affect this sudden miai of 87 (= ) and 89 ( 874) by inserting her kikashi of in the top left corner earlier ( 237).

If Black wanted to enforce an "early" ko-semeai, he should have played Michael Redmond's kikashi of in the bamboo joint even earlier ( 390).

:

White is reduced to one eye.

:

This move prevents another ko-shape. It is sente, containing the threat of , , to create an eye (here the second one) on the upper edge.

White could get more shared liberties with playing at , instead. We did not investigate this thoroughly, but we suppose that there will be no decisive effect on the main line of this sub-variation.

: (A 312)

Now is the latest moment that Black should play Michael Redmond's kikashi in the bamboo joint, if he wanted to build a larger eye in the centre.

However, Black will get a similar result, if he does completely without this kikashi.

:

White is forced to answer locally, with the atari. This is also shown in the theory chapter as FLAG 5a ( 1022). White needed one move to secure life for her group on the left side, but two moves to get two eyes for her group on the upper edge. If she played tenuki now, Black would reduce one of these two groups to only one eye, enforcing the capture of the hanezeki's tail, which loses White the game.

Answering solidly at loses White a decisive move for the ko-fight to come. This is shown in the theory chapter as FLAG 5b ( 1023).

:

Black erases the threat of a potential white eye. If he connected at instead, he would have to take the threat of (which must be answered with ) into account when answering White's coming forcing moves in the upper left.

Playing 93 at will be worse for Black than the main line here.

(Referenced by 138)

: (B 334; C 338)

This atari is the precondition for the following move at .

White could successfully start the ko on the right side "early", with a move at , instead. However, we tried to find a more elegant, and shorter, sequence that allows White to capture this ko as late as possible for the first time. For the resulting ko here, White uses only such moves as ko-threats, which occupy Black's liberties, and no moves that really contain a substantial, damaging, threat.

White could also do without these kikashi in the top left corner, which we had thought of as a kind of precautionary measure in the very beginning of our investigation of Joachim's Ko-Semeai. As we ultimately understood in 2014 (late, but not too late), there is really no need for White to play preparatory moves in the top left corner, in order to create potential for own ko-threats in this area.

:

White plays this kikashi now. Later in the game, a move at might be too slow. White provides her group in the top left with an additional liberty, both getting a significant advantage in the relationship to Black's group in the lower right corner, and preparing the ground for ko-threats, if necessary.

: (A 340)

Black could try to block at , instead, to gain a move in the semeai with White's group. However, Black cannot save his partial groups on the left in the corner simultaneously; so White will win on territory, after capturing the hanezeki's tail, and the entire left side.

: (A 345; B 346)

White gives atari on the upper edge.

She may also play sagari at . However, it does not help White to enlarge her eye space with a move at . A hane at , instead, does not benefit White, if Black is able to get a larger, three-point eye in the centre ( 1142), as he is here, with a move at , or at .

:

It makes no sense for Black to start a ko-fight here.

: (A 347; B 352)

White pre-empts a further ko-shape in the centre, and allows Black to get a larger eye there.

Please note that the exchange of / has been played already, as a mandatory requirement for White's current move.

White could also reduce the size of Black's eye, by playing at , instead. The characteristics of the resulting shape, with a shared ko, are equivalent to those of the larger eye here.

White may also think about playing the hane of , which must be preceded by a move at . We display this sub-variation because of a very surprising result, which highlights the special role of White's two -stones in the lower left corner. However, White will need ko-threats of her own in the top left corner, so this cannot be called technically as good as the main line here.

(Referenced by 341; 342)

:

Black builds a larger eye for his group.

We have chosen this move for technical reasons, with regard to potential ko-threats. If Black connected at 104, instead, he would lose the potential ko-threat of the atari at . Additionally, White could reduce Black's eye in the centre in sente, with a move at 103, destroying another potential Black ko-threat (capturing two white stone inside his eye). Please note that here, in the main line, these potential black ko-threats will not come into play.

:

As already mentioned above, a hane at 105, instead, does not benefit White in the case Black has got the larger eye in the centre ( 1142).

:

Had Black played the "early" Hanezeki Exchange of , , in the very beginning, as in the professional solution, matters would be greatly simplified for White. Please note that the same situation would result, if Black played at here, unnecessarily losing a move in the semeai. So, this is another example of the "early" Hanezeki Exchange not providing any benefit to Black. This is also shown in the theory chapter as FLAG 2a1 ( 1003).

:

This move reduces White's centre group to five effective liberties. From now on, both sides have various options for variations - most of which will result in a change in the order of moves only - but White will still be able to win the game.

: (A 356)

White starts to fill-in her false eyes, so that Black cannot exploit their weaknesses for ko-threats, threatening oiotoshi.

White could also start the ko, with a move at , getting the same result as here.

However, occupying another liberty of Black's group, instead, would be a technical mistake, even after filling-in one or both of White's false eyes. White would still win the game, but must resort to one of her own ko-threats in the top left corner ( 361).

: (A 357)

Black's group has eight effective liberties now. Black does not profit from occupying outside liberties of White's group. Playing on the outside, at , instead, would only deny White the option of choosing the "fake" Punishment Semeai that will be explained as a variation for below ( 359).

As a matter of course, Black is unable to eliminate his weaknesses in the upper left corner with a move at , denying White of her potential ko-threats there. This would be equivalent to loosing a move in the semeai on the right side, giving White an unconditional win.

: (A 359)

White might capture the hanezeki's tail with a move at , instead. This results in a very surprising variation that we found in 2014, just because Black's group has one liberty too many to really suffer from the Punishment Semeai. However, there is the ko again, and White must seek sufficient compensation in the top left corner to win the game.

Again, White should not occupy an outside liberty, forcing Black to connect the hanezeki's tail.

:

Black cannot connect the hanezeki's tail with a move at , instead, because White's centre group has six liberties left. Black would lose the semeai with his connected group on the bottom.

(Referenced by 940)

: (B 361)

White captures the ko on the right side, so reducing the liberties of Black's group to the critical level of less than eight liberties. This moment - her centre group has five liberties left - seems to be the "optimal" one for White to start fighting the ko, because now the ko-fight will not be drawn unnecessarily protracted.

As already mentioned above, it will not prove advantageous for White to occupy another direct liberty, for example at , instead. She would need a really "damage threatening" ko-threat, and not liberty-occupying moves only.

White would also have the "fake" Punishment Semeai available, which has been shown with ( 359). However, this would not be independent from the top left corner, too.

: (A 362)

Black now has two options, but neither of these will be successful.

Here, Black connects the hanezeki's tail, and so captures White's three stones, because his top right group has only seven liberties left. Otherwise, White would capture Black's centre group with a move at 117 herself, thereafter winning the Punishment Semeai ( 888).

Alternatively, Black could use his local ko-threat in the hanezeki, at , giving the same result.

(Referenced by 345)

:

This is the board position after White has played oki into Black's eye in the lower right.

White's group has five liberties, three shared liberties () with Black's group in the upper right, and two direct liberties ().

Black's group in the lower right has five liberties, too, four direct liberties (), and one approach-move liberty ().

Black's group in the upper right has seven liberties, three shared liberties () with White's group, three direct liberties (), and one approach-move liberty ().

:

Black's situation is hopeless. If he captures the ko at 120, instead, White will win the semeai with Black's group in the lower right, using the moves from to . Both groups have five liberties, so White is better off, because she starts the semeai.

:

Here, Black continues by occupying liberties of White's group. Eventually, Black is unable to give atari with a move at . So White wins the game, by capturing Black's group on the lower edge.

Please note that White has five ko-moves ( - ) unused in the top left corner that could become ko-threats. However - White loses a liberty of her group in the top left corner with - two of these would be compensated for by Black's ko-threats on the left side. As we will show in the theory chapter ( 873), Black has no resources available that could match with White's effectively remaining three unused ko-threats.