Tec II.1:

The real story continues with the guzumi in Tec II.15 ( 191). However, we will now provide an overlapping, and much more detailed, outline starting a few moves after Tec I.7 ( 38), with Tec II.1.

After , in Tec II.1, we can begin to see more clearly the issues which will dominate till the end of the game. Closely related issues often arose when we looked at options for .

The -group cannot live fully independently. However, if dies, then lives. The other obvious possibility for to live would be by capturing - for this to happen must force to capture the hanezeki's tail, . Hopefully, this gives time to capture , and then . will make this capture only if needed to protect at least one of , , or .

Tec II.1a:

Note that a simple seki (one eye each, or no eyes each), between and , would not save . would fill all but the last shared liberty (assuming one eye each), and the safe liberty - - in the seki at right, /, and then, at her leisure, simply play at , and capture , before capturing . should be able to capture , but that would not be enough compensation.

The problem is designed precisely so that cannot keep enough outside liberties to avoid the above-mentioned temporary seki, i.e. Black will not able to capture , instead.

There is also the asymmetry with respect to playing at the point of , which makes the issue so hopeless for .

After connected the hanezeki's tail with a move at , simultaneously capturing , needs six moves to capture the just connected group /. Therefore, can only succeed, if has not more than five liberties left.

We will show later in Tec II.4 ( 185) that can safely capture , with a move at , in the case that has not more than six liberties left. The number of 's outside liberties is much smaller than the number of liberties that shares with - not to mention the fact that also has outside liberties, which must occupy. Therefore, it will develop a position, wherein both, and , do not have any outside liberties any more. With only shared liberties left, will be unable to approach successfully.

Perhaps, can sacrifice , if he can capture enough stones? This is what happens in our solution, and gives a small victory.

is stable, and cannot be threatened by .

Tec II.2:

We now identify some conditions that we can use in analysing possible outcomes.

Condition 1: The exchanges of , and , are sente for (but not ), at any time, and have to be played if is to capture . They have been added to make matters simpler and clearer.

(1a): After the exchange, has 22 liberties.

(1b): Without the exchange, has 23 liberties.

Tec II.3:

Condition 2: If, at any stage, plays at and captures the hanezeki's tail, , then must re-capture at .

Tec II.4:

(2a): now requires four more moves to capture , but note that killing is not the same as killing , and ...

(2b): needs a yet further two moves (a total of six) to capture . This would be a disaster for , so she should not capture with a move at unless the -group has less than seven liberties.

Tec II.5:

Condition 3: If plays at , then 's best move is always to play the oki at O. Black then has five liberties.

(Referenced by 183)

Tec II.6:

However, if, after captures at , wants to steal the eye with , then has only four liberties. We now consider the liberties of the group that is attacking (, , or ) - , say.

(3a): For to connect the hanezeki's tail at , and save all of , and , can not have more than five liberties.

Furthermore, saving , does not guarantee the death of , so ...

(3b): If wants also to attack , can not have more than four liberties. And ...

(3c): To continue with the attack on , must then first (remove another three liberties, and so) take all but the last liberty of . From this point onwards, has four liberties, and has six liberties. After the capture at , has nine liberties, has seven liberties.

(3d): ... from which we can see that can save , by connecting at , if has only nine liberties.

Tec II.7:

Some possible outcomes: The fight with .

In Tec II.7, at this very moment, it is 's move, and has 15 liberties. By Condition (1a), has 22 liberties. We now show that if tries to counter-attack , then she will lose too much.

Therefore, has to defend immediately with a move at (which is of our solution).

Tec II.8:

If ever captures the hanezeki's tail, , with , we can see from Condition (2b) that has six liberties. This means that has effective 22 - 6 = 16 liberties, on more liberty than (before capturing ). So - even if she has sente - cannot win the semeai between , and , if she starts occupying liberties of , and lets occupy liberties of , in return. lives, but will capture , and , so over-compensating 's gain by capturing .

Tec II.9:

If ever connects the hanezeki's tail, , with , we can see from Condition (3c) that has nine liberties. From Condition (3b) we know that must have taken eleven (= all but four) liberties of beforehand. Even if takes one of 's liberties - there are now 21 - will win this semeai with one move, because he only needs 11 + 9 = 20 moves to capture . , and , will also die, which is a real disaster for .

Tec II.10:

Some possible outcomes: The fight with .

now closes in, and has a forcing sequence available, which reduces to only one eye. After the dust has settled, we have Tec II.10, where has sente, and has 18 liberties. Note that this is three more liberties than had in the discussion above, so we should expect that can kill , which, by Condition (1a), has 22 liberties.

Tec II.11:

If ever captures the hanezeki's tail, , with , we can see from Condition (2b) that has six liberties. This means that has effective 22 - 6 = 16 liberties, two liberties less than (before capturing ). However, must do so latest after has been reduced to four liberties; otherwise would successfully connect the hanezeki's tail himself, see below. So we have to consider 18 - 4 = 14 effective liberties only for . has sente, so barely wins the semeai between , and , by one single move. This is the Capture Variation of our solution, where , and , live; , and , die; and wins the game by three points.

Note that if at any stage, does not respond to 's moves in this fight, then will die - the loss will be too great for , although captures . This is equivalent to saying that if, either mistakenly loses a liberty, or gains a liberty, then will die without compensation (what we call the Punishment Semeai). These considerations also limit 's options if tries to avoid following with the guzumi exchange of .

Tec II.12:

If ever connects the hanezeki's tail, , with , we can see from Condition (3c) that has nine liberties (and has seven liberties). From Condition (3b) we know that must have taken 14 (= all but four) liberties of beforehand. If takes one of 's liberties - there are now 21 - will win this semeai by two moves, because needed 14 + 9 = 23 moves to capture . This is the Semeai Variation of our solution, where , and , live; , and , die; and wins the game by five points.

Because either wins the Capture Variation even if has sente, or is two moves ahead in the Semeai Variation, might safely leave the semeai path, and start the endgame, as early as she has sente to do so.

Tec II.13:

Some possible outcomes: The fight with .

Now we turn our attention to the fight between , and , in Tec II.13. This is markedly different from the two other fights that we have just examined. There is no need for to capture - only itself.

Tec II.13 (.2):

Unfortunately, for , many of 's liberties are shared with . has to play at immediately to attack 's eye-space. This move also stops from connecting and . Clearly, could play at - not only guaranteeing two eyes for , but taking a liberty of . However, would now save , with a move at , and put such pressure on that would have to capture too soon, thus giving life to , and an easy victory to . So, attacks , and plays at , reducing to one eye; will connect at , and will have no eyes. In this position, has only eight external liberties, but shares eleven liberties with , so 's position is now hopeless.

Tec II.14:

(Referenced by 184)

If the guzumi exchange ( in Tec II.13) had not been played earlier then we have Tec II.14. After playing the exchange of , , could play the eye-and-ko sequence to , before reducing to one eye. Now things are more complicated - there is a necessary-for-survival (i.e. must not lose it if he wants to capture ) external ko around , and fewer shared liberties, both of which benefit slightly. However, as we show, that apparent advantage is not enough (please refer to the variations for (); 225).

Detailed theoretical explanations of this type of ko can be found in a separate chapter ( 1133).

(Referenced by 193)

Tec II.15:

There is another important area that we have not yet fully discussed in this outline - the Guzumi Exchange, , . Some questions are:

- Is obliged to answer 71 with 72, or can she play somewhere at left, or in the top left corner first / instead (variations for ; 432)?

- Might it be better to play the guzumi exchange earlier / later ("Timing of the Guzumi"; 813)?

These questions are considered by us in detail (please follow the references above). We decide that our solution is the optimal one for both and .

Tec II.16:

In the tenuki variations, is forced to live in the upper right (with , , , in principle). Suddenly, the right half of the board has become more or less uninteresting. cannot afford to capture the hanezeki's tail any more (she would have to capture all of , as compensation, and additionally save the lower part of ), so the seki in the lower right quadrant of the board will remain stable.

The focus changes to the left side of the board, and there it is , not , who has to encounter several challenges.

has to care for the safety of all of the three groups , , and , that surround the hanezeki's tail. Additionally, she must capture parts of on the upper edge, and on the left side. However, either will be unable to capture enough in the upper left and on the left side simultaneously, and / or will lose (parts of) her -stones on the left side. In the end, will be ahead by a larger margin than in our solution.

Tec II.15a:

Considering the timing of the guzumi ( 813) leads to the following results.

If played the guzumi exchange earlier (lets say before approximately ), would have kept too much territory in the centre, which fate would have been to become destroyed by the walking hanezeki's tail , instead.

If Black played the guzumi later, he would have lost options, in the top left corner, and on the left side, that were badly needed by him in the tenuki variations.

It seems to us that there might be a grey area (lets say after approximately ), where the endgame value of 's moves, and their inherent threats against , and , begins to overcompensate 's territorial loss, caused by . And it becomes more and more difficult for to win the game.

Tec II.15b:

The guzumi exchange decreases the value to of the Capture Variation - the capture of , resulting in life for - by seven points. Three points are due to the guzumi itself, the earlier Hasami-Tsuke Sequence (, ) will result in a further loss of four points of territory for now, with this special scenario (the Hasami-Tsuke Sequence does not destroy any territory when dies, as it happens in the Semeai Variation).

This stops from playing the Capture Variation - she will choose the Semeai Variation, instead, worth two fewer points for , and so letting win by three points ( 510).

However, without the guzumi exchange inserted, the Hasami-Tsuke Sequence will lose its territorial relevance. Then, it is equivalent to the classical reduction sequence in the upper right corner.

Tec II.16:

The kikashi of - played in the bamboo joint in the top right corner - has been very kindly introduced to us by Michael Redmond 9p. According to him, this is a "natural" suggestion, aiming at providing with an additional liberty.

However, gaining only one additional liberty for is not sufficient to win the game. We can see from Condition (3d) that needs nine liberties to enable to securely connect with a move at . Condition (2b) tells us that can safely capture with a move at , when has seven liberties left. This means that would need a further two liberties - all other surrounding conditions assumed to be unaffected - if wanted to deprive of her option to capture . The latter is not possible in the problem.

We will show that it is best for to answer 's kikashi with the atari of , giving the desired additional liberty, in exchange for some profit in the corner for . 's other option, the solid connection of , has its disadvantages with the ko-fight on the right side that has been mentioned before (Tec. II.14; 190).

Our extensive work on this kikashi is displayed with the variations for () ( 390).

(Referenced by 183)

Tec II.17:

Did we catch all feasible outcomes?

Here, we attempt to check that we have considered all plausible outcomes. We do this by looking at all possible combinations of potential structural outcomes for , with those for . There are four potential outcomes for : all of live, or only one of them dies. For , there are four categories: the hanezeki's tail, , may live, or die - and in each case may live, or die. Obviously, as we see in lower-left of the table, if dies then all of , , and will live.

\

, , and , refer to White's groups

, and , refer to Black's groups

A red frame indicates a captured / dead group

- = not feasible

a - h = see the list below.

For example, "a" is the combination where dies, but both , and live, while all of , and , also live.

-

-

a

-

-

-

b

c

-

-

d

e

f

g

h

-

There are discussions of the following in our text:

a) /

In Joachim's Ko-Semeai, if, unlike the problem, has insufficient ko-threats.

b) /

This could arise only if, either has fewer, or has more, liberties than they can in our solution.

c) /

This is our solution - the Semeai Variation.

d) /

does not reply at 80 after 79, but attacks - applies in our analysis.

e) /

does not reply at 78 after 77, but attacks - possible only if has fewer liberties than in our solution.

f) /

This is the Capture Variation of our solution. 's groups in the hanezeki die.

g) /

The Punishment Semeai, if mistakenly loses a liberty. Also Joachim's Ko-Semeai.

h) /

Circular Hanezeki; also, maybe sacrifices, and the guzumi ignored.

We will continue with part III of the "Technical Notes" later ( 495).