( 980)

(Referenced by 140)

What about the "early" ko for White? This will be White's last hope for success in the sub-variation with .

Let us assume that Black did neither play the three hasami-tsuke moves in the upper right ( / ), nor the throw-in in the centre ( / ).

Ko: ; ; ; ; ; ; ; ; ; ;

:

!!! Let us further assume a "very early" start of the ko-fight by White, combined with a "peaceful", and "uncomplicated", continuation (this means that White will not pre-empt any of Black's ko-threats shown). !!!

White has allowed Black to get all the moves - as ko-threats, which he kept in reserve. Additionally, White allowed Black's larger eye, with the / moves.

We suppose that we are on the "safe" side with our analysis, when we give Black (nearly) everything that he wants to have.

In principle, there is the Hanezeki Exchange of / left, and you might wonder, whether Black might get another ko-threat there (which would be the key for winning).

White needed to play the two move-pairs of / , and / .
Black needed to play the five move-pairs from / to / .

Let us assume that the ko-threats are independent from each other (what they are not really in the problem). Even if Black starts the exchanges (what he really did in the sequence above), we will get the following sequence (exemplary; you might interchange the Black moves as you like):

/ / / / / (pre-empts a Black ko-threat) / . Black is unable to get all five of "his" ko-threats.

Please note that it is White's turn now. This implies that White could "steal" Black another ko-threat, if there was any. This means that Black really needed seven ko-threats, versus White's two, for success with the "early" start of the ko-fight.

:
Now, the time is ripe for White to simplify the matter.

Black's earlier move at destroyed the connection of White's -stones, but left White's group with two outside liberties (one more than without ). But Black got an additional ko-threat at , so the resulting effect is Zero.
On the other hand, White's earlier kikashi in the top left corner provided her with one additional liberty for her centre group, at . This gained liberty enables White to play a protective move on the left side, reducing Black's potential ko-threats in the nakade to only two ko-threats remaining. It has been shown earlier that Black has no chance to pre-empt this reduction of ko-threats in the nakade ( 841).

:
The ko-fight continues.

:
If Black used his ko-threat of in the hanezeki, instead, this would not have any affect on the outcome ( 1003).

Ko: ; ; ;

:
We chose White's gote move in the hanezeki to allow a better comparison with the other cases. White could also play the gote-sente-combination of , and , to get a similar result.

:
Black would lose the semeai with his connected group on the lower edge, if he re-captured the ko (White's centre group has five effective liberties left). So he further occupies liberties, and lets White connect the ko.

:
White wins the semeai by one move. Black cannot give atari at .

Ko:

///:

:
Let us now calculate the number of ko-threats that Black needed to win the semeai - provided that he had any.

Ko:

:
Black's second, and additional, ko-threat.

:
Black's third, and additional, ko-threat.

Ko: ; ; ;

:
Black's fourth, and additional, ko-threat.

:
After having used four additional ko-threats (which he does not have in the real problem), Black re-captures the ko for the last time. White does not have any ko-threats, so Black will give atari at with his next move.

Black's initially played move, at , assumed to benefit Black through hurting White's shape on the upper edge, eventually provided White with a decisive advantage. It is difficult to decide, whether Black should have chosen the main line of Joachim's Ko-Semeai, instead, because here White is forced to encounter a long ko-fight that started "early".