( 986)

(Referenced by 305; 313; 318)

To analyse the effect of an additional external ko, we have to shift Black's -stones to , and to - the latter as a protective move, to render all approach moves in the upper left possible - and White's -stone to the newly created ko-shape.

!!! This precondition must be kept in mind! With positions in the upper left corner, where this protective move is not mandatory, one of White's stones on the right side must be taken off the board, resulting in one more liberty for Black's group in the upper right, favouring Black. !!!

But now, both groups have one liberty "too many". As usual with this case, we will add a pair of stones to the position. We will let Black capture the ko on the upper edge (Black is unable to occupy a shared liberty, instead, due to the then threatening Punishment Semeai), and White occupy another outside liberty of Black's group.

White's group has four liberties (w, 3 * c), and two ko-shapes (m, j). Black's group has five liberties (2 * b, 3 * c), and also two ko-shapes (k, j). Black has captured two of these ko, White only one, so the situation might be a bit favourable for Black.

Black's protective move in the top left corner reduced the liberties of White's -group there. In principle, this would enable Black ko-threats in the nakade. However, as we will see below, these will not come into play here. Therefore, it was not necessary for White to push into Black's top left corner before, to generate ko-threats of her own.

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Black can neither connect the hanezeki's tail, nor play a valid ko-threat in the nakade (please note that we inserted the first moves / of the Nakade Sequence again), so he starts with his ko-threat in the hanezeki.

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White re-captures the ko, and Black has his back up against a wall, because he has no valid ko-threats left.

White's centre-group has too many liberties (please note the interaction of the two ko-shapes), so the atari of on the upper edge is no valid ko-threat for Black ( 1051).
Again thanks to the two ko-shapes in the centre, and on the upper edge, White can do without answering a Black move in the nakade, e.g. at , threatening to capture the entire left side, and to rescue Black's connected group on the lower edge ( 1052).

But, at the most desperate for Black, he would not win, even if he had valid ko-threats available somewhere on the board ( 1053).
Please also note that White would not win the semeai with Black's connected group on the lower edge, if she played at , instead of re-capturing the ko.

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It will not benefit White to choose the semeai with Black's connected group on the lower edge.

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Black simply connects the ko on the upper edge.

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Black has this very surprising ko-threat on the lower edge.

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Black wins the ko-fight.

Please note that it would not help White, if she had valid ko-threats available. The marked double-ko in the centre ( / ) favours Black.

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If White takes the ko on the upper edge, Black occupies the last shared liberty with . Thereafter, White captures another ko with .

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It begins the mutual capturing of one of the three ko.

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This move ends the cycle of a triple-ko. The game ends with no result, according to Japanese rules.

This result is better for White than that of the sub-variation shown before. But White could have done much better, as we will see now.