(Referenced by 1049)

:
Let us finally assume that Black had valid external ko-threats available, which must be answered locally by White. However, these will be of no advantage to Black, for several reasons:

First of all, Black cannot allow White to connect the ko at right, with a move at . As we have seen before, the remaining double-ko / in the centre benefits White.

On the other hand - due to the double-ko of / - Black will not get the chance to connect to ko on the upper edge, with a move at . But this would be a mandatory requirement for winning the ko-fight at right, involving , and .

Ko: ;

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White captures the ko on the upper edge, providing her centre group with an outside liberty.

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And White captures the ko in the centre, as well.

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It will not help Black to re-capture the ko on the upper edge, instead.

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White captures the ko on the right for the last time, simultaneously giving atari on Black's group.

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Finally, White connect the ko at right. The remaining double-ko of 23 / 24 ensures that White will win the game.

///:

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Black re-captures the ko on the upper edge.

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But now, Black can neither capture the ko in the centre, at , nor connect the ko on the upper edge, at . White would connect the ko at right, with a move at , leaving Black helpless.

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Temporarily, Black could restore the situation. But he needed an unlimited supply of ko-threats - that he does not have on the board - to keep this up ultimately