Ko: ; ;

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: ( 942)
We will now consider the necessary means for a Black success.

For the ensuing ko-fight, Black needs one external ko-threat, to be played with , to win.

!!! Here in this chapter, we will display the relevant external ko-threat of both sides, which are decisive for the outcome of the sub-variation, in the top left corner. !!!
Please note that White has not played at yet, and White's group has four liberties left, so the atari at , instead, would be no valid ko-threat for Black ( 949).

As a matter of course, "Black needs XY external ko-threats" has to be understood as "Black needs XY external ko-threats more than White". Here in this diagram, White really has valid ko-threats in the upper left corner, starting with .

!!! In order to simplify our presentation, and to ensure transferability to other positions (where White might have less ko-threats than here), we will not "use" these White ko-threats (which really would be available on the board) throughout this entire chapter, but display these moves in the top left corner, too. !!!

:
Capturing White's two stones with is an inerasable internal ko-threat for Black, and due to the larger eye of his group. However, Black must be aware that he can use this ko-threat as final one only (i.e. when White's centre group has only two liberties left).

:
Under the assumption that White has no valid ko-threat left, Black is able to give atari with eventually, so winning the ko-fight.

Black could win the game, only if he had at least one ko-threat more than White.

But please remember that White - in the problem - really had several ko-threats in the upper left corner, starting with a move at . Thus, Black never had a chance to win this ko-fight.

Ko:

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:
It does not benefit Black to insert parts of the Nakade Sequence ( / ) at a suitable moment earlier in the course of the main line of Joachim's Ko-Semeai. As we have seen earlier ( 947), the sheer amount of 's liberties pre-empts more than two valid Black ko-threats on the left side.

Ko: ; ; ;

:
As an exception from the rule, we will display Black's further ko-threats in the left centre here.

:
White occupies an outside liberty of Black's group now. She must keep two of her ko-threats in the top left corner in reserve, to compensate for Black's forthcoming two ko-threats in the nakade.

:
Beginning with this move, Black has two ko-threats in the nakade, because White's centre group has been reduced to three liberties only.

Ko: ; ; ;

:
This is White's fifth, but only third effective, ko-threat in the upper left corner.

:
Black would win the game, if he had at least one ko-threat more than White. However, neither does Black have a compensation for White's effective three ko-threats in the upper left corner (), nor the badly needed additional external ko-threat (). Black is hopelessly behind.