: ( 231)
White must play this push first, before the hane. This is also shown in the theory chapter as FLAG 9a ( 1055).

:
If White did without, Black would answer at , also taking a liberty of White's group in the top left. But White would have lost her ko-threats in the top left corner.

:
Black prepares the ground for "quick" ko-threats on the left side. However, there will be only one threat, at , that he can use effectively. Black will insert this sequence latest, when White's centre group has six effective liberties left.

:

Black follows the usual sequence. He cannot escape his fate, even if he exchanges for on the left side; please refer to the additional explanation in the theory chapter ( 1063).

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White plays the gote-sente combination in the hanezeki here, to turn Black's potential ko-threat of the atari at into a suicidal one. White's move itself is gote, but ...

:
... Black will be forced to take a liberty of his group himself. So White did not lose a move here.

:
Black connects the hanezeki's tail. Occupying another outside liberty, with a move at , instead, would not make a difference.

Ko: ; ;

: (134 355)
Black must play this ko-threat just now. It will not work any longer, when used one cycle later. We will explain this in a sub-variation, where Black gives atari at , instead.

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Please note that White needs to play a ko-threat of her own in the top left corner here.

:
Black's ko-threat is suicidal, so White gets independent life for her groups in the lower right.

:
White has no ko-threats left that contain an immediate threat. This move, however, will be sufficient to win.
Had Black ever exchanged for before, White would play this move at ; please refer to the additional explanation in the theory chapter ( 1063).

, :
Again, and again, Black is unable to answer White's moves in the lower left.

:
Finally, with this move, White kills Black's marked group on the left side that looked so rock solid before. White wins the game.

Now we can see that White's two -stones are not only on the board for serving endgame purposes.