This is the position that was put forward in Some Endgame Problem 1.
The cut does not work in this case. Because her string is one stone longer, White can give atari at , and after
Black has achieved nothing.
As TuRen? correctly stated, the above is wrong. Black can cut at , provided
is answered at
. If White answers at
, Black plays at
and gets a ko. If White answers at
or
, this variation occurs. Black captures two stones in sente, exactly the same result as in the 'correct' variation below. In fact, this variation is even better than the one below because White's corner is worth 4, rather than 5, points.
here also does not work. Again, Black does not get much for his trouble.
The cut at is tesuji. If White answers at
, the moves to
give Black a ko.
If White connects after , she is unconditionally dead.
If White connects at , she is dead too.
And if White plays atari with , it is ko again (White a is a ko threat, forcing Black b).
White's best move is . After this, White is unconditionally alive, but Black can capture two stones in sente with
. (
is necessary because a black stone at the same point would kill the white group with a snapback).
Unfortunately, in the game where this position occurred (it was in the last round of the preliminaries for the 2001 Dutch Championships, against Marcel Bloemena), I did find , and my opponent did find
, but I missed the black move at
in the previous diagram, and thus thought it would be gote. To avoid this result, I played the terrible move at
, expected White a, Black b and White c (which would be 1 point better than the previous diagram), but of course my opponent answered at
, after which I could not capture the two stones at all - not even in gote.
Instead of in the last two diagrams, the atari here is also possible, but it is not as good. As shown before, Black plays at
, but White avoids the ko with
. Now White has only 4, rather than 5, points.
After , White will have to to play inside because Black threatens a double snap-back.
Charles I've added this diagram to make it clear that Black threatens an atari, leading rather to a combination of snapback and a connect-and-die.
Furthermore, Black can decide to play on this side. Now White saves the two stones, but loses the other two. Furthermore, her territory has shrunk to 3 points only.
For Black to play at , which might look like a vital point, directly, without playing either cut first, also does not work. White connects at
, and Black can still capture the stones: but only in gote.
-- Andre Engels