EndgameProblem33/Attempts

This problem looks so comparatively simple. (It's unsolved...) I'll try!

xela: It's too difficult for me! I suspect it's not a well-posed problem: the best move will depend on what the outside looks like.

Yes.

 

Black plays first and gains. (Let's never mind how Black even got the privilege of playing first in this problem.)

This is Sente No Gote.  

This is one of the first moves that comes to mind.

xela: This choice of is gote. Black a is actually the first move that comes to mind for me, with b as a close second choice.

In the context of understanding the solution of an endgame problem, you might consider One to be a kind of "local sente": if Black were to play C as well, then, the Black stone is obviously alive while One in the second diagram counting( down) from here keeps the stone unsettled and forces Black to find the living move at Two.

What does B do? Black is already alive, ...right?

 

This cut is unreasonable. Two captures and stays alive.

 

White blocks in Sente and gets the other gap. Six takes the vital point of the Bulky Seven in the corner. On second thought, starting with the Hane on the bottom may have been better.

xela: Yes, hane at the bottom in sente looks better to me! This way, the end result is 6 points in the corner. I think black can actually get 7 points here. Also, depending on the outside position, is risky. What if white plays at instead? Can black threaten to escape? Will it turn into seki or ko? In any case, black loses nothing by playing at : later, will be black's privilege, so the end result is the same.

Privilege only works forever after the first game. This is the first game as far as we know. So, Black doesn't have the privilege yet.

 

Five is a hasty inside play. Seven insists on living inside. Eight looks for more fighting liberties. Ten raises the stakes. The inner white stones depend on the Ko and White has local Ko threats starting with A. Depending on the circumstances this might be playable.

 

The inner white stones die if White retreats.

 

This could be it...

 

Four can try to invade the Gun Eight.

xela: Depending on the outside position, white might try at a instead. If black can't make a second eye on the outside, then it will be seki. Is black's loss of a few points in the corner worth more or less than white's loss on the outside? If black simply plays at a (or at or at b), then there's no more complications, and the corner is worth 7 points. This is my vote for the most likely right answer. Or even more simply, could have been at b in the first place, leaving as black's privilege for later.

How is the corner seven points...

 

Two at A is smart but the Atari at Three seems to be a sufficient answer for all of Black's problems.

Black fights.  

Black has another Ko threat at A. White's chance of winning the first stage is one third. If White wins, Black plays at A, White connects at B and Black takes back the Ko. White's chance of winning both stages is one fourth. White's chance of killing the whole group is one twelfth after the first peep. White can also connect at Seven after taking the first stage leaving the other as a ten thousand year Ko. This is slightly more likely to work with one ninth... (By the way, Five dies.)

 

If Black is afraid of Ko, Black can try this...