This situation (altered a little bit for demonstration purposes and removed stones elsewhere) popped up in one of my games a few days ago. I remembered it clearly afterwards because during the game it had quite an impact on me. I was white in this situation. After a risky invasion, I ended up with this group. It was my turn to play and I tenuki'd. I thought my group was safe.

So my question. Is this white group alive? I've done some variations, but maybe higher level players will see it more clearly. My thought right now is that white can live/quasi-get-out, even if it has to sacrifice some stones (well only 1, I think?). But maybe black has a killing move.

So if black can kill: how? and where should've white played to make it safe?



(forget move 1 and 2, was a mistake in making the problem)

And a follow-up question could be, does this change the life/death of white, or not?

Not a trivial problem for me. Didn't read much but 95% confident killable with the extra stone, 70 40 % killable without. Black needs to be careful to avoid giving white a chance to make a ko.
Edit: found stronger white answer.

Interesting, so I think it's normal that we (both around 20kyu) couldn't really figure it out on our own during the game.
Thanks for the reaction

Maybe one final question: say white wants to be safe and "fix" the group. What move gives it max points? So what's white's best move in this situation?

That one's not so easy either! Normally b12 hane and connect would be a good way to live and grow the territory a bit, but here a6 is still a problem. So maybe defending at a7 is the best for points, need to count the endgame carefully*.

P.S. I now think without the extra stone best black can do is a ko to kill, or capture the 4 stones in sente.

* Here's a start. With white living at a7 he gets 5 points, and shaded black area on 3rd line up to line 4 gets 9 (the baseline chosen here is arbitrary, just needs to be far enough for other variations). So white -4 net.

Click Here To Show Diagram Code

[go]$$Wc
$$ | . . . , . .
$$ | ? ? ? . . .
$$ | ? ? X . . .
$$ | ? ? ? . . .
$$ | ? 6 X . X .
$$ | 8 2 O X . .
$$ | 3 4 O O X .
$$ | 9 5 O X . .
$$ | . O X X . .
$$ | 1 . O X . .
$$ | . . O X . .
$$ | O . O X . .
$$ | X O 7 X . .
$$ | X X X X . .
$$ | . . . . . .
$$ | . . . . . .
$$ +------------[/go]

If white lives with b12 and solid connection instead (hanging has a cut problem) then black a6 seems to be sente and capture of b4 too which is sad. My first reading was as below. Here we can assume black a13 white a12 for counting as it's gote for both. For simplicity's sake I will also assume white b6 for black a5 connect is white's sente, but this is actually a bit generous to white (black might ignore and fight ko so not totally white's privilege and black might get to defend the point there). So white gets 5 points again, while black gets 6 in the shaded area plus 2 captures and 1 territory below, 9 total, so same white -4 net as before. However, one thing worth pointing out is that with white living this way he does create some bad aji for black with the peep at a (more serious if white gets the a13 endgame).

Click Here To Show Diagram Code

[go]$$Wc
$$ | . . . , . .
$$ | ? ? ? . . .
$$ | ? ? X . . .
$$ | . 2 ? a . .
$$ | . 1 X . X .
$$ | . 3 O X . .
$$ | . . O O X .
$$ | 7 . O X . .
$$ | . O X X . .
$$ | 5 9 O X . .
$$ | 4 . O X . .
$$ | . 6 O X . .
$$ | X . 8 X . .
$$ | X X X X . .
$$ | . . . . . .
$$ | . . . . . .
$$ +------------[/go]

But actually maybe I didn't play the best for white, how about living like this to make capture of b4 not immediately sente? But actually it is sente with the sequence a-f so I think it ends up with the same count.

Click Here To Show Diagram Code

[go]$$Wc
$$ | . . . , . .
$$ | . . . . . .
$$ | . . X . . .
$$ | . 2 . . . .
$$ | d 1 X . X .
$$ | . 3 O X . .
$$ | b f O O X .
$$ | a c O X . .
$$ | . O X X . .
$$ | 5 7 O X . .
$$ | 4 . O X . .
$$ | . 6 O X . .
$$ | X O e X . .
$$ | X X X X . .
$$ | . . . . . .
$$ | . . . . . .
$$ +------------[/go]