I'm looking at https://www.101weiqi.com/q/39312/:

Click Here To Show Diagram Code

[go]$$Bc19 Black to play
$$ | . . . . . . . . . . . .
$$ | . . . . . . . . . . . .
$$ | . . . . . . . . . . . .
$$ | . O O . O . . . . . . .
$$ | O X O . . O . O . . . .
$$ | . X O X . O X . O . . .
$$ | . X X . . . X . . . . .
$$ | . . X X X X X O O . . .
$$ | . . . O O O O X . . . .
$$ | . . O . O . O X . . . .
$$ | . . . O O O X X . . . .
$$ | . O X . X X . . . . . .
$$ | . X X . . . . . . . . .
$$ | . . . . . . . . . . . .
$$ +------------------------[/go]

I can see three different first moves for black to live or escape. Which one is best, and why? I'm asking because the site marks two of those as incorrect, and I don't agree. I can see why one of the three options is less good than the other two, but I'm not seeing a clear best answer, and neither is KataGo.

I think the idea is that you can connect under. If white tries to stop it then black wins any capturing race, even the one where there is a ko on the inside.

Black has some extra liberties. A ko with three or more approach moves is called 赖皮劫, by at least some Chinese, which means shameless ko. I think that is the point.

I'll admit that I didn't give the possibility of white creating the ko shape much thought but I was uneasy about the number of liberties. I have started to forget what I gave thought to and what I didn't.

When you do connect under you also pick up some points. It seems too difficult to try to put a number on this but I'd expect this to be more 1-2 points. Maybe around 6 even?

If you are going to say this, don't you think you should list your alternatives?

_________________
Dave Sigaty
"Short-lived are both the praiser and the praised, and rememberer and the remembered..."
- Marcus Aurelius; Meditations, VIII 21

I didn't want to give too many spoilers before other people had a chance to look :-)

Click Here To Show Diagram Code

[go]$$Bc19 Black to play
$$ | . . . . . . . . . . . .
$$ | . . . . . . . . . . . .
$$ | . . . . . . . . . . . .
$$ | . O O . O . . . . . . .
$$ | O X O . . O . O . . . .
$$ | . X O X . O X . O . . .
$$ | . X X a . . X . . . . .
$$ | . . X X X X X O O . . .
$$ | . c d O O O O X . . . .
$$ | . b O . O . O X . . . .
$$ | . . . O O O X X . . . .
$$ | . W X . X X . . . . . .
$$ | . X X . . . . . . . . .
$$ | . . . . . . . . . . . .
$$ +------------------------[/go]

It's the half eye at 'a' that makes things interesting. This means that black has the option of living independently, as well as connecting out or winning the capturing race.

The "endorsed" solution at 101weiqi is 'b', connecting out (or winning the capturing race if white tries to prevent the connection; kvasir has already pointed out that the ko potential is worth almost nothing, same as https://lifein19x19.com/viewtopic.php?f=15&t=17090). Instead of 'b', black can also play 'c' or 'd', making miai of connecting or living. It seems to me that black 'd' is inferior, because it lets white rescue the marked stone in sente. KataGo agrees with this assessment. But KataGo rates 'c' and 'b' as pretty much equal. Is there any strong reason to prefer one over the other? Without the half eye at 'a', but with plenty of liberties for black, I think 'b' still works but 'c' and 'd' don't. But for the given position, it seems less clear cut.