Alex Weldon: Aside from one small comment I'd like to make, Dieter is 100% correct, as far as I can tell. I'll leave it on the attempts page for a little while, though, in case someone else sees something neither of us do.
Simply connecting leads to the same ladder. Alex Weldon: The one thing I wanted to say is that here, Black can also exchange a for b and then play at to connect out, if he feels the damage to his upper side position is unacceptable (e.g. if the upper right corner is very important, and the left side of the board isn't important at all). The ladder is probably better in most cases though.
JoelR: To my weak eyes, also deals with the ladder, and does not invite the ko. a and b are still miai for life, so what does Black have?
Incidentally, what is the significance of for this position?
Alex Weldon: Without , Black can get a more favorable result (by threatening White's position on the left) than the one he gets by playing the hamete . I believe that it still results in a ko, but one that White stands to lose a lot from as well. It's complicated, so I'll leave it as an open question to the stronger players.
unkx80: No ladder?
Alex Weldon: Yeah, it's good that this was brought up. I was going to add it myself, since it's kind of cool how Black gets the ladder here. Incidentally, the sagari of is the bad move that White played in the actual game, falling into my evil trap. Somehow, I still managed to lose the game, though. :-P
unkx80: Also note the - sequence. This can be another one-two-three example.
Alex Weldon: Well, yes. It's obvious here that both and are wrong. Black should just play first.
JoelR: It's not clear to me that this is one-two-three. If Black skips , and plays , , he has to come back to , or else White will capture the stones. And why is the wrong response to ? I think White prefers to leave some aji in the ladder stones than to play a move that requires Black to capture.
Alex Weldon: Well, the question is whether White would prefer Black to capture on the upper side, or burst through by capturing in a ladder. My guess is that in most circumstances, White would rather lose the stones in the ladder and save the upper side. In this case, it doesn't matter whether Black plays or first. However, at either juncture, White can choose to give up the top side. If White's going to give up the top side, I believe that exchanging for first is a loss for Black.
Now White plays at a and gets thickness in compensation for losing the top side. If White is going to play this way, Black would rather not have made the - exchange, I think.
Since this way, - isn't good, and W of course won't play if she's planning on keeping the top and letting Black capture in a ladder, I think we can conclude that immediately is at least as good, and in some cases better than first.