ferdi: White can also omit .
rokirovka: What happens if Black tenukis instead of ? I faced this in a game today. After dealing with his tenuki and gaining sente I played . Black played tenuki again. After dealing with that and gaining sente again I played at a. Amazingly, Black played tenuki again (!) and I got to play at b. Finally Black defended with at c, I played at 2, Black played at d and despite all his tenukis Black came out ahead in the battle in this corner. Surely White can do much better here if Black plays so many tenukis.
Herman: Lets explore some options for white....
rokirovka: Herman, thank you so much for this extensive analysis. It's very instructive and helpful. It will take me a while to digest all of it, but it's greatly appreciated.
Tapir: My 2k first thought tells me to play at in sequence 2 diagram directly. This may be worse than sequence 2, but I'd like to know about the status of the corner then.
Herman: After , if black cuts with , will capture two stones
Herman: However, black can play like this and keep the corner. This result is not good for white, it only gains a few points and is gote.
Andy: For the above reason, white should tenuki with instead of capturing the stones in gote. Since white's wall is more solid, white can extend further. I think the further extension plus the possibility to pick up the stones later makes this result ok for white.
Herman: White can also play like this. Now black's corner is smaller.
This is another option. Black's options along the left are more limited now, and black is walking over the second line.
rokirovka: This reminds me a lot of the "pincer variant" in the standard 3-4, high approach, inside contact, solid connection joseki. The following diagram and comments are from the page devoted to that joseki:
"Black can play at if White's extension frustrates Black plans at the top. (This is bad locally, but may be playable overall.) White's compensation is to fence in Black and create substantial thickness. For both players, knowing how to handle White's thickness is key to playing this variation.
"A word about : the connection can also be at a. is a little better than b. (Compare with getting ahead with a one-point jump.)"
Like this, black is sealed into the corner, and white's position toward the left side is better than in the first diagram
Like this, black escapes on the outside, but loses two stones. is mandatory, if black defends at instead, white will connect and black's corner will die. After , black cannot cut at a, because b is atari, so black should exchange b for a, then tenuki
With the exchange of - already in place, black cannot escape to the outside as that will allow white to take the corner.