Why doesn't White atari with 3?

[u/ttytan]

I'm reading Kato Masao's book on the Chinese opening, but I don't understand this joseki. The book says that White should save 1 for later because Black can kill with the a-b-c sequence if White doesn't protect the corner after 4, but I think White can preemptively remove the aji by playing 3 to the right of 2, atari, and then playing 5 at 3.

If I'm reading correctly, the extra atari allows White to extend to the right of 4 if Black tries a-b-c. If Black then ataris to the right of c, White captures next to 1 and Black can't play on 19-6 to prevent the second eye (without getting captured). If Black simply turns to the right of 4 before a-b-c, White plays c and lives.

So, why would White leave behind this aji? If Black's going to play 4 anyways, can't White get something out of it?

[u/sadaharu2624]

The point is white doesn’t want to spend another move here to protect. In your variation where black bends to the right of 4, if white spends another move then white gets gote. In the original variation, if white spends one more move white can also live.

[u/ttytan → u/sadaharu2624]

I see, White gets sente. I want to think that White will follow up by making sabaki with the two stones on the outside, but if that had been the original objective, it seems better to squeeze Black with 3 at 4, etc. Is it easy to save the two stones as it stands? I can think of a couple of moves, but I'm not very good at sabaki yet.

Alternatively, maybe this is a middle game joseki that's good with supporting stones. For example, a White extension at the star point would help to mess with the Black stones on the bottom (plus, the corner is not easy to properly capture).

I guess my question is what is the use case for this joseki. The two weak(?) stones and sente on the outside don't seem enough compensation for an unsettled group in the corner. If I played this myself, I don't know if I'd get enough elsewhere if Black were to kill the corner.

[u/Osmarku → u/ttytan]

Two takeaways: 1. this is a common-ish life and death shape in corner, and 2. This corner is small in points so there’s often more valuable hands elsewhere. You see games where pros play a few hands in a corner and leave a possible living group there

[u/Uberdude85]

Would you like to play white 5 to the right of 2 now? Probably not? But what you are proposing is doing exactly that, just in a different order. So if it's bad in this order it's bad in that order. 

[u/jussius → u/Uberdude85]

Yeah, if white wants to add a move to fix the corner he should just capture. If white extends instead like OP suggested, black gets to block in sente. But anyway it's painfully small life in the corner.

[u/ttytan → u/Uberdude85]

Makes a lot of sense when you put it like that 🤔

[u/ForlornSpark]

So, why would White leave behind this aji? If Black's going to play 4 anyways, can't White get something out of it?

It is exactly backwards from this. If your opponent is going to play some move A anyway, then often forcing them to do so means giving them a favor. Instead, you can let them play A and then get a free move anywhere on the board. Often, you'll realize that playing a move that would've forced A is suboptimal - and now you're free to choose the best possible move.
In this case, corner is simply too small to cling to at the expense of sente so early into the opening. After B minimizes the aji with solid 4, it becomes just a matter of points instead of group strength, aji or full-board development. So W leaves it hanging to tenuki.
Note that even if B kills with a-b-c, it leaves a lot of aji on the right side, meaning W can just use it to start another invasion there while threatening to revive the corner. So this group is closer to life than it seems, and killing it can turn out to be too much of a hassle.

[u/ttytan → u/ForlornSpark]

Thanks for the insights! In that case, is it worth saving the two stones on the outside? Black's three stones in the bottom seem a bit shaky given that the corner is not easy to actually capture.

[u/ForlornSpark → u/ttytan]

B's bottom side stones are decently strong because they can extend on the bottom if W plays in the center, or go to the center, threatening W's 2 stones there, if W plays on the bottom.
So W treats these 2 stones as aji for now without settling local position any further. The simplest way is to sacrifice them by playing on the bottom side and making B capture them, but it's probably better to wait and see how things develop before deciding on any specifics.
Currently, W has some cool moves available like nose tesuji against B's 4 stone, which allows the corner to crawl out and (almost) live even after a-b-c sequence. That's how any move near B 9-3 stone threatens to revive the corner. There are also various moves on the bottom side, which makes developing it harder for B. I think the basic idea of this whole corner sequence is to preemptively make some aji there to make creating a big B framework difficult - as opposed as waiting until the last moment and invading an almost finished area later.

[u/tuerda]

Looks like maybe black was going to play 4 anyway.