4464 enclosure 3-3 invasion
This is the standard joseki for the 3-3 invasion after a 4-4 6-4 corner enclosure. White is alive or will be able to escape at a.
After - , Black can't block at because White will play a and capture either of the marked stones.
Of course, going back to the original diagram, this means that if black adds another stone almost anywhere in this area, it forces white to respond with his corner group.
This is often seen at lower levels. If Black now answers at a, White will comfortably live at b, making a J+1 group.
Dieter: Depending on the surroundings...
Bill: Like this?
Timm(5k): I think White can still escape escape on the side though. But maybe it's still a good result for Black.
In this situation, the 3-3 point is still available to White. There are three main responses for Black.
Timm(5k): The sequence needs confirmation.
Black can simply block at , letting white reduce the corner. After , White has no choice but to fall back at . ( at is possible too.)
Bray(7k): Guo Juan (5p) includes among her list of mistakes in this position. She covers this in "New Typical mistakes 10k - 1d lecture 3"
tapir: Has she in particular listed as mistake or the sequence starting from ? I was taught this to not play at anymore and/or defend a base in the corner once upon the time.
Bray(7k): After , black usually plays or (either is fine). The choice depends on the rest of the board. However, she explicitly lists as an error in the sequence shown in this diagram. Reasons include: it's gote, it's small, and white get a strong shape. She likes the tesuji itself, but in this instance it's mainly a trick play (white falls to pieces if he tries to save the two inside stones).
http://internetgoschool.com/auth/lectures/1116.lecture The whole lecture is quite interesting. I don't have any stake in her site, other than being a member for many years.
tapir: No need to justify yourself for relying on Guo Juan (or any professional, really). I am, in fact, a former pupil myself. I agree.
There is one thing this sequence undeniably achieves: an assured eye in the corner. Guess this justifies the sequence in special cases. (Though can't watch the lecture - membership lapsed.)
aims at attacking the White stones on the outside, but lets him live in the corner.
The third one is the most complicated of all. White is able to live too with correct play and the White stones on the outside are not as weak as with the previous variation.
Much of this material appears at Joseki-related Life-and-Death example 5