Charles posed this problem on Non Joseki Exercise 2
PatrickB: Black must cut at the star-point. All continuations I can see are good for Black. If White gives up the corner, then I see something like this happening:
Which looks good for Black, though I'm not sure that Black should play atari at 5, because it helps White protect her cut at 6.
If White tries to hang tough in the corner, which is what I spent the majority of my time looking at, I see this happening:
And White is in a mess of trouble in corner. If White ataris her way out at a, Black makes a loose-ladder capture at b and has a great position compared to White's low side. If White tries to atari at c, it looks like she loses the corner.
Charles This technique has some virtue for White in joseki where White already has a stone at p or q, leading to a difficult fight. But White can't gain here. Black 3 at a means White lives small in the corner, in gote.
Charles From the point of view of technique, White should omit the play at a and just play 4 here. Then Black 5: sometimes it is correct for Black to play at a, with then White b, Black 5 and White is left with a cutting point. But in general Black won't know whether the follow-up here would be a, b or something else.