3-4 point high approach low extension
This is a Kitani joseki from the 1940s - though not exclusive to him. Black aims to make a very solid stone.
Up to is standard. In this case leaves no weakness behind (compare with the case of at a). This is a tight way to play.
Unusually Black can also play inside, as here. In this main line, played in 2001 in a number of pro games, Black takes a larger corner but White is thicker.
Bill: The principle does not count the stone on the second line. The principle is based upon whether an unsupported invasion can escape or live. So the usual extension is to . (With an extension to a I think that an unsupported invasion can live in gote, at the expense of a huge thickness for White.)
For at b, see BQM186.
antic: Okay, but what if black plays like this? I played a in a game and got a very unsatisfactory result.
Bob McGuigan: The shape in this diagram is crosscut-like and in such a situation it is always useful to ask which of your crosscut stones needs the most help. It seems the white stone on the 3-3 point needs help, so extend its liberties, as does.
Question on the variations resulting when black plays 5 as another hane in the last sequence: BQM186