Hellstroem wrote:
... , but I have tried to get a grip on the 3-3 invasion. This move therefore confuses me a lot. With so many other big points on the board, why would black start a series that can only net him a few points of territory and allow white to build a wall facing an open center?
Black doesn't have much choice but to cut when white double hanes. His only alternative is to just connect (or cut on top first), and live in sente in the corner, but then he would have hardly any territory and white would be strong in both directions.
Black is only playing the 3-3 in the first place because he feels that white doesn't get enough out of it in the end, and that white's wall is not useful enough for him. So this is a natural decision following his original move.
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If we assume that black has a good reason, white's response still confuses me a bit. Wouldn't he welcome this and allow black to follow the standard course, instead of adopting the double-hane approach as he does with move 14? I've tried to rationalize this a couple of ways: either he was hoping to end with sente (which he does, allowing him to play what I thought was an awesome move 22), and/or he was afraid of black cutting later at e4, since black's stone at q16 is a ladder breaker.
The double hane approach is generally geared towards taking the corner after black cuts. White might choose this way if he feels he doesn't need the wall, or that black's small (but strong) group will be misplaced afterwards. This is the normal reason for white to play this way.
In this case, white's choice of atari on top is an unusual choice. As you surmised, this is a way to make white's wall a little bigger in sente. He plays like this because he doesn't mind giving black a little extra territory in return for the chance to attack black's weak group in the top right.
He is not afraid of the E4 cut since, in the normal course of events, it doesn't work for black. The 3-3 joseki allows white to net this stone.