I encountered the large kiema approach to the 4-4 twice in a game today. In response to the slide, I played the marked stone. I know this joseki for the small knight approach, but I can't find anything on it for the large knight. Is this reasonable?

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As I understand it, there are two normal continuations for the small knight approach version. First, white can take the corner:

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Relative to the small kiema version, black gets a bit more influence -- one more stone for the 16-17 rank wall and more usable influence in the top middle (even without the marked stone). White now has the option of extending to A or B, rather than being limited to C or D, and gets an extra point on the 19 rank. Even without the marked stone, neither side seems obviously advantaged.

The second option takes the outside giving black the corner. However, this strategy does not seem to work at all with the large knight's approach.

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This does not seem to work. With the small knight approach variation, white's stone is at C and white plays A, but in this version, it seems that white can be easily split with A. Same with B or C. As a result, this variation seems very good for black. In the game, black tenukied.

L 17 is not joseki, but reasonable in this position. You could also tenuki and play a double approach at C 14.

A few comments. Firstly, you could block at 3-3. With the marked stone being a large rather than small knight's move you make a more efficient territory. For this reason slide is not really a joseki when white made the normal approach and black plays big knight. However here white has the big knight approach so it's different. Does answering the slide at 3-3 seem like a good exchange for white, or black, or even? Hard to say, but white could have invaded at the 3-3 point and lived there, so he lost this opportunity. But also it can be seen as increasing some eyespace for the approach stone in sente before playing an extension/pincer around a.

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There is a shape weakness in the large slide at b above which it seems you are unaware of, and by trying to transfer the normal approach josekis onto it you end up helping white to patch up his thinness and connect stones which aren't yet connected. It's particularly potent with a black stone at l17. White can then live comfortably in the corner so it's not like white has to resign yet, but this is a pretty serious problem. Also white can resist, with 4 at 6 for example.

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$$ | . . . . . . . . . . . . 9 3 5 O 8 . . |
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Thanks! Indeed I had not considered weakness at b. I'll have to investigate that a bit so that I can add it to my tool box.