I have to disagree with Bill's bump. Whilst it can enable you to defend the territory on both sides (but not the corners), it is a vulgar bad-style move that unnecessarily strengthens your opponent and one I have learnt to eliminate from my intuition.
To the original question, the knight's move to one side is the standard answer. Which side is better obviously depends on the rest of the board. A common strategy for black in the 2 4-4s and 3-10 shape (I'm ignoring q7 and d9 for now) is to cap, and then if white answers with a knight's move to one side you invade the 3-3 on the side he answered. The thinking here is "Which side do you want points?", "Oh that one, ok I'll take them away at 3-3". If white then plays out a standard 3-3 invasion joseki the cap for knight's move ends up as an excellent exchange for black as white is overconcentrated. Imagine black played 3-3 first and then capped, white would of course not defend to the left as he is already very strong there.
- Click Here To Show Diagram Code
[go]$$Bc
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 8 . . . . . . . . . . . . . . . . |
$$ | . 7 6 . . . . . . . . . . . . . . . . |
$$ | . 5 4 . . . . . . B . . . . . . . . . |
$$ | . . 3 O . . . W . , . . . . . O . . . |
$$ | . . 1 2 . b . . . O . . . . . . . . . |
$$ | . . a 9 0 . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Xai, you say black's 3 was the move that you didn't know how to answer? What did you expect? If l3 that is good as it's the normal move. When faced with an unexpected move the thought process I suggest is: "What did I expect, and how is his move different?". Another very good idea with unexpected moves is to consider tenuki. A good move elsewhere is unlikely to be that bad (unless the local situation is urgent) So here l3 would have taken a liberty from your k3 stone so you want to answer. But m4 didn't take a liberty so it is much easier for you to ignore.
Cutting at m5 is a plausible suggestion. The shape peep at m6 feels like an overplay to me. But the points that really scream out to me in this position are the 3-3 points: as black my aim would be to live in the corners, quite possibly in sente (obviously white can try some other variation to make it gote) and then so long as the cap doesn't die white has not much territory. So I want to play here (or maybe c4):
- Click Here To Show Diagram Code
[go]$$Bc Corners are key!
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$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . 1 . . . . . . . . . |
$$ | . . . O . . . 2 . , . 3 . . . O . . . |
$$ | . . . 4 . . . . . O . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
The reason I think this corner is more important than the right one is should black invade at c3 the h4 stones ends up overconcentrated. If black then invades the other 3-3 it makes white thick which makes an attack on the capping stones much more powerful (EDIT: but actually if black can 3-3 in sente and then help the centre group maybe white is a bit sad, so I think Bill's q3 suggestion is good too, even though c3 then makes me sad - white can't have everything). And if black attaches at q3 white could play like below and laugh all the way to the bank. White could also consider hane on the outside (r3 at p3) to separate the capping stones and let black live in the corner and then attack the capping stones, but I am unsure of the profit that way. This way is obvious profit.
- Click Here To Show Diagram Code
[go]$$Bc $$$$$$$$$
$$ ---------------------------------------
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$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . X 9 . . . . 6 . . . |
$$ | . . . O . . . O . 8 . X . . 5 O . . . |
$$ | . . . O . . . . . O 7 . . . 3 1 2 . . |
$$ | . . . . . . . . . . . . . . . . 4 . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Here is a nice pro example of ignoring the cap. As white has an extra knight's move on both corners he tenukis to another good point, and is ready to fight when black follows up on his cap with an attachment.
http://gogameguru.com/commentary-kim-ji ... -card-cup/