3-3 invasion variation

I’m a noob, looking for some advice. I recently played Bergamot and it cut like this


What’s the best response to this? I don’t see that sequence in the sesei library joseki page. I extended to L7, but I’m wondering if K7 would have been better.

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I’m not sure, but I don’t know if the tactic applies to 13x13, the influence would be much smaller imho.

Here’s the sequence from the OGS joseki explorer:

You played the correct first move, then your opponent deviated again, which is perfectly ok. The only difference I’d make is to follow-up with a hane or one-point jump rather than extending, which feels slow. It’s hard to predict how things go after that because the fight is complicated.

I think it’s a bit late to ask yourself this question only after black cut.
Black’s cut is supported by their stone at K10, so I think that was a sharp move by black.

A bit earlier, I’m a bit doubtful if move 8 extending at K5 was white’s best choice. White is making a wall, but what is white hoping to get out of that when black already has a stone at D4? I think it’s not easy to convert a wall to profit on a smaller board like 13x13.

So instead of that extension to K5, I’d probably have been more interested in playing for territory with the double hane, aiming to take the corner territory with this joseki: Play Go at online-go.com! | OGS

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Back to this question,

Certainly not. Generally, after a crosscut, atari is bad because it creates too many cutting points. Extending is almost always better.

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