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I just tried a fight that ended up this:

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Can the black stones be killed? It's whites move.

First, let's assume that white's chain is safe and look at it as tsumego. I tried several sequences but it seems that black is dead:

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Second, is this fight naive or realistic? I was just trying to cope with black invasion stone at F3 and tried to seal it. Maybe there is a better approach how to treat it? Let him live peacefully and just build wall on the 4th line?

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    In the second to last picture, 7 should be either at 9 or at C3. Once black gets 15, there is absolutely no way to kill it - however, the shown sequence is not correct in several places. For instance, 19 should definitely be at 20, and black can very easily live with 21 at M2, even though he has even better ways. – mafu Jan 29 '15 at 11:15
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    I know there is a book which explains this sort of situation, but I just can't remember which one it was. It also covered why 7 is a mistake (a classic - everyone made it at one point in their Go career, I bet). – mafu Jan 29 '15 at 11:20
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In general, this kind of fight is going to get you into trouble - you have a bunch of separate groups to take care of. If your strategy before Black's invasion was sound, then you should be able to get a useful wall out of the invasion. In that case, it's generally better to just keep extending along the fourth line. So, instead of 20, I would just extend. Black gets two points/move, and you're getting thickness that's worth more.

In the first diagram, if 39 is at 40, then isn't Black alive?

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    "if 39 is at 40, then isn't Black alive?" looks correct to me also. – Forget I was ever here Jan 28 '15 at 23:00
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Black is just hardly alive, as you can see from this diagram:


$$Wm30
$$ |...OOXXXXXXOO......|
$$ |....12.6.435.......|
$$ |...................|
$$ -------------------
$$

Now white can play a big point elsewhere. White's position to the outer side look solid.

When white comes back in the endgame, the result may look like


$$Wm36
$$ |...OOXXXXXXOO......|
$$ |....OX.X.XOO.......|
$$ |.....21534.........|
$$ --------------------
$$

and black lives in a seki with 0 points of area.

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