1. Black's connection
First of all, Black has to decide whether to connect or not. For details, please read endgame connect or not.
Isn't it a mistake to play if you're not going to connect? ~srn347
anonymous: As in many cases it depends on the rest of the board. If were a ko threat and the value of the ko is smaller than potential the damage to Black from not connecting but larger than the damage to White from not playing , then Black might not connect.
If he decides to connect, there are basically three ways for Black to do so: a, b, and c.
2. White's shape
When White has two stones on the second line, covered by black stones on the third as here, the hane tsugi is not possible because of Black's atari at . This situation is considered to be Black's endgame sente.
With three stones, there are some problems. An attempt by white to hane-tsugi may be met by a throw-in (a liberty stealing tesuji) where white expects to play . The ko that results if white does not connect with does not help white. Therefore at is often correct (a case of One-Two-Three).
3. Black's shape
Black should stretch once, then block.
With present, Black has another weakness to be careful of. If he blocks at , is severe. If Black captures at a, White b will at least capture two stones and destroy black's defence line. If Black b, White c is more than White could expect to begin with.
Here too, Black should cede a little territory. The empty triangle of is best when there is no eye shape at stake:
If Black plays in fear of bad shape, he loses two more points compared to the previous diagram.
4. Avoid Ko
A: It is because of ko.
Bleedo:This is a ko to always avoid since black can always extend 2 as a ko threat.
Alex: Always to avoid for who? Yeah, Black can extend from the atari as a ko threat, sure, but just because he has a local threat doesn't make the ko good for him. This is hanami ko for White, so it's Black who should avoid it, unless he's got way more threats than White. It only costs two points to back down, and a lot more if Black loses.
fractic: Also, if Black extends from 2 the ko becomes bigger and that will make it easier for white to profit from, since Black will need bigger ko-threaths.
If the ko is serious to you, or you know you are a ko loser, don't atari! Although this costs you 2 points, do you feel it is much better if you let W invade your territory (when you lose the ko)? :-)