Fernobob:I've heard people say that this base for black isn't enough to be settled, but what's a good way to attack or defend it? In my experience a doesn't really work, and I can't see anything else that might. Maybe given how strong white is here, he could just wall black in and he wouldn't have enough space, but what if white isn't quite as strong, or maybe is strong in other directions?
BobWhoosta: In the original diagram I'm pretty sure that white can kill given another move, but white is so overconcentrated it's almost silly to look at. The second diagram is more interesting, and also more realistic imo. I'll take a look at it.
The first thing to see is that a move at a is probably wrong. First, white should seal black in with a move at b. This is either sente, or black is already dead. IF he can live, he will perfect white on the outside with all the forcing moves as he thrashes around to live. But this might not be your point. I think your question is really: How do I stab out a base for the two space extension?? If I'm right on this, we go back to the original diagram:
This is a very simple sequence you should know. There are others, but the idea is the placement at makes miai of and , and also leaves a difficult cut at a. So when black plays and white plays , black is suddenly wondering about how he can keep connected. This is a sequence to play if you want a running group into the middle (in a general game position, here this should totally kill).
Now, there are other ways to attack the two space extension that depend on surrounding situations. Usually when you are attacking stones you are actually forcing them into life, so you need to understand that the idea is to profit from the forcing moves, as it is very difficult to actually kill a group in go. After all, he only needs two eyes, and you need to prevent ALL possibilities of two eyes WHILE surrounding and preventing escape AND protecting your own groups from being cut and killed. That's a lot easier of a task for the defending side.
So, let's look at this two space extension again, only in a generic position.
In general, a is used to stab out the base, and create a running group to attack. This will usually only be good if you have stones on BOTH sides of the group, as otherwise you play low and white will just take another base when he gets the opportunity. The attack will be profitable if black can get a few forcing moves to complete something in the center, otherwise it's best to leave it.
b is a special purpose move, and will almost always force white into life. If you have HEAVY support on the sides, it will stab out the base, and is a more forceful attack than a, but most often it is used to strengthen one side or the other in exchange for settling the white group. In other words, b almost always results in some kind of trade.
c is most often the best direction to attack the stones from, but the least used by players all the way up to SDK!! It builds influence in the center, and forces the black stones low. A lot of times the first move is a peep, and the followup attaches like this:
Play can get complicated from here depending on what both sides want, but the kikashi of and can often be very valuable.
It seems nobody has yet gone into defending.
First, when it is possible, the best defense is to extend along the side, at a or b. In the remainder I will be assuming that this is impossible because there are white stones at the b points or thereabouts.
The standard defense is to jump towards the center, most usually with a one-point jump . Note that in this case (where white is stronger on the right), black prefers to jump on the left: If in the future black decides to give up one of the two stones, he'd rather sacrifice the right one than the left one, because it is closer to white's thickness. Also, note that white has a good yosu miru move at a - it threatens to either cut through between the original two stones or between and the stones below it. White will often play a immediately or very soon; however, after black has answered, white may well forsake the cut for the time being, because cutting does tend to strengthen black.
If black wants to live on the side, attaching at is the way to go, but in most cases this is not a good move. If white simply defends, she gets strengthened a lot...
If the white stone would be on the fourth line (which is however much rarer), sliding under it is a good way to stabilize the black group. Now white does not have the possibility to get strengthened as much as in the previous diagrams. - AndreEngels