BQM 7 / A Suitable Case For Treatment

Sub-page of BQM7
How should Black invade the White framework?

This position is from BQM7.

It's Black to play, somewhere inside White's framework. This is an extreme case, with just about half the board in White's hands, as far as we can tell.

What, if anything, can framework theory do for us here?

The prior discussion is all about the area around White's enclosure (marked stones). Why assume this is the correct direction of play? White has a very thick wall above, on the left side. Suppose one tries to stay away from thickness, as the proverb suggests.

A fresh start comes from looking again at where Black might live.

Where can Black live in the White framework?

Black could try to develop a group in any of the areas suggested by the letters a, b, ..., f. (From the virtual groups point of view, we want to consider the fates of all six virtual groups.)

Now from experience we know for example that an invasion at b fails (invading an enclosure), while an invasion at e lives. We aren't so sure of a, c, d, f: playing in these areas will create a weak group.

The first point, though, is that Black cannot make all six groups live. White must be allowed some territory. Also Black is trying to win, not just to play a type of greedy go.

How many groups can Black make live here?

Actually, making two groups live would probably do Black very well. It would certainly do Black credit. White would probably then have to rely on points in the centre. Black might do as well there as White.

Which two groups? Now we get to a really good question. Black can live in the lower right corner. In sente or in gote? Can't answer that absolutely, but the standard 3-3 invasion would end in sente for Black.

One possible way for Black to make two groups live is to invade the lower right at e, therefore; to end in sente; and then to live once more.

Which other place to live? Now we are getting down to it. Living at e does bad things to chances of living at d or f. It looks like life at c, to avoid the thickness on the left side already mentioned.

Sample treatment

Put in place the 3-3 invasion sequence lower right. Then is the technique to get stones in place in the direction of c, making the most of the aji near b. Black's new group on the lower side is hard to kill.

White gets some territory and thickness this way, but the left side is close to Overconcentrated shape. Positions like these aren't easy to count - who will get the point p/q later, and how will it affect the score?

But isn't Black doing well enough here?

Another possibility