L+2 group

Keywords: Life & Death

The L+2 group is an L group with a leg on both sides.

L+2 group

The L+2 group is alive. The corner territory can be reasonably counted as 6 points. We will have a look at: the defense against the hane from either side; how to deflect attacks from within; and the status of this group when White has a stone on either of the marked points.

1. Defence against a hane

First hane

Against the hane from the short side, one should defend at the 1-2 point. Now there are two sure eyes at the circled points.

First hane: failure

Answering at the 2-2 point leads to seki - or to ko if that is what Black really wants (see bent four in the corner).

Second hane

Against the hane from the long side, one should defend at the 2-2 point. Now there are two sure eyes at the circled points.

Lives, but...

Suppose the marked stone is added. Now is sente. If was played at a then the addition of white stones at and b would not be sente at all.

When Black ignores the sente move

Black cannot play at a to secure the second eye.

When Black ignores the sente move

One eye to none, White wins the capturing race.

2. Attacks from within

Attack at 1-2
Attack at other 1-2
Attack at 1-3

Here a and b become miai.

Attack at 2-2

Here a and b become miai.

3. An extra stone

If white has the descent marked by the circle in the diagram, the L+2 group is no longer unconditionally alive. However, a white descent at the point marked by a square in the diagram does not affect the status of the group.

L+2 group

4. Weak leg

L+2 group with a weak leg

If Black has a weak leg, White can kill with a rogue ko (in this case, also a two-stage ko).

White makes a rogue ko

Black cannot play atari at a because of a shortage of liberties.

5. Weak leg (2)

L+2 group with a weak leg

In this shape, white can make ko fight with White a.

L+2 group with a weak leg

and is best response of black.

Follow up (1) after W's attack.
Follow up (2) after W's attack.

This is the ko fight.

Tapir: Forcing with , , before fighting the Ko, is a waste of internal ko threats.

^Tapir is erroneous and should not write comments so confidently lest he not only make himself look like a fool, but worse, miseducate others. It does NOT waste Ko threats. In fact, you can't even start the Ko without playing ,,. Either of the immediate ataris are a lot worse. If doubt remains on the matter, this has been played in pro games multiple times. (Someone stronger than Tapir)

tapir: Please be so nice and simply correct, best with explanation, and move on next time. It is a wiki, after all. My thought process probably was: Black can fight a ko in the corner already after , threat, answer, recaptures the corner stone.

The ko I saw: threat, answer

I see now that this ko is not worth fighting for, but this needs explaining. (Fighting the approach ko is better for Black than fighting a direct ko over the corner stone.)

After Black 1...

Above shape can be made by black's probing move - , in real games.

After Black 1...

Andy: Why make the / exchange? Wouldn't it be usual to play at with tripod or sabaki options instead?

unkx80: This is common as well. When to play and when to play directly at is difficult to answer.

After Black 1...

unkx80: In this result, Black gets slightly less and White has sente. Which is better for Black?

tapir: It is white's choice isn't it. If Black plays before , I've seen White changing directions and taking the corner. (in professional games)