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Aliases (info)
TheLGroupIsDead

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LifeAndDeath

Referenced by
TFG7Solution
KanazawaProblem71
TsumegoFromGames6
KanazawaHint80
BQM50

 

L-Group
Path: LifeAndDeath   · Prev: Seki   · Next: TheLongLGroup
   

1. The basic shape: the L-group

[Diagram]
Diag.: The L-group

The black shape in this corner is called the L-group. This shape is dead even if black plays first. The proverb says: The L-group is dead.


[Diagram]
Diag.: Attempt 1

The 1-2 point of black 1 looks like a good option to start with, but after white 6, it is clear that black can get only one eye.


[Diagram]
Diag.: Attempt 2

The other 1-2 point is even easier to refute. White 2 is the vital point of the bulky five.


[Diagram]
Diag.: Attempt 3

Black 1 also seems a valid attempt, but with the vital point of 2, followed by the hane at 4, white kills black again.


[Diagram]
Diag.: Attempt 4

Black 1 tries to make the eyespace as large as possible, but it is not large enough. After white 6, the position may at first sight look like a seki, but closer inspection shows that black is again dead.



2. The L+1-groups: L-groups with a "leg"

[Diagram]
Diag.: first L+1

If there is a 'leg' added to the L-group, it lives or dies according to sente. Black can live by playing on the 1-2 point as shown.


[Diagram]
Diag.: Black lives

[Diagram]
Diag.: White kills

White can kill by playing hane at 1. This reduces the shape to the standard L-group, which we already know is dead.


[Diagram]
Diag.: Second L+1

If the leg is on the other side, again the position depends on sente. Now the 2-2 point is the vital point for Black.


[Diagram]
Diag.: Black lives

[Diagram]
Diag.: White kills

Again, reducing Black to a basic L-group by a hane, kills the corner.



3. The L+2-group: a leg on both sides

[Diagram]
Diag.: L+2

If the L-group has two legs, it 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.


3.1. Defense against a hane

[Diagram]
Diag.: 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.


[Diagram]
Diag.: 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).


[Diagram]
Diag.: 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.


[Diagram]
Diag.: Second hane: failure

Answering this hane at 1-2 leads to disaster. Black can't play 8 at 'a' due of shortage of liberties. If Black 6 at 'a', White 7 at 6 kills: see rectangular six in the corner.


3.2. Attacks from within

[Diagram]
Diag.: Attack at 1-2

[Diagram]
Diag.: Attack at other 1-2

[Diagram]
Diag.: Attack at 1-3

'a' and 'b' become miai


[Diagram]
Diag.: Attack at 2-2

'a' and 'b' become miai


3.3 An extra stone

In many of the variations above, Black suffers from shortage of liberties as soon as one of the circled points is filled by White.

[Diagram]
Diag.: L+2



4. Applications

[Diagram]
Diag.: less than L

Knowing the L-group, its status and the way in which it is killed, can be very useful to speed up your calculations of life and death in the corner. Several positions can be solved by realizing that they are somehow 'like an L-group'. We used this strategy above to show that the L+1 groups are killed by a hane without needing further calculations, it can also be used for groups like this one: The shape that would be made if white plays 1 here, is even less than an L-group plus one move, and so black can be certain that he will be able to kill white after white plays at 1.

Here is another example of how knowing the basic shapes can spectacularly increase the speed and accuracy of your analysis.


[Diagram]
Diag.: Ogawa's analysis

Referring to this position in her book on the endgame, Ogawa Tomoko wrote on page 18: "The time had come to capture at 1. In terms of the left edge alone, this move was worth sixteen points. It gave White additional profit on the upper edge by making White 'a' sente."

For somebody who doesn't know the L group, it would take a fair amount of time to consider the various follow-up moves in this area to the endgame capture at 1. However with the knowledge of this basic shape readily available in your head, this is a 5 second analysis. White 1 takes away an option for the black corner group by capturing on the left side. What's left in the corner would be a dead L group if White had both 'a' and 'b'. This means that White 'a' is sente, as Black must answer at 'b'.



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Path: LifeAndDeath   · Prev: Seki   · Next: TheLongLGroup
This is a copy of the living page "L-Group" at Sensei's Library.
(C) the Authors, published under the OpenContent License V1.0.