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TheLGroupIsDead

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Referenced by
EyeDefinitionDisc...
L1Group
TheEmptyTriangleI...
L2Group
LongLGroup
GuineaPigsFeedback
AddingPagesDiscus...
KanazawaSolutionSix
JGroups
33PointWhenDoesIt...
KanazawaProblem38
BQM56
KanazawaProblem71
KanazawaSolution79
KanazawaHint80
KanazawaSolution80
TsumegoFromGames6
BQM50
MetaDiscussion2001
Oct16Solution

 

L-group
Path: LifeAndDeath   · Prev: Seki   · Next: L1Group
  Difficulty: Advanced   Keywords: Life & Death, Proverb

1. The basic shape: the L-group

[Diagram]
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]
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]
Attempt 2

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


[Diagram]
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]
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. See Rectangular Six In The Corner.


[Diagram]
Attempt 5

If Black expands his eyespace from the other side, White's hane at 2 turns it into a bulky five at best, and White 4 hits the vital point.


[Diagram]
Hanes and outside liberties

Note that no combination of edge hanes and outside liberties help Black. The same sequences given above still work for White.



2. Related shapes


3. Applications

[Diagram]
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 on the L+1 Group page 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. For another example, take a look at the Oct 16 problem.

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


[Diagram]
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.



Dansc: I was once told that this shouldn't be called an 'L group' but a certain comb formation. The term 'L group' supposedly actually refers to a bent four shape. What's the 'official' name of this group?

Dieter: It's called L-group in Davies' work. Since that work has been the first source for Western knowledge of life and death, everybody calls it that way.


Authors



Path: LifeAndDeath   · Prev: Seki   · Next: L1Group
This is a copy of the living page "L-group" at Sensei's Library.
(OC) 2003 the Authors, published under the OpenContent License V1.0.