L-group

  Difficulty: Advanced   Keywords: Life & Death, Proverb

Japanese: カギ型 (kagi gata)

Table of contents

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  

B1 here is killed by the placement at W2. Note that the result is a bulky five dead shape minus a stone at circle.

[Diagram]
Attempt 2  

If B1 occupies one of the 1-2 points, then W2 occupies the vital point of the bulky five.

[Diagram]
Attempt 3  

The other 1-2 point of B1 looks like a good option to start with, but after W4, B5 and W6 the white stones form a three in a row and so Black has only one eye.

If Black plays B5 at W6, White will play W6 at B5. Again Black has only one eye.

[Diagram]
Attempt 3 Continued  

White can capture the group with W5 after W1 and W3. It is a grave mistake to play W5 before the black group is in atari. But as long as the surrounding group is not threatened these moves are better left unplayed.

[Diagram]
Attempt 4  

B1 also seems a valid attempt, but with the vital point of W2, followed by the hane at W4, White kills Black again.

[Diagram]
Attempt 5  

If B1 makes a descent to enlarge his eyespace as large as possible, then the hane W2 can reduce the eyespace to a bulky five.

[Diagram]
Attempt 6  

If Black expands his eyespace from the other side, White's hane at W2 turns it into a bulky five at best, and W4 hits the vital point.

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

Q: Really? What about black's attempt 4 above?

A: See next diagram

[Diagram]
Attempt 4  

Herman: Although with the presence of the marked stones, B5 captures W4, this only results in a false eye. If black tries B5 at W6 instead, white will extend with W6 at B5, and black's eye will be false.


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 W1 here, is even less than an L group with one extra move at the marked stone, and so Black can be certain that he will be able to kill White after White plays at W1. For another example, take a look at the OD1P - Oct 16 Problem.

this looks much more like a tripod group that has been blocked on both sides, than a kind of L-group. the next example seems clearer

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 W1. 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 W1. However with the knowledge of this basic shape readily available in your head, this is a 5 second analysis. W1 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.


The L-group in capturing races

[Diagram]
Maximizing liberties  

Should the L-group get involved in a capturing race, B1 and B3 is a well-known method of maximizing the liberties of the L-group itself. After B5, the L-group has eight liberties (seven from the bulky five and one from the circle point).

[Diagram]
Minimizing liberties  

Conversely, if White is to minimize the liberties of the L-group, W1 and W3 are standard tesuji moves, making miai of a and b. (If B2 is played at a, then W3 plays at B2, and Black has surprisingly few liberties.)


Related shapes



L-group last edited by 90.227.230.134 on May 24, 2012 - 11:51
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