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The L Group Is Dead
Difficulty: Advanced
Keywords: Proverb, Life & Death
The black shape in this corner is called the L-group. The proverb says that this shape is dead even if black plays first.
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.
The other 1-2 point is even easier to refute. White 2 is the vital point of the bulky five.
Black 1 also seems a valid attempt, but with the vital point of 2, followed by the hane at 4, white kills black again.
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.
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.
White can kill by playing hane at 1. This reduces the shape to the standard L-group, which we already know is dead.
If the leg is on the other side, again the position depends on sente. Black 1 is one method to live, the hane at A is one method to kill.
If the L-group has two legs, it is unconditionally alive. Here we see one white attempt fail. You can search out some other variations for yourself.
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.
Referring to this position in her book on the endgame, Tomoko Ogawa 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'.
--Andre Engels (2D Europe) This is a copy of the living page "The L Group Is Dead" at Sensei's Library. (C) the Authors, published under the OpenContent License V1.0. |