L+1 group

  Difficulty: Intermediate   Keywords: Life & Death

An L+1 group is an L group with a leg. The leg can be at the short side or the long side of the L shape. In both cases the group lives or dies according to who plays first.

Table of contents

First L+1 group

[Diagram]
First L+1 group  

The first L+1 group lives or dies according to who plays first.


Living

[Diagram]
Black lives  

Black should live by playing on the 1-2 point as shown.

[Diagram]
Black also lives, but white's got better prospects  

Black could also live by playing at the 2-1 point, but white could then close at a in sente. Plus, if white needed to play b, this would be sente as it threatens to turn the corner into a ko.

[Diagram]
Seki. Black can play 'a' to get a ko.  

Other possible defenses end up in ko or seki, depending on black's choice, as the next two diagrams show.

[Diagram]
Same result.  

White 2 is the only move. White 2 at the vital point fails to Black 2 at 4.


Killing

[Diagram]
White kills 1  

White can kill by playing hane at W1. This reduces the shape to the standard L group, which we already know is dead.

[Diagram]
White kills 2  

W1 also kills. After W3, a and b are miai. However, Black may try B2 at b, W3 at B2 and now B4 at c is a concrete threat (it is just a ko in the above diagram). In life and death situations in general, attacks from outside should be considered first, inside plays last.

[Diagram]
White kills 3  

What happens if White plays on Black's vital point? "Your opponent's good move is your good move" does apply here as well? Yes, white still can kill. After W7, it is a Bent four in the corner. But this method is generally inferior because if White's outside wall have lost eyes, he must start the ko in the corner.


First L+1 group, hane on one side

[Diagram]
First L+1 group, hane on one side  

The extra hane gives a sense of security.

[Diagram]
White cannot kill this way  

The throw-in at W1 no longer works: B2 jumps and lives. If W3 makes a placement, B4 connects, and White cannot connect at a due to shortage of liberties, otherwise Black captures three to make an eye.

[Diagram]
White kills  

However, White can kill by the hane at W1 followed by the placement at W3. B4 tries to live, but W5 forces B6, so W7 makes a throw in and kills. Note the importance of the white+circle stone.


First L+1 group, hane on both sides

[Diagram]
First L+1 group, hane on both sides  

The first L+1 group with hane on both sides is alive if it has an external liberty. However, when the group has no external liberties, White can turn it into a ten-thousand year ko.

Patrick Traill: According to Guo Juan in [ext] this lesson in her Internet Go School, the attacker has these options:

[Diagram]
Main line  

The key tesuji here is W3.

[Diagram]
Main line  

This sequence leads to a ten-thousand year ko, however white can do better by getting a multi-step ko as shown below.

[Diagram]
Main line  

Black can also get a multi step ko (for white) sequence, which should be better than ten-thousand year ko.

[Diagram]
Main line  

White must first win this ko in the corner...

[Diagram]
Main line  

Black can get rid of ko threats before continuing. If white wants to continue, he must play yet another ko to force the atari.

[Diagram]
Main line  

Only now does the real ko for the life of the corner start. Black usually should be able to win this or receive ample compensation elsewhere in the steps white took.


Second L+1 group

[Diagram]
Second L+1 group  

If the leg is on the other side, again the position depends on who plays first.


Living

[Diagram]
Black lives  

Now the 2-2 point is the vital point for Black.

[Diagram]
Black also lives, but smaller  

As for the first L+1 group, black could live like this, but then one of the two yose moves would be sente for white.


Killing

[Diagram]
White kills  

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


Second L+1-group, hane one side

[Diagram]
Second L+1-group, hane one side  

The hane at black+circle may seem to give some help in living.

[Diagram]
White cannot kill this way  

The throw-in at W1 doesn't work anymore. Black lives with B2: White can not connect at a because Black can capture three to make an eye.

[Diagram]
White kills  

To kill, W1 can go straight to the 2-2 point. After W7, Black is dead. See the addendum of the rectangular six in the corner page. Study: Would the marked White stone still be needed if the Black hane was at the top?


Second L+1-group, hane on both sides

[Diagram]
Problem  

The two hane stones give some degree of security.

[Diagram]
Solution  

The attachment at W1 leads to ko.


Second L+1 group, weak leg

[Diagram]
Second L+1 group  

The second L+1 group with a weak leg is also unsettled. White can kill at a or Black can live by playing at a.


[Diagram]
Defend here ?  

Timm (10k) Isn't this unconditionally alive ? I can't kill it. And if it's alive, is it inferior to 'a' ?
Andy W plays at a. The points b are then miai to kill.

fractic: That's not correct Andy.

[Diagram]
a doesn't kill  

fractic: Black lives like this. However B1 is inferior to the other 1-2 point. After B1 white can play hane at B5 in sente reducing Black's territory to at most 4 points. Whereas with the other 1-2 point White needs to play 2 gote hanes to reduce Black to 4 points. So B1 is worse pointwise. Also White playing at circle threatens ko but there are no such sente moves with the other 1-2 point.

[Diagram]
Sente decent (B3 tenuki)  

fractic: This ko is what happens if Black ignores the descent of W2. So all in all B1 does live but it has two downsides.


Timm: Thanks for the explanations ! I am still unconfident reading these subtle issues. I've seen it now ! I've added the diagram along with the reason why it's incorrect.


See also:


L+1 group last edited by hnishy on November 30, 2022 - 23:40
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