L+1 group
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.
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First L+1 group
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.
Other possible defenses end up in ko or seki, depending on black's choice, as the next two diagrams show.
White can kill by playing hane at . This reduces the shape to the standard L group, which we already know is dead.
What happens if White plays on Blacks vital point? (Just thinking about "Your opponent's good move is your good move" does that apply here as well? I think Black is dead as well but am i correct?
First L+1 group, hane on one side
The throw-in at no longer works:
jumps and lives. If
makes a placement,
connects, and White cannot connect at a due to shortage of liberties, otherwise Black captures three to make an eye.
However, White can kill by the hane at followed by the placement at
.
tries to live, but
forces
, so
makes a throw in and kills. Note the importance of the
stone.
First L+1 group, hane on both sides
PJT: To Do: Clean this section up
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 this lesson in her Internet Go School, the attacker has these options:
- a ten-thousand year ko in gote:
a,
b,
c, … in problems
17 (defence) &
20 (attack);
- a sente seki:
a,
b,
d,
e, … in problems
18 (defence) &
19 (attack);
- a double ko:
f,
g,
e,
d, … in the lecture from 15:51 and problem
16 (defence).
The best moves by both players lead to a ten-thousand year ko.
IronChefSakai: I'm a bit confused, if the best moves by both players leads to a ten-thousand year ko, but the multi-step ko for White is better for Black, then how are these moves actually the best moves for Black?
Herman: The line below was added by some anonymous editor years ago, but looks like nonsense to me. The throw-in in the second diagram is bad. If white just takes an external liberty immediately (at
in that diagram) the end result seems to be a direct ko which white takes first, worse than the ten-thousand year ko.
zlh: Nope. The throw-in is a good move. Otherwise b can connect there to make a seki.
Black can also get a multi step ko (for white) sequence, which should be better than ten-thousand year ko.
Black can get rid of ko threats before continuing. If white wants to continue, he must play yet another ko to force the atari.
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
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
Second L+1-group, hane one side
The throw-in at doesn't work anymore. Black lives with
: White can not connect at a because Black can capture three to make an eye.
To kill, can go straight to the 2-2 point. After
, 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
Second L+1 group, weak leg
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.
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.
fractic: Black lives like this. However is inferior to the other 1-2 point. After
white can play hane at
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
is worse pointwise. Also White playing at
threatens ko but there are no such sente moves with the other 1-2 point.
fractic: This ko is what happens if Black ignores the descent of . So all in all
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: