Puzzle collection to practice killing the L group

[antonTobi]

This arrangement of white stones is called “the L group”:

It comes up a lot in games, so it is quite useful to know that it can be killed even if white plays first!

Here is a collection of 10 puzzles I created to help you practice killing this shape:

Click here to go to the puzzles

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Let me know in this thread if you have further questions about any of the problems or variations!

[benjito]

What a nice collection! I found the “play away” variations particularly helpful, since I don’t usually think about what move make the L group alive again.

[shinuito]

It looks pretty nice, I didn’t spot anything with the variations or the comments.

Of course the last puzzle lacked emojis

[antonTobi]

You’ll notice I almost ran out of symbols on that last screen, good to know I can resort to emoji next time!

(although the fact that they are probably not displayed consistently for everybody makes them a bit less attractive)

[shinuito]

The emojis were more for a bit of fun anyway the emoji version in case it shows wildly different or worse not at all!

It was more just custom labels in case you do run out. That is shift+click with the letters tool selected, and then add whichever letter, number, symbol etc.

[benjito]

@shinuito

The emojis were more for a bit of fun anyway the emoji version in case it shows wildly different or worse not at all!

I think this might be private?

[shinuito]

Good point. I forgot to hit the save button after unchecking the box

[antonTobi]

I think this emoji style looks even nicer on the board actually

Image

[yebellz]

@antonTobi

A trick for remembering the killing miai pairs

• creates a bulky five and its vital point
• creates a bulky five and its vital point
• descent one side, hane on the other
• hanes or playing in the “corners” don’t help

[shinuito]

Yeah I have to agree that that one does look better

[antonTobi]

I included the final summary diagram because I think it’s quite neat how the refutations come in pairs (and of course this is not a coincidence, it’s because white playing at both points of any of the pairs would create a living shape)

For reference, here is the original one with shapes instead of emoji

That said, memorizing this image is probably not the best way to learn the shape! Instead, once you’ve played out all the variations and internalized them, the right moves will just be instinctive (and this instinct will also help you in similar but not identical shapes).

Also, there are often multiple ways to kill, and you have to pick the right one for the situation.

In the position below, A is perhaps the most obvious way to kill since it reduces the shape to the well-known bulky-five. But actually B is usually the correct move!

Exercise for the reader: Why is B better than A?

[Feijoa]

@antonTobi

Exercise for the reader: Why is B better than A?

I can’t figure it out.

Some attempts

We are looking for a general reason to prefer the surprising 2-1 move B over hane A.

• Number of follow-up ko threats - 2 in both cases:

  
  

• Aji that might be useful in connection to outside fighting - after the extra moves above, B lets the white stones get closer to the outside. So it seems worse from that perspective.

• What happens when the outside liberties get filled - B looks like it has a very slight advantage in that Black can ignore the first threat and by White and still get to ko? But why would the liberties get filled if there is not some aji to defend against?

[Uberdude]

A means white gets a ko liberty which can be annoying if you have to actually capture in a semeai.

[Feijoa]

Oh, I see.

And even with infinite ko threats, it looks like it takes more moves to actually capture? I made a puzzle to test: L-group descent on short side, capturing race.

[antonTobi]

Indeed, B is better for liberties than A.

In this position, black needs 5 more moves to capture (6 moves in total including the first one):

White answering locally can not gain more liberties (in fact I believe all white’s responses reduce white’s liberties).

Now let’s compare with when black captures this way:

Let’s disregard the ko liberty and assume that black gets to make this exchange for free:

How many moves will it take black to capture now? Try counting yourself first before checking the answer below!

Answer

White has more liberties than it may first appear because she has a big eye.

https://senseis.xmp.net/?BigEyeLiberties

A089071 on OEIS

If we already know from the above links that the bulky five-shape has 8 liberties, we can count the liberties in this case as follows:
8 liberties (from the big eye) - 1 liberty (for the stone that black already played inside) + 1 liberty (on the outside)

If we want to recount ourselves from first principles, we play out the capturing sequence but counting only moves that white does not respond to.

Thus we count these first 3 moves, but not the next one where black puts white into atari:

Continuing:

Now white is reduced to a small eye, so she no longer gains liberties by capturing: If white does not respond here, black needs one more move, for 8 moves total. If white does respond, we should not count move 7 as a move that black had to spend (since he got it in sente). Then there are two moves remaining in the resulting shape:

For a total of 6+2=8 moves.

Conclusion: even disregarding the ko liberty, the difference between A and B is 2 whole liberties!

[antonTobi]

There are a couple mistakes in the variations (capturing races is a complicated business!).

In this position, white can play J5 or D9 to save the corner group:

And in fact, if white responds here:

Then white wins the capturing race because of eye vs no eye.

So the problem needs to be modified to give black more liberties on the outside.

[Feijoa]

Thanks, maybe I got it right now:

@antonTobi

Let’s disregard the ko liberty

And in my new setup, White still wins without fighting the ko, so I guess that ko becomes relevant only with a few more external liberties?