Semeai result?

jlt · Post by **jlt** » Wed Dec 07, 2022 12:29 pm

Click Here To Show Diagram Code: [go]$$Wc $$ +---------------------------------------+ $$ | . . . . O . . . 5 6 7 . X O X X . . . | $$ | . X X X O O . 4 1 2 3 . . O O X . . . | $$ | . . O X O X O . X X O O O O O X X . . | $$ | . X X O X . O O X O O X X X X O X . . | $$ | X . . O O O X O O X O O X O O O O X . | $$ | X . O . O X X O X X X X X X O O X X . |[/go]

Click Here To Show Diagram Code: [go]$$Wc $$ +---------------------------------------+ $$ | . . . . O . . 8 . X O . X O X X . . . | $$ | . X X X O O . X . X O . . O O X . . . | $$ | . . O X O X O 9 X X O O O O O X X . . | $$ | . X X O X . O O X O O X X X X O X . . | $$ | X . . O O O X O O X O O X O O O O X . | $$ | X . O . O X X O X X X X X X O O X X . |[/go]

Click Here To Show Diagram Code: [go]$$Wc $$ +---------------------------------------+ $$ | . . . . O . . . 4 . 7 . X O X X . . . | $$ | . X X X O O . 6 1 2 3 . . O O X . . . | $$ | . . O X O X O 5 X X O O O O O X X . . | $$ | . X X O X . O O X O O X X X X O X . . | $$ | X . . O O O X O O X O O X O O O O X . | $$ | X . O . O X X O X X X X X X O O X X . |[/go]

dany · Post by **dany** » Wed Dec 07, 2022 12:59 pm

jlt wrote:
$$Wc
$$ +---------------------------------------+
$$ | . . . . O . . . 5 6 7 . X O X X . . . |
$$ | . X X X O O . 4 1 2 3 . . O O X . . . |
$$ | . . O X O X O . X X O O O O O X X . . |
$$ | . X X O X . O O X O O X X X X O X . . |
$$ | X . . O O O X O O X O O X O O O O X . |
$$ | X . O . O X X O X X X X X X O O X X . |
Click Here To Show Diagram Code
[go]$$Wc $$ +---------------------------------------+ $$ | . . . . O . . . 5 6 7 . X O X X . . . | $$ | . X X X O O . 4 1 2 3 . . O O X . . . | $$ | . . O X O X O . X X O O O O O X X . . | $$ | . X X O X . O O X O O X X X X O X . . | $$ | X . . O O O X O O X O O X O O O O X . | $$ | X . O . O X X O X X X X X X O O X X . |[/go]

$$Wc
$$ +---------------------------------------+
$$ | . . . . O . . 8 . X O . X O X X . . . |
$$ | . X X X O O . X . X O . . O O X . . . |
$$ | . . O X O X O 9 X X O O O O O X X . . |
$$ | . X X O X . O O X O O X X X X O X . . |
$$ | X . . O O O X O O X O O X O O O O X . |
$$ | X . O . O X X O X X X X X X O O X X . |
Click Here To Show Diagram Code
[go]$$Wc $$ +---------------------------------------+ $$ | . . . . O . . 8 . X O . X O X X . . . | $$ | . X X X O O . X . X O . . O O X . . . | $$ | . . O X O X O 9 X X O O O O O X X . . | $$ | . X X O X . O O X O O X X X X O X . . | $$ | X . . O O O X O O X O O X O O O O X . | $$ | X . O . O X X O X X X X X X O O X X . |[/go]

$$Wc
$$ +---------------------------------------+
$$ | . . . . O . . . 4 . 7 . X O X X . . . |
$$ | . X X X O O . 6 1 2 3 . . O O X . . . |
$$ | . . O X O X O 5 X X O O O O O X X . . |
$$ | . X X O X . O O X O O X X X X O X . . |
$$ | X . . O O O X O O X O O X O O O O X . |
$$ | X . O . O X X O X X X X X X O O X X . |
Click Here To Show Diagram Code
[go]$$Wc $$ +---------------------------------------+ $$ | . . . . O . . . 4 . 7 . X O X X . . . | $$ | . X X X O O . 6 1 2 3 . . O O X . . . | $$ | . . O X O X O 5 X X O O O O O X X . . | $$ | . X X O X . O O X O O X X X X O X . . | $$ | X . . O O O X O O X O O X O O O O X . | $$ | X . O . O X X O X X X X X X O O X X . |[/go]

Black 4

Click Here To Show Diagram Code: [go]$$Wc $$ +---------------------------------------+ $$ | . . . . O . . . . . 4 . X O X X . . . | $$ | . X X X O O . . 1 2 3 . . O O X . . . | $$ | . . O X O X O . X X O O O O O X X . . | $$ | . X X O X . O O X O O X X X X O X . . | $$ | X . . O O O X O O X O O X O O O O X . | $$ | X . O . O X X O X X X X X X O O X X . |[/go]

Kirby · Post by **Kirby** » Wed Dec 07, 2022 1:51 pm

lightvector wrote:
Kirby wrote:Can't white just do this?
Then what about this?
$$Wc Seki?
$$ +---------------------------------------+
$$ | . . . . O . . 9 8 6 4 0 X O X X . . . |
$$ | . X X X O O . 5 2 1 3 . . O O X . . . |
$$ | . . O X O X O 7 X X O O O O O X X . . |
$$ | . X X O X . O O X O O X X X X O X . . |
$$ | X . . O O O X O O X O O X O O O O X . |
$$ | X . O . O X X O X X X X X X O O X X . |
$$ | X O . . O O X O X . . X . X X O X . X |
$$ | O . . . O X X X . . X O X X O O O X . |
$$ | . O . O X X . . X X O O O X . O X . X |
$$ | . . . O O O X O X X O . O . . O X X . |
$$ | . . O . . . X X O O X O O O . O X O . |
$$ | . X O X X X X O O X X . O . O . O X . |
$$ | . O O O X O O O . . . . O . O O X . . |
$$ | . O X X X O . O O X . . . O X X X X . |
$$ | O O X . X . O . O X . . . O O X O . . |
$$ | O X O O O O O O X O . . O O X O O . . |
$$ | X X X X O X X O X O O O . O X X O X . |
$$ | . . X . X . . X X X O X O X X O X . X |
$$ | . . . . . . . . X . . . . . . . . X . |
$$ +---------------------------------------+
Click Here To Show Diagram Code
[go]$$Wc Seki? $$ +---------------------------------------+ $$ | . . . . O . . 9 8 6 4 0 X O X X . . . | $$ | . X X X O O . 5 2 1 3 . . O O X . . . | $$ | . . O X O X O 7 X X O O O O O X X . . | $$ | . X X O X . O O X O O X X X X O X . . | $$ | X . . O O O X O O X O O X O O O O X . | $$ | X . O . O X X O X X X X X X O O X X . | $$ | X O . . O O X O X . . X . X X O X . X | $$ | O . . . O X X X . . X O X X O O O X . | $$ | . O . O X X . . X X O O O X . O X . X | $$ | . . . O O O X O X X O . O . . O X X . | $$ | . . O . . . X X O O X O O O . O X O . | $$ | . X O X X X X O O X X . O . O . O X . | $$ | . O O O X O O O . . . . O . O O X . . | $$ | . O X X X O . O O X . . . O X X X X . | $$ | O O X . X . O . O X . . . O O X O . . | $$ | O X O O O O O O X O . . O O X O O . . | $$ | X X X X O X X O X O O O . O X X O X . | $$ | . . X . X . . X X X O X O X X O X . X | $$ | . . . . . . . . X . . . . . . . . X . | $$ +---------------------------------------+[/go]

$$Wc Ko?
$$ +---------------------------------------+
$$ | . . . . O . . . . 5 4 . X O X X . . . |
$$ | . X X X O O . . 2 1 3 6 . O O X . . . |
$$ | . . O X O X O . X X O O O O O X X . . |
$$ | . X X O X . O O X O O X X X X O X . . |
$$ | X . . O O O X O O X O O X O O O O X . |
$$ | X . O . O X X O X X X X X X O O X X . |
$$ | X O . . O O X O X . . X . X X O X . X |
$$ | O . . . O X X X . . X O X X O O O X . |
$$ | . O . O X X . . X X O O O X . O X . X |
$$ | . . . O O O X O X X O . O . . O X X . |
$$ | . . O . . . X X O O X O O O . O X O . |
$$ | . X O X X X X O O X X . O . O . O X . |
$$ | . O O O X O O O . . . . O . O O X . . |
$$ | . O X X X O . O O X . . . O X X X X . |
$$ | O O X . X . O . O X . . . O O X O . . |
$$ | O X O O O O O O X O . . O O X O O . . |
$$ | X X X X O X X O X O O O . O X X O X . |
$$ | . . X . X . . X X X O X O X X O X . X |
$$ | . . . . . . . . X . . . . . . . . X . |
$$ +---------------------------------------+
Click Here To Show Diagram Code
[go]$$Wc Ko? $$ +---------------------------------------+ $$ | . . . . O . . . . 5 4 . X O X X . . . | $$ | . X X X O O . . 2 1 3 6 . O O X . . . | $$ | . . O X O X O . X X O O O O O X X . . | $$ | . X X O X . O O X O O X X X X O X . . | $$ | X . . O O O X O O X O O X O O O O X . | $$ | X . O . O X X O X X X X X X O O X X . | $$ | X O . . O O X O X . . X . X X O X . X | $$ | O . . . O X X X . . X O X X O O O X . | $$ | . O . O X X . . X X O O O X . O X . X | $$ | . . . O O O X O X X O . O . . O X X . | $$ | . . O . . . X X O O X O O O . O X O . | $$ | . X O X X X X O O X X . O . O . O X . | $$ | . O O O X O O O . . . . O . O O X . . | $$ | . O X X X O . O O X . . . O X X X X . | $$ | O O X . X . O . O X . . . O O X O . . | $$ | O X O O O O O O X O . . O O X O O . . | $$ | X X X X O X X O X O O O . O X X O X . | $$ | . . X . X . . X X X O X O X X O X . X | $$ | . . . . . . . . X . . . . . . . . X . | $$ +---------------------------------------+[/go]

Touché! Nice.

jlt · Post by **jlt** » Wed Dec 07, 2022 2:13 pm

I can't find the other solution. Can someone else see it?

Gérard TAILLE · Post by **Gérard TAILLE** » Wed Dec 07, 2022 2:19 pm

jlt wrote:I can't find the other solution. Can someone else see it?

dany · Post by **dany** » Thu Dec 08, 2022 6:20 am

Gérard TAILLE wrote:
jlt wrote:I can't find the other solution. Can someone else see it?

$$W
$$ +---------------------------------------+
$$ | . . . . O . . . . . . . X O X X . . . |
$$ | . X X X O O . . . . 1 . . O O X . . . |
$$ | . . O X O X O . X X O O O O O X X . . |
$$ | . X X O X . O O X O O X X X X O X . . |
$$ | X . . O O O X O O X O O X O O O O X . |
$$ | X . O . O X X O X X X X X X O O X X . |
$$ | X O . . O O X O X . . X . X X O X . X |
$$ | O . . . O X X X . . X O X X O O O X . |
$$ | . O . O X X . . X X O O O X . O X . X |
$$ | . . . O O O X O X X O . O . . O X X . |
$$ | . . O . . . X X O O X O O O . O X O . |
$$ | . X O X X X X O O X X . O . O . O X . |
$$ | . O O O X O O O . . . . O . O O X . . |
$$ | . O X X X O . O O X . . . O X X X X . |
$$ | O O X . X . O . O X . . . O O X O . . |
$$ | O X O O O O O O X O . . O O X O O . . |
$$ | X X X X O X X O X O O O . O X X O X . |
$$ | . . X . X . . X X X O X O X X O X . X |
$$ | . . . . . . . . X . . . . . . . . X . |
$$ +---------------------------------------+
Click Here To Show Diagram Code
[go]$$W $$ +---------------------------------------+ $$ | . . . . O . . . . . . . X O X X . . . | $$ | . X X X O O . . . . 1 . . O O X . . . | $$ | . . O X O X O . X X O O O O O X X . . | $$ | . X X O X . O O X O O X X X X O X . . | $$ | X . . O O O X O O X O O X O O O O X . | $$ | X . O . O X X O X X X X X X O O X X . | $$ | X O . . O O X O X . . X . X X O X . X | $$ | O . . . O X X X . . X O X X O O O X . | $$ | . O . O X X . . X X O O O X . O X . X | $$ | . . . O O O X O X X O . O . . O X X . | $$ | . . O . . . X X O O X O O O . O X O . | $$ | . X O X X X X O O X X . O . O . O X . | $$ | . O O O X O O O . . . . O . O O X . . | $$ | . O X X X O . O O X . . . O X X X X . | $$ | O O X . X . O . O X . . . O O X O . . | $$ | O X O O O O O O X O . . O O X O O . . | $$ | X X X X O X X O X O O O . O X X O X . | $$ | . . X . X . . X X X O X O X X O X . X | $$ | . . . . . . . . X . . . . . . . . X . | $$ +---------------------------------------+[/go]

Yes

Click Here To Show Diagram Code: [go]$$W $$ +---------------------------------------+ $$ | . . . . O . . . 4 3 5 . X O X X . . . | $$ | . X X X O O . . . 2 1 . . O O X . . . | $$ | . . O X O X O . X X O O O O O X X . . | $$ | . X X O X . O O X O O X X X X O X . . | $$ | X . . O O O X O O X O O X O O O O X . | $$ | X . O . O X X O X X X X X X O O X X . |[/go]

Click Here To Show Diagram Code: [go]$$W $$ +---------------------------------------+ $$ | . . . . O . . . . 3 2 . X O X X . . . | $$ | . X X X O O . . 5 . 1 4 . O O X . . . | $$ | . . O X O X O . X X O O O O O X X . . | $$ | . X X O X . O O X O O X X X X O X . . | $$ | X . . O O O X O O X O O X O O O O X . | $$ | X . O . O X X O X X X X X X O O X X . |[/go]

Gérard TAILLE · Post by **Gérard TAILLE** » Thu Dec 08, 2022 8:57 am

Let's comme back to an interesting position mentionned by jlt.

After some simplification here is the basic semeai:

Click Here To Show Diagram Code: [go]$$Bc Black to play $$ +---------------------------------------+ $$ | . . . . . . O . X X O O a O O X X . . | $$ | . . . . . . O . X . X . O O O X X . . | $$ | . . . . . . O O X X O O O O O X . . . | $$ | . . . . . . O O O O X X X X X X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

This semeai is quite simple to read and black is clearly dead.

My question is the following : how do you analyse this semeai ?

As far as I am concerned I consider the point "a" as a real eye and I conclude we are in meari-menashi configuration.

Click Here To Show Diagram Code: [go]$$Bc Black to play $$ +---------------------------------------+ $$ | . . . . . . O M X X O O C O O X X . . | $$ | . . . . . . O M X C X C O O O X X . . | $$ | . . . . . . O O X X O O O O O X . . . | $$ | . . . . . . O O O O X X X X X X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

white has three liberties while black has only txo external liberties => black is dead.

My point is the following : this approach is true only because white has no external liberty.

Click Here To Show Diagram Code: [go]$$Bc Black to play $$ +---------------------------------------+ $$ | . . . . . . O . X X O O a O O b X . . | $$ | . . . . . . O . X . X . O O O X X . . | $$ | . . . . . . O . X X O O O O O X . . . | $$ | . . . . . . O O O O X X X X X X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

In this position, due to the liberty at "b" I do not consider that "a" is a real eye.

My analyse is now the following:
In order to win black must play

Click Here To Show Diagram Code: [go]$$B $$ +---------------------------------------+ $$ | . . . . . . O . X X O O . O O . X . . | $$ | . . . . . . O . X 1 X 3 O O O X X . . | $$ | . . . . . . O . X X O O O O O X . . . | $$ | . . . . . . O O O O X X X X X X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

and it will follow the exchange

Click Here To Show Diagram Code: [go]$$B $$ +---------------------------------------+ $$ | . . . . . . O . X X O 6 5 O O . X . . | $$ | . . . . . . O . X X X X O O O X X . . | $$ | . . . . . . O . X X O O O O O X . . . | $$ | . . . . . . O O O O X X X X X X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

Having this exchange

in mind the initial position is equivalent to

Click Here To Show Diagram Code: [go]$$B $$ +---------------------------------------+ $$ | . . . . . . O . X X . O a O O . X . . | $$ | . . . . . . O . X d X c O O O X X . . | $$ | . . . . . . O . X X O O O O O X . . . | $$ | . . . . . . O O O O X X X X X X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

on condition black begins by moves at "c" and "d"

Now my analyse is quite different :

Click Here To Show Diagram Code: [go]$$Bc Black to play $$ +---------------------------------------+ $$ | . . . . . . O M X X M O C O O C X . . | $$ | . . . . . . O M X C X C O O O X X . . | $$ | . . . . . . O M X X O O O O O X . . . | $$ | . . . . . . O O O O X X X X X X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

white has four liberties and black also has four liberties => black wins the semeai.

Note: with a real eye then meari-menashi approach applies:

Click Here To Show Diagram Code: [go]$$B $$ +---------------------------------------+ $$ | . . . . . . O . X X O O O . O . X . . | $$ | . . . . . . O . X . X . O O O X X . . | $$ | . . . . . . O . X X O O O O O X . . . | $$ | . . . . . . O O O O X X X X X X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

Click Here To Show Diagram Code: [go]$$Bc Black to play $$ +---------------------------------------+ $$ | . . . . . . O M X X O O O C O C X . . | $$ | . . . . . . O M X C X C O O O X X . . | $$ | . . . . . . O M X X O O O O O X . . . | $$ | . . . . . . O O O O X X X X X X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

and here white wins the semeai

jlt · Post by **jlt** » Thu Dec 08, 2022 10:19 am

Gérard TAILLE wrote: After some simplification here is the basic semeai:
$$Bc Black to play
$$ +---------------------------------------+
$$ | . . . . . X O . X X O O a O O X X . . |
$$ | . . . . . X O . X . X . O O O X X . . |
$$ | . . . . . X O O X X O O O O O X . . . |
$$ | . . . . . X O O O O X X X X X X . . . |
$$ | . . . . . X X X X X X . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
Click Here To Show Diagram Code
[go]$$Bc Black to play $$ +---------------------------------------+ $$ | . . . . . X O . X X O O a O O X X . . | $$ | . . . . . X O . X . X . O O O X X . . | $$ | . . . . . X O O X X O O O O O X . . . | $$ | . . . . . X O O O O X X X X X X . . . | $$ | . . . . . X X X X X X . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . |[/go]
This semeai is quite simple to read and black is clearly dead.

Black can play H18...

Gérard TAILLE · Post by **Gérard TAILLE** » Thu Dec 08, 2022 10:39 am

jlt wrote:
Gérard TAILLE wrote: After some simplification here is the basic semeai:
$$Bc Black to play
$$ +---------------------------------------+
$$ | . . . . . X O . X X O O a O O X X . . |
$$ | . . . . . X O . X . X . O O O X X . . |
$$ | . . . . . X O O X X O O O O O X . . . |
$$ | . . . . . X O O O O X X X X X X . . . |
$$ | . . . . . X X X X X X . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
Click Here To Show Diagram Code
[go]$$Bc Black to play $$ +---------------------------------------+ $$ | . . . . . X O . X X O O a O O X X . . | $$ | . . . . . X O . X . X . O O O X X . . | $$ | . . . . . X O O X X O O O O O X . . . | $$ | . . . . . X O O O O X X X X X X . . . | $$ | . . . . . X X X X X X . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . |[/go]
This semeai is quite simple to read and black is clearly dead.
Black can play H18...

Oops, diagrams now corrected. Thank you jlt

jlt · Post by **jlt** » Thu Dec 08, 2022 2:11 pm

I don't have a better way of analyzing the position, I'll just add that from this

Click Here To Show Diagram Code: [go]$$Bc Black to play $$ +---------------------------------------+ $$ | . . . . . . O . X X O O a O O X X . . | $$ | . . . . . . O c X b X . O O O X X . . | $$ | . . . . . . O O X X O O O O O X . . . | $$ | . . . . . . O O O O X X X X X X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

In this semeai, if Black wants to win he needs to play b, and White responds with c, so the position becomes

Click Here To Show Diagram Code: [go]$$Bc Black to play $$ +---------------------------------------+ $$ | . . . . . . O . X X O O . O O X X . . | $$ | . . . . . . O O X X X . O O O X X . . | $$ | . . . . . . O O X X O O O O O X . . . | $$ | . . . . . . O O O O X X X X X X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

and the analysis is slightly easier.

In the same way, starting from

Click Here To Show Diagram Code: [go]$$Bc Black to play $$ +---------------------------------------+ $$ | . . . . . . O . X X O O a O O . X . . | $$ | . . . . . . O . X b X . O O O X X . . | $$ | . . . . . . O c X X O O O O O X . . . | $$ | . . . . . . O O O O X X X X X X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

I still consider that the exchange b-c has been made so the position is equivalent to the following:

Click Here To Show Diagram Code: [go]$$Bc Black to play $$ +---------------------------------------+ $$ | . . . . . . O . X X O O . O O . X . . | $$ | . . . . . . O . X X X . O O O X X . . | $$ | . . . . . . O X X X O O O O O X . . . | $$ | . . . . . . O O O O X X X X X X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

dhu163 · Post by **dhu163** » Thu Dec 08, 2022 3:07 pm

As far as I am concerned I consider the point "a" as a real eye and I conclude we are in meari-menashi configuration.

What is meari-menashi?

Following Wolfe's seki graph theory, I think the calculation principle is iterating that a group needs 2 eye-like liberties to survive, namely places where the opponent can't play without giving you at least 1 permanent liberty there.

This occurs usually (always?) only when at that point the opponent dies themselves if they play there, generally by losing a semeai. Hence they at least need 2 other liberties (except for snapback, under the stones etc.), and must reduce your liberties. Playing on a mutual liberty reduces the liberties of both sides by 1 at the cost of a move. This is also true for connecting a weak point such as N19. Because B can get a liberty in sente by capturing, this is a follow up.

I would call internal liberties those which even after capturing you don't live. Are there any others than those found in eyes? Not sure what the official definition (s) is.
External liberties are those where you cannot expect to capture a group there. Note that it is optional whether or not to include potential small eyes in this.

Counting liberties instead of points using CGT, we have that normal external liberties are of the form
{1|-1} to the marginal liberties. Chilling by a tax of 1 per move equates this to 0, i.e. not interesting. Normal internal liberties are the same.j
Normal mutual liberties have marginals of
{0|0}. Chilling makes them negative {-1|1}. They are worse than playing external liberties. However sometimes there are 1st line kosumi tesuji which may be critical, though normally it only works in combination with another weak point.

What does the eye shape look like above?

{{{{2|0}|0}|-1}|0}

The way the eye comes into play is that W starts off with a bonus 3 liberties that B must fill to survive. K18 becomes one of these as an approach liberty. These act equivalently to internal liberties though they appear mutually. At the end of it, B can get an extra liberty in sente which makes these more urgent than normal external/internal liberties.

I don't know if CGT has a convenient way of representing this. Because the number of liberties at every node matters, not just at the leaf nodes because the semeai may end after any move if a group is captured. The marginal liberties isn't completely sufficient because the exact liberties matters.

It is like the local situation is
-3
| \
-2 0
| \
-1 0
| \
2 0
\
0

If B is down to 1 liberties after filling the first 2 approach liberties, W's next move can play that liberty to kill. Then B needs 3 external liberties to survive. In that case, W has 3 approach liberties.

Tsumego problems are difficult and interesting when comparing close marginal gains. Basically if the number of approach liberties is slightly different, a different result boundary appears. I don't know what sort of situations exist let alone their results.

For example what if W has 3 approach liberties from 2 different directions? Then perhaps W get a sneaky extra liberty from this by defending the side which is stronger. i.e. if B has 3 external liberties on both sides, W wins even if B plays first. If one side is 3 and the other is 4, I think we have a golden chicken standing on one leg situation and it is seki. If both sides are 4, then I think it is ko.
nb, if the example situation is copied, it doesn't work as then W has 2 eyes under optimal play. I'm not quite sure how to set up approach liberties in a different way though. I assume a semeai which B can win is required.

Gérard TAILLE · Post by **Gérard TAILLE** » Fri Dec 09, 2022 5:08 am

dhu163 wrote: What is meari-menashi?

see https://senseis.xmp.net/?MeAriMeNashi

Gérard TAILLE · Post by **Gérard TAILLE** » Fri Dec 09, 2022 11:36 am

dhu163 wrote: Following Wolfe's seki graph theory, I think the calculation principle is iterating that a group needs 2 eye-like liberties to survive ...

I do not know Wolfe's seki graph theory but your statement above seems strange to me.
In one hand you mentionned a SEKI graph theory but in other hand you say that a group needs 2 eye-like liberties to survive.
Does that mean that in a seki the associated liberties are considered eye-like liberties?

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dhu163 · Post by **dhu163** » Fri Dec 09, 2022 11:42 am

That is what I meant yes, though I can't remember what Wolfe called them.

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