GT territory rules:: Honte's loops and cycles

Cassandra · Post by **Cassandra** » Sat Aug 28, 2021 12:53 pm

Gérard TAILLE wrote:
$$B black to play and win
$$ +------------------------
$$ | . X X X X O O X . X . |
$$ | O O O X X O O O X X X |
$$ | . . . X X O O . O X O |
$$ | a X X X X O O O O O . |
$$ | . . O X X O O O O O O |
$$ | . O O . X O X X X X X |
$$ | X X X X X O X . . X . |
$$ | O O O O O X X X . X . |
$$ | . O X X X X . . X X X |
$$ | O O b X . . . . . . . |
$$ | O . O X . . . . . . . |
$$ +------------------------
Click Here To Show Diagram Code
[go]$$B black to play and win $$ +------------------------ $$ | . X X X X O O X . X . | $$ | O O O X X O O O X X X | $$ | . . . X X O O . O X O | $$ | a X X X X O O O O O . | $$ | . . O X X O O O O O O | $$ | . O O . X O X X X X X | $$ | X X X X X O X . . X . | $$ | O O O O O X X X . X . | $$ | . O X X X X . . X X X | $$ | O O b X . . . . . . . | $$ | O . O X . . . . . . . | $$ +------------------------[/go]
Be serious Honte which move do you prefer to see, a or b?
BTW did you appreciate this problem?

The problem was very nice, thank you.

Click Here To Show Diagram Code: [go]$$B Black to play and win $$ +------------------------ $$ | . X X X X O O Z b Z c | $$ | O O O X X O O O Z Z Z | $$ | . . . X X O O . O Z O | $$ | d X X X X O O O O O . | $$ | . . O X X O O O O O O | $$ | . O O . X O X X X X X | $$ | X X X X X O X . . X . | $$ | P P P P P X X X . X . | $$ | . P X X X X . . X X X | $$ | P P a X . . . . . . . | $$ | P . P X . . . . . . . | $$ +------------------------[/go]

As I already told you, Honte chose "a".
Black can kill White's 10 stones in the lower left corner with "a", while White can capture only 6 Black stones in the upper right corner. Black will gain by this exchange.
Please note that White must invest another move for taking Black's stones off the board, while Black can leave the position in the lower left as it is.
Capturing into a double-ko is not a valid (ko-) threat per se!

A Black move at "c" is a mistake, as it loses one point of territory unnecessarily.

Black might even pass and let White live in the lower left with a move at "a".
In this case, White does have only 2 points of territory (in the lower left corner).
Black wins by his large territory in the lower right, even if he lets White turn the upper left corner into a seki.

This is a very one-sided position.

Cassandra · Post by **Cassandra** » Sat Aug 28, 2021 12:57 pm

Gérard TAILLE wrote:I expected
$$B
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . . . . . ? O ? W ? . . . . . . . |
$$ | . . . , . . . ? . ? . ? . . . , . . . |
$$ | . ? ? ? ? ? . ? ? ? ? ? . ? ? ? ? ? . |
$$ | . ? O . . ? . . . . . . . ? . ? O ? . |
$$ | . ? . . X ? . . . . . . . ? B ? . ? . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . ? W ? . ? . . . . . . . ? . . O ? . |
$$ | . ? . ? X ? . . . . . . . ? X . . ? . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . , . . . ? . ? . ? . . . , . . . |
$$ | . . . . . . . ? X ? B ? . . . . . . . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+
$$ {AR M17 Q15}
$$ {AR Q12 Q9}
$$ {AR Q6 M3}
$$ {AR H3 D6}
$$ {AR D9 D12}
$$ {AR D15 H17}
Click Here To Show Diagram Code
[go]$$B $$ +---------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . ? ? ? ? ? . . . . . . . | $$ | . . . . . . . ? O ? W ? . . . . . . . | $$ | . . . , . . . ? . ? . ? . . . , . . . | $$ | . ? ? ? ? ? . ? ? ? ? ? . ? ? ? ? ? . | $$ | . ? O . . ? . . . . . . . ? . ? O ? . | $$ | . ? . . X ? . . . . . . . ? B ? . ? . | $$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . | $$ | . ? W ? . ? . . . . . . . ? . . O ? . | $$ | . ? . ? X ? . . . . . . . ? X . . ? . | $$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . | $$ | . . . . . . . ? ? ? ? ? . . . . . . . | $$ | . . . , . . . ? . ? . ? . . . , . . . | $$ | . . . . . . . ? X ? B ? . . . . . . . | $$ | . . . . . . . ? ? ? ? ? . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ +---------------------------------------+ $$ {AR M17 Q15} $$ {AR Q12 Q9} $$ {AR Q6 M3} $$ {AR H3 D6} $$ {AR D9 D12} $$ {AR D15 H17}[/go]

Yes, indeed, this is another option. Thank you very much.

Probably more consistent to have "pass" connected to the arrows also here in this diagram.
I am sure, something will think about this overnight unconciously.

Gérard TAILLE · Post by **Gérard TAILLE** » Sat Aug 28, 2021 1:02 pm

Cassandra wrote:
Gérard TAILLE wrote:I expected
$$B
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . . . . . ? O ? W ? . . . . . . . |
$$ | . . . , . . . ? . ? . ? . . . , . . . |
$$ | . ? ? ? ? ? . ? ? ? ? ? . ? ? ? ? ? . |
$$ | . ? O ? . ? . . . . . . . ? . ? O ? . |
$$ | . ? . ? X ? . . . . . . . ? B ? . ? . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . ? W ? . ? . . . . . . . ? . ? O ? . |
$$ | . ? . ? X ? . . . . . . . ? X ? . ? . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . , . . . ? . ? . ? . . . , . . . |
$$ | . . . . . . . ? X ? B ? . . . . . . . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+
$$ {AR M17 Q15}
$$ {AR Q12 Q9}
$$ {AR Q6 M3}
$$ {AR H3 D6}
$$ {AR D9 D12}
$$ {AR D15 H17}
Click Here To Show Diagram Code
[go]$$B $$ +---------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . ? ? ? ? ? . . . . . . . | $$ | . . . . . . . ? O ? W ? . . . . . . . | $$ | . . . , . . . ? . ? . ? . . . , . . . | $$ | . ? ? ? ? ? . ? ? ? ? ? . ? ? ? ? ? . | $$ | . ? O ? . ? . . . . . . . ? . ? O ? . | $$ | . ? . ? X ? . . . . . . . ? B ? . ? . | $$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . | $$ | . ? W ? . ? . . . . . . . ? . ? O ? . | $$ | . ? . ? X ? . . . . . . . ? X ? . ? . | $$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . | $$ | . . . . . . . ? ? ? ? ? . . . . . . . | $$ | . . . , . . . ? . ? . ? . . . , . . . | $$ | . . . . . . . ? X ? B ? . . . . . . . | $$ | . . . . . . . ? ? ? ? ? . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ +---------------------------------------+ $$ {AR M17 Q15} $$ {AR Q12 Q9} $$ {AR Q6 M3} $$ {AR H3 D6} $$ {AR D9 D12} $$ {AR D15 H17}[/go]
Yes, indeed, this is another option. Thank you very much.

Probably more consistent to have "pass" connected to the arrows also here in this diagram.
I am sure, something will think about this overnight unconciously.

BTW with such diagram, when no marked stone appears then you know for sure that the last move were a pass weren't it? => that way the diagram is simplified.

Cassandra · Post by **Cassandra** » Sat Aug 28, 2021 7:29 pm

Honte's magic DOUBLE-KO spell (contd)

##### What is a DOUBLE-Ko during "play"? #####

We showed in viewtopic.php?p=266991#p266991 the only useful use of initiating (one halve of, to be precise) a DOUBLE-KO cycle is that it can prevent a currently "hot" SIMPLE-ko-shape to vanish (either by filling it or by capturing something in its surrounding).

To be honest, there is one more:
One of both opponents initiates a GENUINE TRIPLE-ko cycle of the compound. A cycle that they WILL NEVER let END.
For what purpose? They do not want to reach the GENUINE end of the game, as this would be favourable for their opponent.

##### What is a DOUBLE-Ko during "status confirmation"? #####

At first sight, it has the same features as during "play".

However, the second use case would have the purpose to NEVER reach the GENUINE end of a status confirmation, which would be DISADVANTAGEOUS for the initiating player.
But we are IN "status confirmation" in order to identify the status of groups, thus such a behaviour does not make sense at all, doesn't it?

It is common understanding that the player who is free to exit a cycle without damage, while his opponent is forced to linger in it, has the upper hand.

How can we effectively prevent the behavior described above? Well, we'll just let the double-ko vanish!

##### The WORDS of Honte's magic DOUBLE-KO spell #####

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

This is a typical double-ko formation.
The currently "hot" ko are marked with triangles.

Click Here To Show Diagram Code: [go]$$Bc $$ +---------------+ $$ | . X Q . O X . | $$ | X X X O O X . | $$ | . X O O X X . | $$ | Y O . O X . . | $$ | O O O O X . . | $$ | X X X X X . . | $$ | . . . . . . . | $$ +---------------+ $$ {AR C7 G7} $$ {AR A4 A7}[/go]

Honte uses his magic wand while speaking "MOVE TOWARDS YOUR ALLIES!"

Click Here To Show Diagram Code: [go]$$Bc $$ +---------------+ $$ | . X T Q O X . | $$ | X X X O O X . | $$ | Y X O O X X . | $$ | T O . O X . . | $$ | O O O O X . . | $$ | X X X X X . . | $$ | . . . . . . . | $$ +---------------+[/go]

After Honte used his magic wand...

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

... the DOUBLE-ko has vanished and become a genuine seki.

Cassandra · Post by **Cassandra** » Sat Aug 28, 2021 7:52 pm

Honte's magic DOUBLE-KO spell (contd)

##### Application examples #####

Triple-ko

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

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

Expected / intended result.

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

After Honte used his magic wand...

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

Genuine seki.

J89 L&D example 25

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

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

Expected / intended result.

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

After Honte used his magic wand...

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

Genuine seki.

J89 L&D example 8

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

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

Expected / intended result.

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

After Honte used his magic wand...

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

Me ari me nashi.

J89 L&D example 16

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

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

Expected / intended result.

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

After Honte used his magic wand...

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

Left: Two eyes vs. one eye. => Right: Dissolving of the temporary seki.

J89 L&D example 17

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

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

Expected / intended result.

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

After Honte used his magic wand...

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

Left: Dead bent-four-in-the-corner. => Right: Dissolving of the temporary seki.

J89 L&D example 18

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

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

Expected / intended result.

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

After Honte used his magic wand...

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

Left: Dead bent-four-in-the-corner. => Right: Dissolving of the temporary seki.

"HIGHLANDER" director's cut - for adults only

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

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

Viewed from TEA City on a foggy day.

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

After Honte used his magic wand...

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

Viewed from TEA City in bright sunshine.

"HIGHLANDER" defused version

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

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

Viewed from GT City on a foggy day.

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

After Honte used his magic wand...

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

Viewed from GT City in bright sunshine.

GT City's Central Park - seen from above

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

In the morning mist.

Click Here To Show Diagram Code: [go]$$B $$ ----------------- $$ | W Z C Z C W C | $$ | C W Z Z Z W W | $$ | W C W W Z Z W | $$ | W W W C W Z W | $$ | X X W W Z Z W | $$ | . X X W W W C | $$ | X . X X X W W | $$ -----------------[/go]

Yesterday evening - illuminated.

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

After Honte used his magic wand...

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

Two eyes vs. no eye.

++++++++++++++++++++

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

Ten o'clock in the morning. Some people are strolling around.

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

After Honte used his magic wand...

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

Me ari me nashi.

Cassandra · Post by **Cassandra** » Sun Aug 29, 2021 3:28 am

Loops with a cycle-length of pseudo 6 (contd)

The earth suddenly trembled between rubble and scrub - an earthquake!
There was a huge landslide ahead of us that blocked access to District 6 for all eternity. It is estimated that "He Who Cannot Be Named" had his hands in it magically.

We later heard that GT City's central office building was also collapsed by the earthquake. Thank goodness no one was killed or injured because everyone there was on a research expedition.
There are rumors that GT City will not rebuild its central building, but will leave its ruins as a reminder of a glorious past in which people still believed in the healing properties of "loops". After all, they have more than enough empty office space.

Now let's share what was seen after the earthquake.

##### After the earthquake #####

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

===== GT territory rules =====

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

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

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

created a ko-shape.

Click Here To Show Diagram Code: [go]$$B $$ +-------------+ $$ | 4 X . X . X | $$ | . O X X X X | $$ | O O O X O O | $$ | . . X O O . | $$ | X X X X O O | $$ | . X . X O . | $$ +-------------+[/go]

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

created a ko-shape.

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

captures into a ko-shape.

Click Here To Show Diagram Code: [go]$$B :w6: pass $$ +-------------+ $$ | Q X . X . X | $$ | ? Q X X X X | $$ | Q O O X O O | $$ | . . X O O . | $$ | X X X X O O | $$ | . X . X O . | $$ +-------------+[/go]

passes.
The resulting position is a "critical" one.

White claims for creating a "permanently prohibited ko", making a ko-capture at the shadowed point taboo for Black.

Click Here To Show Diagram Code: [go]$$Bm7 $$ +-------------+ $$ | 1 X 2 X . X | $$ | X O X X X X | $$ | O O O X O O | $$ | . . X O O . | $$ | X X X X O O | $$ | . X . X O . | $$ +-------------+[/go]

Click Here To Show Diagram Code: [go]$$Bm7 $$ +-------------+ $$ | . 3 . X . X | $$ | . O X X X X | $$ | O O O X O O | $$ | . . X O O . | $$ | X X X X O O | $$ | . X . X O . | $$ +-------------+[/go]

Click Here To Show Diagram Code: [go]$$Bm7 $$ +-------------+ $$ | . Y . Y . X | $$ | . O Y X X X | $$ | O O O X O O | $$ | . . X O O . | $$ | X X X X O O | $$ | . X . X O . | $$ +-------------+[/go]

created a ko-shape.

Click Here To Show Diagram Code: [go]$$Bm7 $$ +-------------+ $$ | 4 X . X . X | $$ | . O X X X X | $$ | O O O X O O | $$ | . . X O O . | $$ | X X X X O O | $$ | . X . X O . | $$ +-------------+[/go]

Click Here To Show Diagram Code: [go]$$Bm7 $$ +-------------+ $$ | Q X . X . X | $$ | ? Q X X X X | $$ | Q O O X O O | $$ | . . X O O . | $$ | X X X X O O | $$ | . X . X O . | $$ +-------------+[/go]

created a "permanently prohibited ko".

Click Here To Show Diagram Code: [go]$$Bm7 :b11: pass $$ +-------------+ $$ | Q X . X . X | $$ | ? Q X X X X | $$ | Q O O X O O | $$ | . . X O O . | $$ | X X X X O O | $$ | . X . X O . | $$ +-------------+[/go]

Black can only "pass", as the shadowed point has become taboo for him.

Click Here To Show Diagram Code: [go]$$Bm11 :b13: pass $$ +-------------+ $$ | O X 2 X 4 X | $$ | . O X X X X | $$ | O O O X O O | $$ | . . X O O . | $$ | X X X X O O | $$ | . X . X O . | $$ +-------------+[/go]

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

Two eye formation for White, but NOT occupying the entire board.

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

NO territory for White on the entire board.

White should have taken Black's stones at the top off the board before the game stopped, and occupied the DAME of

thereafter.

===== "Two-eyed alive" world =====

As can be seen above, the cycle as a length of 6, but it includes a White "pass", so the cycle length is "pseudo 6" only.

-------------------------

The cycle-length pseudo 6 fulfills the condition

cl = 2 + 4n (n = 0, 1, 2, 3, ...).

Therefore, the last GENUINE move of that (uninterrupted) cycle is forbidden.

Next run:

As can be seen above, White will be able to create a two-eye-formation in the upper part of the board by capturing Black's stones at the top.

-------------------------

Click Here To Show Diagram Code: [go]$$B $$ +-------------+ $$ | a Z b Z c Z | $$ | Z W Z Z Z Z | $$ | W W W Z W W | $$ | T T B W W . | $$ | B B B B W W | $$ | . B . B W . | $$ +-------------+[/go]

Concluding result of status confirmation.

Black should have occupied the DAME

before the game stopped, forcing White to take his stones at the top off the board with moves at a, b, and c.

Gérard TAILLE · Post by **Gérard TAILLE** » Sun Aug 29, 2021 6:39 am

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

Oops it seems the earthquake has not only attacked the structure of the building of the city but also the foundation of the rule itself.
In either rule, if you look at the marked black group you see two eyes at "e" locations and two dame points at "d" locations. => obviouly the game is not finished because you cannot imagine black allowing the existence of these dame with the consequence that the eye points "e" will not be counted as territory.

OK let's assume that black decides to pass

Can white claim for a territory at the top of the board?

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

Always due to the dame "d" it is not possible because the outside border marked here above is not valid (two empy locations)

With this kind of unfinished game you not even need to start an hupothetical play.

Surely I have to find a safe-deposit-box in order to protect my rule against an earthquake.

Gérard TAILLE · Post by **Gérard TAILLE** » Sun Aug 29, 2021 7:14 am

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

How do you recognise a double ko? Depending of the environment you cannot replace the position above by the following can you?

Click Here To Show Diagram Code: [go]$$Bc $$ +---------------+ $$ | . X X X . X X | $$ | O O X X X X X | $$ | O . O O X O . | $$ | O O O . O O O | $$ | . . . O . O . | $$ | . . . O O O O | $$ | . . . . . . . | $$ +---------------+ $$ {AR A7 A6} $$ {AR G5 G6} $$[/go]

Cassandra · Post by **Cassandra** » Sun Aug 29, 2021 7:25 am

Gérard TAILLE wrote:
$$B
$$ +---------------+
$$ | O X X X . X X |
$$ | a O X X X X b |
$$ | O . O O X O X |
$$ | O O O . O O O |
$$ | . . . O . O . |
$$ | . . . O O O O |
$$ | . . . . . . . |
$$ +---------------+
$$
Click Here To Show Diagram Code
[go]$$B $$ +---------------+ $$ | O X X X . X X | $$ | a O X X X X b | $$ | O . O O X O X | $$ | O O O . O O O | $$ | . . . O . O . | $$ | . . . O O O O | $$ | . . . . . . . | $$ +---------------+ $$[/go]
How do you recognise a double ko? Depending of the environment you cannot replace the position above by the following can you?
$$Bc
$$ +---------------+
$$ | . X X X . X X |
$$ | O O X X X X X |
$$ | O . O O X O . |
$$ | O O O . O O O |
$$ | . . . O . O . |
$$ | . . . O O O O |
$$ | . . . . . . . |
$$ +---------------+
$$ {AR A7 A6}
$$ {AR G5 G6}
$$
Click Here To Show Diagram Code
[go]$$Bc $$ +---------------+ $$ | . X X X . X X | $$ | O O X X X X X | $$ | O . O O X O . | $$ | O O O . O O O | $$ | . . . O . O . | $$ | . . . O O O O | $$ | . . . . . . . | $$ +---------------+ $$ {AR A7 A6} $$ {AR G5 G6} $$[/go]

I suppose that...

Click Here To Show Diagram Code: [go]$$Bc $$ +---------------+ $$ | T X X X C X X | $$ | Q O X X X X Y | $$ | O C O O X O T | $$ | O O O C O O O | $$ | . . . O . O . | $$ | . . . O O O O | $$ | . . . . . . . | $$ +---------------+[/go]

... (two eyes vs. one eye) will make you easier understand that Black's group at the top is dead than...

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

... playing

in your head.

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

Black's group has one genuine, and two false, eyes -- and so is dead. Same result as after Honte's magic spell.

Gérard TAILLE · Post by **Gérard TAILLE** » Sun Aug 29, 2021 8:21 am

Cassandra wrote:
Gérard TAILLE wrote:
$$B
$$ +---------------+
$$ | O X X X . X X |
$$ | a O X X X X b |
$$ | O . O O X O X |
$$ | O O O . O O O |
$$ | . . . O . O . |
$$ | . . . O O O O |
$$ | . . . . . . . |
$$ +---------------+
$$
Click Here To Show Diagram Code
[go]$$B $$ +---------------+ $$ | O X X X . X X | $$ | a O X X X X b | $$ | O . O O X O X | $$ | O O O . O O O | $$ | . . . O . O . | $$ | . . . O O O O | $$ | . . . . . . . | $$ +---------------+ $$[/go]
How do you recognise a double ko? Depending of the environment you cannot replace the position above by the following can you?
$$Bc
$$ +---------------+
$$ | . X X X . X X |
$$ | O O X X X X X |
$$ | O . O O X O . |
$$ | O O O . O O O |
$$ | . . . O . O . |
$$ | . . . O O O O |
$$ | . . . . . . . |
$$ +---------------+
$$ {AR A7 A6}
$$ {AR G5 G6}
$$
Click Here To Show Diagram Code
[go]$$Bc $$ +---------------+ $$ | . X X X . X X | $$ | O O X X X X X | $$ | O . O O X O . | $$ | O O O . O O O | $$ | . . . O . O . | $$ | . . . O O O O | $$ | . . . . . . . | $$ +---------------+ $$ {AR A7 A6} $$ {AR G5 G6} $$[/go]
I suppose that...

$$Bc
$$ +---------------+
$$ | T X X X C X X |
$$ | Q O X X X X Y |
$$ | O C O O X O T |
$$ | O O O C O O O |
$$ | . . . O . O . |
$$ | . . . O O O O |
$$ | . . . . . . . |
$$ +---------------+
Click Here To Show Diagram Code
[go]$$Bc $$ +---------------+ $$ | T X X X C X X | $$ | Q O X X X X Y | $$ | O C O O X O T | $$ | O O O C O O O | $$ | . . . O . O . | $$ | . . . O O O O | $$ | . . . . . . . | $$ +---------------+[/go]
... (two eyes vs. one eye) will make you easier understand that Black's group at the top is dead than...

$$B
$$ +---------------+
$$ | O X X X . X X |
$$ | 1 O X X X X . |
$$ | O 2 O O X O X |
$$ | O O O . O O O |
$$ | . . . O . O . |
$$ | . . . O O O O |
$$ | . . . . . . . |
$$ +---------------+$$
Click Here To Show Diagram Code
[go]$$B $$ +---------------+ $$ | O X X X . X X | $$ | 1 O X X X X . | $$ | O 2 O O X O X | $$ | O O O . O O O | $$ | . . . O . O . | $$ | . . . O O O O | $$ | . . . . . . . | $$ +---------------+$$[/go]
... playing in your head.

$$B
$$ +---------------+
$$ | M X X X C X X |
$$ | X P X X X X M |
$$ | O O O O X P X |
$$ | O O O C O O O |
$$ | . . . O C O . |
$$ | . . . O O O O |
$$ | . . . . . . . |
$$ +---------------+$$
Click Here To Show Diagram Code
[go]$$B $$ +---------------+ $$ | M X X X C X X | $$ | X P X X X X M | $$ | O O O O X P X | $$ | O O O C O O O | $$ | . . . O C O . | $$ | . . . O O O O | $$ | . . . . . . . | $$ +---------------+$$[/go]
Black's group has one genuine, and two false, eyes -- and so is dead. Same result as after Honte's magic spell.

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

Honte's magic wand will clearly disadvantaged black won't it? => it is almost a double ko but it is not really one.

Cassandra · Post by **Cassandra** » Sun Aug 29, 2021 10:32 am

About compositions of four ko-shapes

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

This is the example with four ko-shapes that Gérard kindly provided to me.

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

The four ko-shapes are a, b, c and d.

All three groups in question have TWO liberties each.
-- White's group at the left has one liberty at e in her eye, and another one in the neighbored double-ko (at a or b).
-- Black's group in the centre has one liberty in the double-ko at left (at a or b), and another one in the double-ko at right (at c or d)
-- White's group at the left has one liberty at f in her eye, and another one in the neighbored double-ko (at c or d).

Thus, we can expect this position being a seki.

##### Honte's magic DOUBLE-KO spell #####

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

After Honte used his magic wand...

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

... we can easily see that the position is seki.

No wonder that this is the fastest method, as magic was involved.

##### GT territory rules #####

Second fastest is using the GENUINE quadruple-ko cycle.

Click Here To Show Diagram Code: [go]$$B GENUINE quadruple-ko cycle $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O X X X O O O | $$ | O O X 2 X 4 X O O | $$ | O O O X X X O O O | $$ | . O 1 O X O 3 O . | $$ +-------------------+[/go]

Click Here To Show Diagram Code: [go]$$B GENUINE quadruple-ko cycle $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O X X X O O O | $$ | O O 5 O X O 7 O O | $$ | O O O X X X O O O | $$ | . O X 6 X 8 X O . | $$ +-------------------+[/go]

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

Same position as eight moves before.

Neither side will ever create a two-eye-formation in the lower part of the board.
==> NO territory.

--------------------------

Using the "permanent prohibited ko" feature will neither shorten nor ease the sequences required.
It seems to me that "permanent prohibited ko" will be most useful in ASYMMETRICAL positions.

Click Here To Show Diagram Code: [go]$$B Status confirmation for White groups $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O X X X O O O | $$ | O O X . X . X O O | $$ | O O Q X X X O O O | $$ | . O 1 Q X O . O . | $$ +-------------------+[/go]

We will start with trying to find out, whether White will be able to create a two-eye-formation at the bottom.

Click Here To Show Diagram Code: [go]$$B Status confirmation for White groups $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O Y X X O O O | $$ | O O Y 2 X . X O O | $$ | O O O Y X X O O O | $$ | . O X . X O . O . | $$ +-------------------+[/go]

Click Here To Show Diagram Code: [go]$$B Status confirmation for White groups; :b3: pass $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O Y X X O O O | $$ | O O T P X . X O O | $$ | O O O Y X X O O O | $$ | . O X . X O . O . | $$ +-------------------+[/go]

Black also claims "permanently prohibited ko" for

.

Click Here To Show Diagram Code: [go]$$B Status confirmation for White groups $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O X X Y O O O | $$ | O O . O X 4 Y O O | $$ | O O O X X Y O O O | $$ | . O X . X O . O . | $$ +-------------------+[/go]

Click Here To Show Diagram Code: [go]$$B Status confirmation for White groups $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O Q X X X O O O | $$ | O O 5 Q X O . O O | $$ | O O Q X X X O O O | $$ | . O X . X O . O . | $$ +-------------------+[/go]

Click Here To Show Diagram Code: [go]$$B Status confirmation for White groups $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O X X X O O O | $$ | O O X . X O . O O | $$ | O O O Y X X O O O | $$ | . O Y 6 X O . O . | $$ +-------------------+[/go]

Click Here To Show Diagram Code: [go]$$B Status confirmation for White groups $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O Y X X Q O O | $$ | O O Y M X Q 7 O O | $$ | O O O Y X X Q O O | $$ | . O . O X O . O . | $$ +-------------------+[/go]

White must not capture into the ko-shape at left.

Click Here To Show Diagram Code: [go]$$B Status confirmation for White groups; :w8: pass $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O Y X X Q O O | $$ | O O Y M X T Z O O | $$ | O O O Y X X Q O O | $$ | . O . O X O . O . | $$ +-------------------+[/go]

White must not capture into the ko-shape at left, instead.
White also claims "permanently prohibited ko" for

.

Click Here To Show Diagram Code: [go]$$B Status confirmation for White groups $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O X X X O O O | $$ | O O X . X . X O O | $$ | O O Q X X X O O O | $$ | . O 9 Q X O . O . | $$ +-------------------+[/go]

Click Here To Show Diagram Code: [go]$$Wm10 Status confirmation for White groups $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O Y X Y O O O | $$ | O O Y M X 1 Y O O | $$ | O O O Y X Y O O O | $$ | 2 O X . X O . O . | $$ +-------------------+[/go]

must not capture into the ko-shape at left, instead.

==> NO White territory.

------------------------

Click Here To Show Diagram Code: [go]$$W Status confirmation for Black groups $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O X X Y O O O | $$ | O O X . X 1 Y O O | $$ | O O O X X Y O O O | $$ | . O . O X O . O . | $$ +-------------------+[/go]

Will Black be able to create a two-eye-formation at the bottom?

Click Here To Show Diagram Code: [go]$$W Status confirmation for Black groups $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O X X X O O O | $$ | O O X . X O . O O | $$ | O O O X X X Q O O | $$ | . O . O X Q 2 O . | $$ +-------------------+[/go]

Click Here To Show Diagram Code: [go]$$W Status confirmation for Black groups; :w3: pass $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O X X X O O O | $$ | O O X . X O . O O | $$ | O O O X X X Q O O | $$ | . O . O X T Z O . | $$ +-------------------+[/go]

White also claims "permanently prohibited ko" for

.

Click Here To Show Diagram Code: [go]$$W Status confirmation for Black groups $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O X X X Q O O | $$ | O O X . X Q 4 O O | $$ | O O O X X X Q O O | $$ | . O . O X . X O . | $$ +-------------------+[/go]

Click Here To Show Diagram Code: [go]$$W Status confirmation for Black groups $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O X X X O O O | $$ | O O X . X . X O O | $$ | O O O X X Y O O O | $$ | . O . O X 5 Y O . | $$ +-------------------+[/go]

Click Here To Show Diagram Code: [go]$$W Status confirmation for Black groups; :b6: pass $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O X X X O O O | $$ | O O X . X . X O O | $$ | O O O X X Y O O O | $$ | . O . O X P T O . | $$ +-------------------+[/go]

Black also claims "permanently prohibited ko" for

.
This does not have any effect, as Black must not re-capture into that ko-shape anyway.

Click Here To Show Diagram Code: [go]$$W Status confirmation for Black groups $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O X X Y O O O | $$ | O O X . X 7 Y O O | $$ | O O O X X Y O O O | $$ | . O . O X O . O . | $$ +-------------------+[/go]

Click Here To Show Diagram Code: [go]$$W Status confirmation for Black groups $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O X X X O O O | $$ | O O X . X O . O O | $$ | O O Q X X X Q O O | $$ | . O 8 Q X Q M O . | $$ +-------------------+[/go]

Black must not re-capture at right, instead.

Click Here To Show Diagram Code: [go]$$W Status confirmation for Black groups $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O Y X X O O O | $$ | O O Y 9 X O . O O | $$ | O O O Y X X O O O | $$ | . O X . X O . O . | $$ +-------------------+[/go]

Click Here To Show Diagram Code: [go]$$Bm10 Status confirmation for Black groups $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O X X X Q O O | $$ | O O . O X Q 1 O O | $$ | O O O X X X Q O O | $$ | . O X . X Q M O . | $$ +-------------------+[/go]

Black must not re-capture into the lower ko-shape.

Click Here To Show Diagram Code: [go]$$Bm10 Status confirmation for Black groups; :w11: pass $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O X X X Q O O | $$ | O O . O X T Z O O | $$ | O O O X X X Q O O | $$ | . O X . X O . O . | $$ +-------------------+[/go]

White also claims "permanently prohibited ko" for

.

Click Here To Show Diagram Code: [go]$$Bm10 Status confirmation for Black groups $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O Q X X X O O O | $$ | O O 3 Q X . X O O | $$ | O O Q X X X O O O | $$ | . O X . X O . O . | $$ +-------------------+[/go]

Click Here To Show Diagram Code: [go]$$Bm10 Status confirmation for Black groups $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O X X X O O O | $$ | O O X . X . X O O | $$ | O O O Y X X O O O | $$ | . O Y 4 X O . O . | $$ +-------------------+[/go]

Click Here To Show Diagram Code: [go]$$Bm10 Status confirmation for Black groups; :b14: pass $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O X X X O O O | $$ | O O X . X . X O O | $$ | O O O Y X X Q O O | $$ | . O T P X Q M O . | $$ +-------------------+[/go]

Black must not re-capture into the lower ko-shape at right, instead.
Black also claims "permanently prohibited ko" for

.

Click Here To Show Diagram Code: [go]$$Bm10 Status confirmation for Black groups $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O Y X X O O O | $$ | O O Y 6 X . X O O | $$ | O O O Y X X O O O | $$ | . O . O X O . O . | $$ +-------------------+[/go]

Click Here To Show Diagram Code: [go]$$Bm10 Status confirmation for Black groups; :b16: pass $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O Y X X O O O | $$ | O O . O X 8 X O O | $$ | O O O Y X X Q O O | $$ | . O . O X Q M O . | $$ +-------------------+[/go]

Black must not re-capture into the lower ko-shape at right.

==> NO Black territory.

Gérard TAILLE · Post by **Gérard TAILLE** » Sun Aug 29, 2021 11:04 am

Cassandra wrote:About compositions of four ko-shapes

$$B
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X O O O |
$$ | O O X . X . X O O |
$$ | O O O X X X O O O |
$$ | . O . O X O . O . |
$$ +-------------------+
Click Here To Show Diagram Code
[go]$$B $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O X X X O O O | $$ | O O X . X . X O O | $$ | O O O X X X O O O | $$ | . O . O X O . O . | $$ +-------------------+[/go]
This is the example with four ko-shapes that Gérard kindly provided to me.

$$B
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O Y X Y O O O |
$$ | O O Y b X c Y O O |
$$ | O O Q Y X Y Q O O |
$$ | e O a Q X Q d O f |
$$ +-------------------+
Click Here To Show Diagram Code
[go]$$B $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O Y X Y O O O | $$ | O O Y b X c Y O O | $$ | O O Q Y X Y Q O O | $$ | e O a Q X Q d O f | $$ +-------------------+[/go]
The four ko-shapes are a, b, c and d.

All three groups in question have TWO liberties each.
-- White's group at the left has one liberty at e in her eye, and another one in the neighbored double-ko (at a or b).
-- Black's group in the centre has one liberty in the double-ko at left (at a or b), and another one in the double-ko at right (at c or d)
-- White's group at the left has one liberty at f in her eye, and another one in the neighbored double-ko (at c or d).

Thus, we can expect this position being a seki.

##### Honte's magic DOUBLE-KO spell #####

$$B
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X O O O |
$$ | O O T Y X Y T O O |
$$ | O O O X X X O O O |
$$ | . O Q T X T Q O . |
$$ +-------------------+
Click Here To Show Diagram Code
[go]$$B $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O X X X O O O | $$ | O O T Y X Y T O O | $$ | O O O X X X O O O | $$ | . O Q T X T Q O . | $$ +-------------------+[/go]
After Honte used his magic wand...

$$B
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . B B B B . . |
$$ | . B B B @ @ B B . |
$$ | B B @ @ # @ @ B B |
$$ | @ @ @ # # # @ @ @ |
$$ | @ @ . # # # . @ @ |
$$ | @ @ @ # # # @ @ @ |
$$ | . @ @ . # . @ @ . |
$$ +-------------------+
Click Here To Show Diagram Code
[go]$$B $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . B B B B . . | $$ | . B B B @ @ B B . | $$ | B B @ @ # @ @ B B | $$ | @ @ @ # # # @ @ @ | $$ | @ @ . # # # . @ @ | $$ | @ @ @ # # # @ @ @ | $$ | . @ @ . # . @ @ . | $$ +-------------------+[/go]
... we can easily see that the position is seki.

No wonder that this is the fastest method, as magic was involved.

##### GT territory rules #####

Second fastest is using the GENUINE quadruple-ko cycle.

$$B GENUINE quadruple-ko cycle
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X O O O |
$$ | O O X 2 X 4 X O O |
$$ | O O O X X X O O O |
$$ | . O 1 O X O 3 O . |
$$ +-------------------+
Click Here To Show Diagram Code
[go]$$B GENUINE quadruple-ko cycle $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O X X X O O O | $$ | O O X 2 X 4 X O O | $$ | O O O X X X O O O | $$ | . O 1 O X O 3 O . | $$ +-------------------+[/go]

$$B GENUINE quadruple-ko cycle
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X O O O |
$$ | O O 5 O X O 7 O O |
$$ | O O O X X X O O O |
$$ | . O X 6 X 8 X O . |
$$ +-------------------+
Click Here To Show Diagram Code
[go]$$B GENUINE quadruple-ko cycle $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O X X X O O O | $$ | O O 5 O X O 7 O O | $$ | O O O X X X O O O | $$ | . O X 6 X 8 X O . | $$ +-------------------+[/go]

$$B GENUINE quadruple-ko cycle
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X O O O |
$$ | O O X . X . X O O |
$$ | O O O X X X O O O |
$$ | . O . O X O . O . |
$$ +-------------------+
Click Here To Show Diagram Code
[go]$$B GENUINE quadruple-ko cycle $$ +-------------------+ $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . X X X X . . | $$ | . X X X O O X X . | $$ | X X O O X O O X X | $$ | O O O X X X O O O | $$ | O O X . X . X O O | $$ | O O O X X X O O O | $$ | . O . O X O . O . | $$ +-------------------+[/go]
Same position as eight moves before.

"GT territory rule" do not handle loops by trying to recognize them really (I mean recognizing that the same position appeared already in the previous moves). "GT territory rule" looks only to an infinity of "critical" positions. Assuming white claim for a territory at the bottom of the board then it is black to play and obviously black can play only atari moves to which white has to answer by puting a stone on the board => no "critical" positions at all => no "permanent prohibited ko" => the loop cannot be break => No territory.
That's all you can do with "GT territory rule". Remember, if the attacker wants to break a loop she must first prove she can reach "critical" positions an infinite number of time, with the defender playing first in the hypothetical play. Here the attacker cannot even reach only one "critical" position => the loop cannot be breaked.

In J2003 the analyse seems more complicated if not strange: the big white and black groups of stones are all alive, the four isolated stones involved in the ko are dead (they can be captured and no new permanently alive stone can be created) => the four empty locations in the ko are dame (they are not surrounded by only living stones) => the three big alive groups have dame => seki

Cassandra · Post by **Cassandra** » Sun Aug 29, 2021 11:56 am

Gérard TAILLE wrote:"GT territory rule" do not handle loops by trying to recognize them really (I mean recognizing that the same position appeared already in the previous moves). "GT territory rule" looks only to an infinity of "critical" positions. Assuming white claim for a territory at the bottom of the board then it is black to play and obviously black can play only atari moves to which white has to answer by puting a stone on the board => no "critical" positions at all => no "permanent prohibited ko" => the loop cannot be break => No territory.
That's all you can do with "GT territory rule". Remember, if the attacker wants to break a loop she must first prove she can reach "critical" positions an infinite number of time, with the defender playing first in the hypothetical play. Here the attacker cannot even reach only one "critical" position => the loop cannot be breaked.

It seems I wrote a throwback to GT City's Roaring Twenties.

You too still seem to like to remember that "looping" time.

Cassandra · Post by **Cassandra** » Sun Aug 29, 2021 12:48 pm

"HIGHLANDER 2 –– At the very most there can be one"

Honte's magic DOUBLE-ko spell reduces the number of ko-shapes that are really effective in a formation under status consideration.
The number of ko-shapes effectively remaining will be

1 or 0.

ONE ko-shape:

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

Effective number of ko-shapes: 1

TWO ko-shapes:

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

Two ko-shapes.

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

After Honte used his magic wand...

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

Effective number of ko-shapes: 0

THREE ko-shapes:

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

Three ko-shapes.

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

After Honte used his magic wand...

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

Effective number of ko-shapes: 1

FOUR ko-shapes:

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

Four ko-shapes.

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

After Honte used his magic wand...

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

Effective number of ko-shapes: 0

Gérard TAILLE · Post by **Gérard TAILLE** » Sun Aug 29, 2021 1:32 pm

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

Two kos.
Applying Honte's magic wand would be a disaster for white wouldn't it?

Life In 19x19

GT territory rules:: Honte's loops and cycles

Re: GT territory rules:: Honte's loops and cycles

Re: GT territory rules:: Honte's loops and cycles

Re: GT territory rules:: Honte's loops and cycles

Re: GT territory rules:: Honte's loops and cycles

Re: GT territory rules:: Honte's loops and cycles

Re: GT territory rules:: Honte's loops and cycles

Re: GT territory rules:: Honte's loops and cycles

Re: GT territory rules:: Honte's loops and cycles

Re: GT territory rules:: Honte's loops and cycles

Re: GT territory rules:: Honte's loops and cycles

Re: GT territory rules:: Honte's loops and cycles

Re: GT territory rules:: Honte's loops and cycles

Re: GT territory rules:: Honte's loops and cycles

Re: GT territory rules:: Honte's loops and cycles

Re: GT territory rules:: Honte's loops and cycles