GT territory rules:: Honte's loops and cycles

Cassandra · Post by **Cassandra** » Thu Aug 26, 2021 12:21 am

Loops with a cycle-length of 4

District #4 is a desolate industrial area.
Honte had to look for a long time before we finally stood in front of a tourist attraction, perhaps the only one there.

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

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

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

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

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

We have reached the starting position. The cycle has a length of 4.

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

Click Here To Show Diagram Code: [go]$$Bm5 $$ +-------------------+ $$ | . O 1 X . O X . . | $$ | X O O O X X O O O | $$ | X X X X X O O . . | $$ | O O O O O O . . . | $$ | . . . . , . . . . | $$ | . . . . . . . . . |[/go]

Click Here To Show Diagram Code: [go]$$Bm5 :w6: pass $$ +-------------------+ $$ | 3 O X X . O X . . | $$ | X O O O X X O O O | $$ | X X X X X O O . . | $$ | O O O O O O . . . | $$ | . . . . , . . . . | $$ | . . . . . . . . . |[/go]

Click Here To Show Diagram Code: [go]$$Bm5 $$ +-------------------+ $$ | X . X X . O X . . | $$ | X . . . X X O O O | $$ | X X X X X O O . . | $$ | O O O O O O . . . | $$ | . . . . , . . . . | $$ | . . . . . . . . . |[/go]

White is unable to pass with

Variation:

Click Here To Show Diagram Code: [go]$$Bm5 $$ +-------------------+ $$ | . O X X 2 O X . . | $$ | X O O O X X O O O | $$ | X X X X X O O . . | $$ | O O O O O O . . . | $$ | . . . . , . . . . | $$ | . . . . . . . . . |[/go]

Click Here To Show Diagram Code: [go]$$Bm5 $$ +-------------------+ $$ | . O . 3 O O X . . | $$ | X O O O X X O O O | $$ | X X X X X O O . . | $$ | O O O O O O . . . | $$ | . . . . , . . . . | $$ | . . . . . . . . . |[/go]

Click Here To Show Diagram Code: [go]$$Bm5 :w8: pass $$ +-------------------+ $$ | . O . X . 5 X . . | $$ | X O O O X X O O O | $$ | X X X X X O O . . | $$ | O O O O O O . . . | $$ | . . . . , . . . . | $$ | . . . . . . . . . |[/go]

White is unable to pass with

Next run:

White is unable to interrupt the cycle, which therefore is an ENFORCED one.
White is unable to create a two-eye formation in the upper part of the board.
=> NO White territory

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

For the status assessment of Black's group, White could pass for her first move, whereafter the same sequences as above would apply.

Alternatively, she might want to shorten the matter:

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

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

Black cannot get more than one eye.

Black is unable to create a two-eye formation.
=> NO Black territory

##### "Two-eyed alive" world #####

The cycle-length 4 does not fulfill the condition

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

Therefore, there will be no ban of the cycle's last move.
The same sequences as shown above will apply.

=> Black's stones in the upper left are "seki-alive".
=> White's stones in the upper left are "seki-alive".

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

After the status assessment for all groups has been completed:

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

=> The upper left part of the board is a seki.

####################
####################

For the sake of completeness, let's try to find out what would happen after a ban of the cycle's last move.

Next run:

Click Here To Show Diagram Code: [go]$$Bm5 $$ +-------------------+ $$ | . O 1 X 2 O X . . | $$ | X O O O X X O O O | $$ | X X X X X O O . . | $$ | O O O O O O . . . | $$ | . . . . , . . . . | $$ | . . . . . . . . . |[/go]

Click Here To Show Diagram Code: [go]$$Bm5 $$ +-------------------+ $$ | . O . 3 O O X . . | $$ | X O O O X X O O O | $$ | X X X X X O O . . | $$ | O O O O O O . . . | $$ | . . . . , . . . . | $$ | . . . . . . . . . |[/go]

Click Here To Show Diagram Code: [go]$$Bm5 $$ +-------------------+ $$ | . O . X . ? X . . | $$ | X O O O X X O O O | $$ | X X X X X O O . . | $$ | O O O O O O . . . | $$ | . . . . , . . . . | $$ | . . . . . . . . . |[/go]

White is hindered to occupy the shadowed point, as this was the move that completed the cycle.

Click Here To Show Diagram Code: [go]$$Bm5 $$ +-------------------+ $$ | . O . X . 5 X 4 . | $$ | X O O O X X O O O | $$ | X X X X X O O . . | $$ | O O O O O O . . . | $$ | . . . . , . . . . | $$ | . . . . . . . . . |[/go]

The position has become seki.
Same result as above. White is unable to achieve "two-eyed alive" for her group in the corner.

Gérard TAILLE · Post by **Gérard TAILLE** » Thu Aug 26, 2021 2:09 am

Cassandra wrote:
$$Bm5 :b5: :w6: pass
$$ +---------------+
$$ | . O . X O . . |
$$ | X O X X O . . |
$$ | . X X O O . . |
$$ | X X O , . . . |
$$ | O O O . O . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ +---------------+
Click Here To Show Diagram Code
[go]$$Bm5 :b5: :w6: pass $$ +---------------+ $$ | . O . X O . . | $$ | X O X X O . . | $$ | . X X O O . . | $$ | X X O , . . . | $$ | O O O . O . . | $$ | . . . . . . . | $$ | . . . . . . . | $$ +---------------+[/go]
Black cannot prevent this.
=> White has a loop.

I said there is a misunderstanding when I saw you claiming "White has a loop". Obviously white has not a loop because she cannot force black to play. Black has not to help white building a loop, at least in GT territory rule context.
Only black can show a loop (that is true) but it happens that this loop has not good caracteristics for black in the context of GT territory rule.

If now you are taking about loops in general (and not loops in the context of GT territory rule) then surely you will be also interested by loops created by a cooperation of white and black.

I do not know if that could help you in your analysis but :
1) I can see loops which could be forced both players
2) I can see loops which could be forced by only one player
3) I can see loops which could be created only a cooperation of the two players
4) I can see loops with or without kos
5) I can see loops with or without pass for one player or for both players
6) and OC one can also look for other caracteristics of a loop (starting position, existence of critical position or whatever you want)

It is not an easy subject Thomas and I do not know exactly what your are aiming for. Sure I would like to help you (that is my basic understanding of a forum discussion) but for the time being I do not see where you are trying to go.

Cassandra · Post by **Cassandra** » Thu Aug 26, 2021 2:19 am

You're pretty impatient, aren't you?
Is there any deadline for the publication of your rules?

However: "Haste makes waste!"
Good things need their time...

But you are really lucky.
On the way to District #6, Honte just unearthed a paper that will not only ease our forthcoming reports from there, but also answer your questions related to my understanding of "cycle" (/ "loop").

Cassandra · Post by **Cassandra** » Thu Aug 26, 2021 3:05 am

About compositions of three ko-shapes

The road to District 6 is currently still blocked with rubble and undergrowth; we are in the process of clearing our way.

However, Honte has unearthed a piece of paper that you can read to bridge the waiting time. The reports from District 6 that follow later can then be kept much shorter and easier to understand.

Click Here To Show Diagram Code: [go]$$B $$ ? ? ? ? ? ? ? ? ? ? ? $$ ? ? ? ? ? ? ? ? ? ? ? $$ ? ? X X X X X X X ? ? $$ ? ? X O X O X c X ? ? $$ ? ? O a O b O X O ? ? $$ ? ? O O O O O O O ? ? $$ ? ? ? ? ? ? ? ? ? ? ? $$ ? ? ? ? ? ? ? ? ? ? ?[/go]

Just visualise this simplest of all compositions with three ko-shapes. Please do not worry about what could be around it.
In order to be able to address the three ko-shapes individually, they are marked with "a", "b" and "c".

Click Here To Show Diagram Code: [go]$$B $$ ? ? ? ? ? $$ ? O O c ? $$ ? a b X ? $$ ? ? ? ? ?[/go]

This concentrated form will save a lot of space.

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

In the following, for the sake of simplicity, we will dispense with explicitly specifying the markings.

##### GENUINE triple-ko cycle #####

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

This diagram shows the GENUINE triple-ko cycle.
The marked stones are those that have been played last.

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

Please note that if we had decided to choose

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

for the position at the top of the diagram, a similar ENFORCED cycle would develop.

This cycle would contain the mirrored positions above, and start with the position in the lower right.

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

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

Click Here To Show Diagram Code: [go]$$B $$ ? ? ? ? ? ? ? ? ? ? ? $$ ? ? ? ? ? ? ? ? ? ? ? $$ ? ? X X X X X X X ? ? $$ ? ? X O X . X . X ? ? $$ ? ? O . O X O X O ? ? $$ ? ? O O O O O O O ? ? $$ ? ? ? ? ? 1 ? ? ? ? ? $$ ? ? ? ? ? ? ? ? ? ? ?[/go]

You will easily recognise that...

Click Here To Show Diagram Code: [go]$$B $$ ? ? ? ? ? ? ? ? ? ? ? $$ ? ? ? ? ? ? ? ? ? ? ? $$ ? ? X X X X X X X ? ? $$ ? ? X O X 2 X . X ? ? $$ ? ? O . O X O X O ? ? $$ ? ? O O O O O O O ? ? $$ ? ? ? ? ? ? ? ? ? ? ? $$ ? ? ? ? ? ? ? ? ? ? ?[/go]

... once any af the six variants is reached -- i.e. the cycle is entered -- there is NO escape.
A GENUINE triple-ko cycle is ENFORCED.

Click Here To Show Diagram Code: [go]$$B $$ +---------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . ? ? ? ? ? . . . . . . . | $$ | . . . . . . . ? O W . ? . . . . . . . | $$ | . . . , . . . ? . . X ? . . . , . . . | $$ | . ? ? ? ? ? . ? ? ? ? ? . ? ? ? ? ? . | $$ | . ? O . . ? . . . . . . . ? . O . ? . | $$ | . ? . X B ? . M M M M M . ? B . X ? . | $$ | . ? ? ? ? ? . M . . . M . ? ? ? ? ? . | $$ | . . . . . . . M X X Y M . . . . . . . | $$ | . . . , . . . M M M M M . . . , . . . | $$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . | $$ | . ? W . O ? . . . Q . . . ? . O W ? . | $$ | . ? . X . ? . . . . . . . ? X . . ? . | $$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . | $$ | . . . . . . . ? ? ? ? ? . . . . . . . | $$ | . . . , . . . ? . . O ? . . . , . . . | $$ | . . . . . . . ? X B . ? . . . . . . . | $$ | . . . . . . . ? ? ? ? ? . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ +---------------------------------------+ $$ {AR M17 Q15} $$ {AR Q12 Q9} $$ {AR Q6 M3} $$ {AR H3 D6} $$ {AR D9 D12} $$ {AR D15 H17} $$ {AR K5 K7} $$ {AR K9 K10}[/go]

If any player (White here) ever played a move outside the cycle, the cycle would end!

----------------------
EDIT

Thus, the following diagram might be a more suitable presentation for this CLOSED CIRCLE.

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

[/color]

Gérard TAILLE · Post by **Gérard TAILLE** » Thu Aug 26, 2021 6:32 am

Cassandra wrote: Next run:

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

$$W :b2: pass
$$ +---------------+
$$ | . O . X . X O |
$$ | O O O X X X O |
$$ | X O ? O X O O |
$$ | X O O X X O . |
$$ | X X X O O O O |
$$ | . . X X X O . |
$$ | . . X . X O . |
$$ +---------------+
Click Here To Show Diagram Code
[go]$$W :b2: pass $$ +---------------+ $$ | . O . X . X O | $$ | O O O X X X O | $$ | X O ? O X O O | $$ | X O O X X O . | $$ | X X X O O O O | $$ | . . X X X O . | $$ | . . X . X O . | $$ +---------------+[/go]
A Black move at the shadowed point is forbidden, as this would be the move to complete the current cycle.

$$W :w3: pass
$$ +---------------+
$$ | . O a X . X O |
$$ | O O O X X X O |
$$ | X O . O X O O |
$$ | X O O X X O . |
$$ | X X X O O O O |
$$ | . . X X X O . |
$$ | . . X . X O . |
$$ +---------------+
Click Here To Show Diagram Code
[go]$$W :w3: pass $$ +---------------+ $$ | . O a X . X O | $$ | O O O X X X O | $$ | X O . O X O O | $$ | X O O X X O . | $$ | X X X O O O O | $$ | . . X X X O . | $$ | . . X . X O . | $$ +---------------+[/go]
I leave it to you to find out why giving atari at "a" instead, would be a grave mistake.

$$W :b4: :w5: pass for end of status confirmation
$$ +---------------+
$$ | . O . # . # O |
$$ | O O O # # # O |
$$ | X O . O # O O |
$$ | X O O # # O . |
$$ | X X X O O O O |
$$ | . . X X X O . |
$$ | . . X . X O . |
$$ +---------------+
Click Here To Show Diagram Code
[go]$$W :b4: :w5: pass for end of status confirmation $$ +---------------+ $$ | . O . # . # O | $$ | O O O # # # O | $$ | X O . O # O O | $$ | X O O # # O . | $$ | X X X O O O O | $$ | . . X X X O . | $$ | . . X . X O . | $$ +---------------+[/go]
Black was unable to create a "two-eyed alive" group in the upper part of the board.
However, not all of his stones disappeared forever.
=> Black's group is "in-seki alive".

the sentence "However, not all of his stones disappeared forever" tells me that the objective of all the sequence is not quite clear.

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

I understood that the objective for black was only to try and build a "two-eyed alive" group on something in the corner but on what exactly in your example above?
1) the

stone ?
2) the

stones ?
3) both

in

? (which would be the case with GT territory rule)
Is it an objective to try to save a part of black stones as suggested in your sentence "However, not all of his stones disappeared forever" ?

Cassandra · Post by **Cassandra** » Thu Aug 26, 2021 6:36 am

About compositions of three ko-shapes (contd)

##### OPTIONAL triple-ko cycles #1 #####

Click Here To Show Diagram Code: [go]$$B $$ ? ? ? ? ? ? ? ? ? ? ? ? $$ ? ? ? ? ? ? ? ? ? ? ? ? $$ ? ? X X X X X X X ? ? ? $$ ? ? X O X O X c X X ? ? $$ ? ? O a O b O X O C ? ? $$ ? ? O O O O O O O ? ? ? $$ ? ? ? ? ? ? ? ? ? ? ? ? $$ ? ? ? ? ? ? ? ? ? ? ? ?[/go]

Let's add a SHARED liberty to the GENUINE triple-ko.

Click Here To Show Diagram Code: [go]$$Bc $$ +---------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . ? ? ? ? ? . . . . . . . | $$ | . . . . . . . ? O W . ? . . . . . . . | $$ | . . . , . . . ? . . X C . . . , . . . | $$ | . ? ? ? ? ? . ? ? ? ? ? . ? ? ? ? ? . | $$ | . ? O . . ? . . . . . . . ? . O . ? . | $$ | . ? . X B C . . . . . . . ? B . X C . | $$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . | $$ | . ? W . O ? . . . . . . . ? . O W ? . | $$ | . ? . X . C . . . . . . . ? X . . C . | $$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . | $$ | . . . . . . . ? ? ? ? ? . . . . . . . | $$ | . . . , . . . ? . . O ? . . . , . . . | $$ | . . . . . . . ? X B . C . . . . . . . | $$ | . . . . . . . ? ? ? ? ? . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ +---------------------------------------+ $$ {AR M17 Q15} $$ {AR Q12 Q9} $$ {AR Q6 M3} $$ {AR H3 D6} $$ {AR D9 D12} $$ {AR D15 H17} $$ {AR J2 J1} $$ {AR K2 K1} $$ {AR L2 L1}[/go]

This diagram shows a triple-ko cycle that is similar to the GENUINE one.
The marked stones are those that have been played last.

However, both sides are free to leave the cycle shown (symbolised by the "triple-arrow" at the bottom of the diagram).
This exit can be taken at every position of the cycle. We chose the bottom one for an exemplary case.

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

Click Here To Show Diagram Code: [go]$$B $$ +---------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . Y . . . . . Q . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . | $$ | . ? W . . ? . . . . . . . ? . . O ? . | $$ | . ? . X X C . . . . . . . ? X X . B . | $$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . Y . . . . . , . . . | $$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . | $$ | . ? . . . ? . . . . . . . ? . . O ? . | $$ | . ? X X B C . . . . . . . ? X X . ? . | $$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . M M M M M . . . , . . . | $$ | . . . . . . . M e n d M . . . . . . . | $$ | . . . . . . . M M M M M . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ +---------------------------------------+ $$ {AR K16 F8} $$ {AR D9 D12} $$ {AR D15 D16} $$ {AR J19 J18} $$ {AR K19 K18} $$ {AR P12 P9} $$ {AR Q12 Q9} $$ {AR R12 R9} $$ {AR L19 L18} $$ {AR C18 C19} $$ {AR D18 D19} $$ {AR E18 E19} $$ {AR K16 O14} $$ {AR K16 K11} $$ {AR K9 K4}[/go]

White plays

outside the cycle. Black has three options now.

LEFT:

captures into the remaining ko.

has to capture into one of the other ko-shapes, as Black's move was an atari.

must be played outside the triple-ko, as there is no ko-shape remaining Black could capture in.
This returns into the OPTIONAL cycle.
Both sides exchanged one move each outside the triple-ko, what they could have done anyway.

RIGHT:

occupies the shared liberty.
This starts the GENUINE triple-ko cycle.

MIDDLE:

is played outside the triple-ko.
This is a clear sign that Black does not want to continue the triple-ko cycle.
Both sides exchanged one move each outside the triple-ko, what they could have done anyway.

Cassandra · Post by **Cassandra** » Thu Aug 26, 2021 7:22 am

Gérard TAILLE wrote:Is it an objective to try to save a part of black stones as suggested in your sentence "However, not all of his stones disappeared forever" ?

There is the option of "seki", isn't it?

Let me clarify, what "two-eyed alive" in the FIRST step of the status confirmation is:

##### Two-eyed alive #####

Option #1:
Black already HAS a formation that includes (at least) two "sure" eyes, and no matter how many moves White is allowed to play in a row, she remains unable to capture Black's formation (aka "pass-alive").
Black could transform his formation into one that includes (at least) two forbidden points for White by occupying all but one board points inside any of his eyes.
If his formation had more than two eyes, he might be forced to fill his surplus eyes to comply with rules specialists who can only count to two.

Option #2:
Black is able to CREATE a formation that fulfills option #1, even is White is allowed to move first.

Option #3:
Black is able to CREATE a formation that fulfills option #1, even is White is allowed to move first, end even if Black stones were captured by White, but ALL of these could be re-established on the board (aka "snap-back", "nakade").
("Re-established" == A specific board point is occupied by a Black stone => capture => This specific board point is occupied by a Black stone or an eye-point.)

##### In-seki alive #####

For every formation that CANNOT become "two-eyed alive":

Option #1:
Black already HAS a formation that cannot be captured by White, even if White is allowed to move first (aka GENUINE seki).

Option #2:
Black is able to re-establish AT LEAST ONE stone of his formation, even if White is allowed to move first, and even if his stones were captured by White (see e.g. the four-stone group of "three points without capturing").
(These formations are likely to become part of a seki in step #2 of the status confirmation.)

##### Not alive #####

For every formation that CANNOT become "in-seki alive" (aka "can be captured" -- without any re-establishment, to be clear -- e.g. uncaptured stones in a remaining ko-shape, e.g. in a double-ko).

(I refrained from choosing "dead" as technical term, as it will be decided only in step #2 of the status confirmation, whether these stones will become captives. Please see e.g. the uncaptured single stones in a double-ko again.)

Gérard TAILLE · Post by **Gérard TAILLE** » Thu Aug 26, 2021 8:28 am

Cassandra wrote:
Gérard TAILLE wrote:Is it an objective to try to save a part of black stones as suggested in your sentence "However, not all of his stones disappeared forever" ?
There is the option of "seki", isn't it?

Let me clarify, what "two-eyed alive" in the FIRST step of the status confirmation is:

##### Two-eyed alive #####

Option #1:
Black already HAS a formation that includes (at least) two "sure" eyes, and no matter how many moves White is allowed to play in a row, she remains unable to capture Black's formation (aka "pass-alive").
Black could transform his formation into one that includes (at least) two forbidden points for White by occupying all but one board points inside any of his eyes.
If his formation had more than two eyes, he might be forced to fill his surplus eyes to comply with rules specialists who can only count to two.

Option #2:
Black is able to CREATE a formation that fulfills option #1, even is White is allowed to move first.

Option #3:
Black is able to CREATE a formation that fulfills option #1, even is White is allowed to move first, end even if Black stones were captured by White, but ALL of these could be re-established on the board (aka "snap-back", "nakade").
("Re-established" == A specific board point is occupied by a Black stone => capture => This specific board point is occupied by a Black stone or an eye-point.)

##### In-seki alive #####

For every formation that CANNOT become "two-eyed alive":

Option #1:
Black already HAS a formation that cannot be captured by White, even if White is allowed to move first (aka GENUINE seki).

Option #2:
Black is able to re-establish AT LEAST ONE stone of his formation, even if White is allowed to move first, and even if his stones were captured by White (see e.g. the four-stone group of "three points without capturing").
(These formations are likely to become part of a seki in step #2 of the status confirmation.)

##### Not alive #####

For every formation that CANNOT become "in-seki alive" (aka "can be captured" -- without any re-establishment, to be clear -- e.g. uncaptured stones in a remaining ko-shape, e.g. in a double-ko).

(I refrained from choosing "dead" as technical term, as it will be decided only in step #2 of the status confirmation, whether these stones will become captives. Please see e.g. the uncaptured single stones in a double-ko again.)

Does that means that you changed your mind (this is not a reproach Thomas, drafts written during analyses are here to be changed aren't they)?

in your post viewtopic.php?p=266812#p266812 you write
"Please remember that status confirmation is a "YES / NO" issue only."

Now I see three possible results : two-eyed alive, in-seki alive, or dead

Is it true?

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

BTW I see in this diagram:
1) the

stone is dead
2) the

stones are "in-seki alive"
That is the point I saw when writting my prvious post; all black stones have not the same status and this was not quite clear in your post.

There is another small point. You did not clarify how many successive passes you allow.

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

In this position with black trying to build a two eye formation, and white to play first it follows:

Click Here To Show Diagram Code: [go]$$W :b2: pass, :w3: pass $$ +---------------+ $$ | O O . X . X O | $$ | O O O X X X O | $$ | X O X 1 X O O | $$ | X O O X X O . | $$ | X X X O O O O | $$ | . . X X X O . | $$ | . . X . X O . | $$ +---------------+[/go]

and it is clear that black should be allowed to now take the ko.
Is it a good understanding that two passes do not end your STATUS CONFIRMATION phase?

Cassandra · Post by **Cassandra** » Thu Aug 26, 2021 9:28 am

Gérard TAILLE wrote:Does that means that you changed your mind (this is not a reproach Thomas, drafts written during analyses are here to be changed aren't they)?

in your post viewtopic.php?p=266812#p266812 you write
"Please remember that status confirmation is a "YES / NO" issue only."

I did not change my mind. At that time, we were talking about "two-eyed alive" only.

Is a formation "two-eyed alive"?
=> YES => finished.
=> NO => Is a formation "in-seki alive"?
=> YES => finished.
=> NO => finished ("not alive").

IF type(formation) = two-eye-formation
THEN status = "two-eyed-alive"
ELSEIF type(formation) = uncapturable
THEN status = "in-seki alive"
ELSE status = "not alive"
ENDIF

Now I see three possible results : two-eyed alive, in-seki alive, or dead

Is it true?

$$W
$$ +---------------+
$$ | . O . Y . Y O |
$$ | O O O Y Y Y O |
$$ | X O B . Y O O |
$$ | X O O Y Y O . |
$$ | X X X O O O O |
$$ | . . X X X O . |
$$ | . . X . X O . |
$$ +---------------+
Click Here To Show Diagram Code
[go]$$W $$ +---------------+ $$ | . O . Y . Y O | $$ | O O O Y Y Y O | $$ | X O B . Y O O | $$ | X O O Y Y O . | $$ | X X X O O O O | $$ | . . X X X O . | $$ | . . X . X O . | $$ +---------------+[/go]
BTW I see in this diagram:
1) the stone is dead
2) the stones are "in-seki alive"
That is the point I saw when writting my prvious post; all black stones have not the same status and this was not quite clear in your post.

Click Here To Show Diagram Code: [go]$$W final position of the game $$ +---------------+ $$ | . O . X . X O | $$ | O O O X X X O | $$ | X O X . X O O | $$ | X O O X X O . | $$ | X X X O O O O | $$ | . . X X X O . | $$ | O . X . X O X | $$ +---------------+[/go]

Click Here To Show Diagram Code: [go]$$W result of status confirmation $$ +---------------+ $$ | . @ . # . # W | $$ | @ @ @ # # # W | $$ | B @ Z . # W W | $$ | B @ @ # # W . | $$ | B B B W W W W | $$ | . . B B B W . | $$ | P . B . B W Z | $$ +---------------+[/go]

"two-eyed alive"

"in-seki alive"

"not alive"

Click Here To Show Diagram Code: [go]$$W result of identifying territory $$ +---------------+ $$ | . O . X . X O | $$ | O O O X X X O | $$ | X O X . X O O | $$ | X O O X X O T | $$ | X X X O O O O | $$ | S S X X X O T | $$ | @ S X . X O Y | $$ +---------------+[/go]

Black territory

White territory

There is another small point. You did not clarify how many successive passes you allow.

$$W
$$ +---------------+
$$ | O O . X . X O |
$$ | O O O X X X O |
$$ | X O X . X O O |
$$ | X O O X X O . |
$$ | X X X O O O O |
$$ | . . X X X O . |
$$ | . . X . X O . |
$$ +---------------+
Click Here To Show Diagram Code
[go]$$W $$ +---------------+ $$ | O O . X . X O | $$ | O O O X X X O | $$ | X O X . X O O | $$ | X O O X X O . | $$ | X X X O O O O | $$ | . . X X X O . | $$ | . . X . X O . | $$ +---------------+[/go]
In this position with black trying to build a two eye formation, and white to play first it follows:
$$W :b2: pass, :w3: pass
$$ +---------------+
$$ | O O . X . X O |
$$ | O O O X X X O |
$$ | X O X 1 X O O |
$$ | X O O X X O . |
$$ | X X X O O O O |
$$ | . . X X X O . |
$$ | . . X . X O . |
$$ +---------------+
Click Here To Show Diagram Code
[go]$$W :b2: pass, :w3: pass $$ +---------------+ $$ | O O . X . X O | $$ | O O O X X X O | $$ | X O X 1 X O O | $$ | X O O X X O . | $$ | X X X O O O O | $$ | . . X X X O . | $$ | . . X . X O . | $$ +---------------+[/go]
and it is clear that black should be allowed to now take the ko.
Is it a good understanding that two passes do not end your STATUS CONFIRMATION phase?

Let's assume that we have reached the effective end of the status confirmation of a White formation, and the discusison was about "two-eyed alive" only.

= "pass" says either
-- "I don't see any way to prevent your group from becoming "two-eyed alive". Let's stop our discussion here.", or
-- "I don't see any possibility for you to bring your formation into the "two-eyed alive" status. Do you agree?"

= "pass" says either
-- "Yes, it really is. Good idea to stop discussion here. I agree.", or
-- "Yes, unfortunately that is the case. I have thought about it for a long time, but can't find a way to succeed. Let's end the discussion here, okay?

= "pass"
-- is either superfluous, as both Black and White already signaled that they wanted to end the discussion, or
-- says "Discussion end".

= "pass",

= "pass" during "play" is complete nonsense (during status confirmation as well, BTW), as it has the same effect as

= ko-capture,

= ko-capture (capturing

to be clear). Both is nothing more than a waste of time, as an earlier board status is repeated.
Therefore, TWO "pass" are sufficient for ending "play", as the objective for both "moves" is the same: "Let's end 'play.'"
A third "pass" during "play" is superfluous.

During status confirmation, Black's and White's aims are different, as can be seen above. Therefore, a THIRD (successive) pass is needed.

Gérard TAILLE · Post by **Gérard TAILLE** » Thu Aug 26, 2021 10:55 am

Cassandra wrote:
$$B
$$ +---------------+
$$ | . O . X O . . |
$$ | X O X X O . . |
$$ | . X X O O . . |
$$ | X X O , . . . |
$$ | O O O . O . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ +---------------+
Click Here To Show Diagram Code
[go]$$B $$ +---------------+ $$ | . O . X O . . | $$ | X O X X O . . | $$ | . X X O O . . | $$ | X X O , . . . | $$ | O O O . O . . | $$ | . . . . . . . | $$ | . . . . . . . | $$ +---------------+[/go]
##### "Two-eyed alive" world #####

The cycle-length pseudo 4 does not fulfill the condition

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

I guess I missed something.
Could you clarify what is this condition you are referring to?
Is is due to fact that in "sending two return one" you have 3 plays and 1 pass?

Cassandra · Post by **Cassandra** » Thu Aug 26, 2021 11:22 am

Gérard TAILLE wrote:
Cassandra wrote:
$$B
$$ +---------------+
$$ | . O . X O . . |
$$ | X O X X O . . |
$$ | . X X O O . . |
$$ | X X O , . . . |
$$ | O O O . O . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ +---------------+
Click Here To Show Diagram Code
[go]$$B $$ +---------------+ $$ | . O . X O . . | $$ | X O X X O . . | $$ | . X X O O . . | $$ | X X O , . . . | $$ | O O O . O . . | $$ | . . . . . . . | $$ | . . . . . . . | $$ +---------------+[/go]
##### "Two-eyed alive" world #####

The cycle-length pseudo 4 does not fulfill the condition

cl = 2 + 2n (n = 0, 1, 2, 3, ...).
I guess I missed something.
Could you clarify what is this condition you are referring to?
Is is due to fact that in "sending two return one" you have 3 plays and 1 pass?

Oh sorry, my German English. Probably "equation" would have been clearer, instead of "condition".

It is my current feeling, and I think it will be confirmed by Honte's walks, that length 4n cycles are fundamentally different from length (2 + 4n) cycles.
Length 4n cycles (i.e. 4, 8, 12, ...) are likely to cause no complications at all, I suppose, while (2 + 4n) cycles (i.e. [2,] 6, 10, ...) will be difficult to see through.

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

As a matter of course, cycles in the game of cannot have odd-numbered lenths, as it takes two to tango.

"Sending three, returning one" above has three GENUINE moves, and needs an additional White "pass" to become a cycle. As a matter of course, White could play tenuki, instead, which might be evidence that we do not have a GENUINE cycle here.
Yes, you are right, this was the reason to choose "pseudo".

To give you another example:
You asked me to give my assessment of the sequence

ko-capture

pass

ko-capture

pass

pass
This sequence has a cycle-lenth of pseudo 6.
2 GENUINE moves + 4 pass.

I think that I will come back to your desire after having finished the "OPTIONAL triple-ko" issue.

Gérard TAILLE · Post by **Gérard TAILLE** » Thu Aug 26, 2021 12:09 pm

Cassandra wrote:
Gérard TAILLE wrote:
Cassandra wrote:
$$B
$$ +---------------+
$$ | . O . X O . . |
$$ | X O X X O . . |
$$ | . X X O O . . |
$$ | X X O , . . . |
$$ | O O O . O . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ +---------------+
Click Here To Show Diagram Code
[go]$$B $$ +---------------+ $$ | . O . X O . . | $$ | X O X X O . . | $$ | . X X O O . . | $$ | X X O , . . . | $$ | O O O . O . . | $$ | . . . . . . . | $$ | . . . . . . . | $$ +---------------+[/go]
##### "Two-eyed alive" world #####

The cycle-length pseudo 4 does not fulfill the condition

cl = 2 + 2n (n = 0, 1, 2, 3, ...).
I guess I missed something.
Could you clarify what is this condition you are referring to?
Is is due to fact that in "sending two return one" you have 3 plays and 1 pass?
Oh sorry, my German English. Probably "equation" would have been clearer, instead of "condition".

It is my current feeling, and I think it will be confirmed by Honte's walks, that length 2n cycles are fundamentally different from length (2 + 2n) cycles.
Length 2n cycles (i.e. 4, 8, 12, ...) are likely to cause no complications at all, I suppose, while (2 + 2n) cycles (i.e. [2,] 6, 10, ...) will be difficult to see through.

Oops don't you mean 2+4n or 4n cycles?

Cassandra · Post by **Cassandra** » Thu Aug 26, 2021 12:21 pm

Gérard TAILLE wrote:Oops don't you mean 2+4n or 4n cycles?

Thank you very much indeed for the clue. No wonder you couldn't understand the formula.

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

EDIT:
Just corrected the affected postings.

Gérard TAILLE · Post by **Gérard TAILLE** » Thu Aug 26, 2021 12:29 pm

Cassandra wrote:
Gérard TAILLE wrote:How can you define here a cycle and its length?
Thank you very much indeed for the examples, Gérard.

I am afraid you will have to keep your patience for a while, as at least District #4 lies between Honte and District #6.

And I "feel" that the Districts # 2n will have other properties than the Districts # 2 + 2n.
So, if you have any specific / special examples with a cycle-length of 4, which you would like to be examined here, please let me know.

Dear Thomas,

Just for curiosity here is an example of "cooperative" loop of length 4

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

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

I do not know if it could be of interest for you.

Cassandra · Post by **Cassandra** » Thu Aug 26, 2021 12:40 pm

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

Thank you for taking the time to search.

It's going to be difficult to put something like that into a status confirmation, right?

Please remember that the "mysterious" formations ALWAYS contain ko-shapes, usually three. Which is the main reason for their large variety and quantity.
3 ko means a cycle-length of at least 6.

But a cycle-length of 4 is impossible with a double-ko.

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