GT territory rules:: Honte's loops and cycles

Cassandra · **#21**

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 :wt:

outside the cycle. Black has three options now.

LEFT:
:bc:

captures into the remaining ko.
:wc:

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

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:
:bc:

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

MIDDLE:
:bt:

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 · **#22**

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? :razz:

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 · **#23**

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? :razz:

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 https://lifein19x19.com/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 :bc:

stone is dead
2) the :bt:

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]$$W pass, pass $$ +---------------+ $$ | O O . X . X O | $$ | 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 · **#24**

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 https://lifein19x19.com/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

Quote:

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 :bc:

stone is dead
2) the :bt:

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"
:ws:

"in-seki alive"
:wx:

"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
:et:

White territory

Quote:

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]$$W pass, pass $$ +---------------+ $$ | O O . X . X O | $$ | 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.

:b1:

= "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?"

:w2:

= "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?

:b3:

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

:b1:

= "pass",

= "pass" during "play" is complete nonsense (during status confirmation as well, BTW), as it has the same effect as :b1:

= ko-capture, :w2:

= ko-capture (capturing :b1:

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 · **#25**

Cassandra wrote:

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 · **#26**

Gérard TAILLE wrote:

Cassandra wrote:

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
:b1:

ko-capture
:w2:

pass

pass

ko-capture
:b5:

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 · **#27**

Cassandra wrote:

Gérard TAILLE wrote:

Cassandra wrote:

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 · **#28**

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 · **#29**

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 · **#30**

Gérard TAILLE wrote:

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.

Gérard TAILLE · **#31**

Cassandra wrote:

Gérard TAILLE wrote:

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.

Isn't it exactly the same sequence you showed with chosei?

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]

As a consequence, maybe the point is to exclude such sequence when our go knowledge tells us the sequence is stupid.

Gérard TAILLE · **#32**

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? :razz:

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").

What black group are you refering to?

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

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

Cassandra · **#33**

Gérard TAILLE wrote:

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

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

Very nice try!
If you did not succeed with option #1, just give option #2 a try. This will free you from the shackles you put on yourself. ;-)

Compare this matter here with the perhaps iterative process for identifying the "proper" borders under your GT territory rules.
Once you failed with claiming territory for a quite large composition of strings, you would try a smaller one, won't you?

Cassandra · **#34**

Gérard TAILLE wrote:

Isn't it exactly the same sequence you showed with chosei?

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]

Yes, but I am sure that you will not find many more of such positions.
This was the only one that I found in all the materials on rules that I looked into.

Quote:

As a consequence, maybe the point is to exclude such sequence when our go knowledge tells us the sequence is stupid.

No, under no circumstances!
Rulesets, general principles etc. must be able to handle supposedly nonsensical examples consistently.

However, as usual you are too impatient here. Honte cannot be everywhere at the same time. :razz:

Cassandra · **#35**

About compositions of three ko-shapes (contd)

##### OPTIONAL triple-ko cycles #2 #####

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

Let's add ONE EYE EACH to the GENUINE triple-ko.

Click Here To Show Diagram Code: [go]$$B $$ +---------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . ? ? ? ? S . . . . . . . | $$ | . . . . . . . ? O W . ? . . . . . . . | $$ | . . . , . . . ? . . X ? . . . , . . . | $$ | . ? ? ? ? S . ? ? ? ? S . ? ? ? ? S . | $$ | . ? O . . ? . . . . . . . ? . O . ? . | $$ | . ? . X B ? . . . . . . . ? B . X ? . | $$ | . ? ? ? ? S . . . . . . . ? ? ? ? S . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . ? ? ? ? S . . . . . . . ? ? ? ? S . | $$ | . ? W . O ? . . . . . . . ? . O W ? . | $$ | . ? . X . ? . . . . . . . ? X . . ? . | $$ | . ? ? ? ? S . . . . . . . ? ? ? ? S . | $$ | . . . . . . . ? ? ? ? S . . . . . . . | $$ | . . . , . . . ? . . O ? . . . , . . . | $$ | . . . . . . . ? X B . ? . . . . . . . | $$ | . . . . . . . ? ? ? ? S . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ +---------------------------------------+ $$ {AR M17 Q15} $$ {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]$$B $$ +---------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . Y . . . . . Q . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . ? ? ? ? S . . . . . . . ? ? ? ? S . | $$ | . ? W . . ? . . . . . . . ? . B O ? . | $$ | . ? . X X ? . . . . . . . ? X X . ? . | $$ | . ? ? ? ? S . . . . . . . ? ? ? ? S . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . Y . . . . . , . . . | $$ | . ? ? ? ? S . . . . . . . M M M M S . | $$ | . ? . . . ? . . . . . . . M . M O M . | $$ | . ? X X B ? . . . . . . . M X M . M . | $$ | . ? ? ? ? S . . . . . . . M M M M S . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . 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 :wt:

outside the cycle. Black has three options now.

LEFT:
:bc:

captures into the remaining ko.
:wc:

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

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:
:bc:

fills one of the three ko-shapes.
It remains a double-ko with one eye each.
This terminates the triple-ko, of course.

MIDDLE:
:bt:

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.

Gérard TAILLE · **#36**

Cassandra wrote:

Gérard TAILLE wrote:

Isn't it exactly the same sequence you showed with chosei?

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]

Yes, but I am sure that you will not find many more of such positions.
This was the only one that I found in all the materials on rules that I looked into.

Quote:

As a consequence, maybe the point is to exclude such sequence when our go knowledge tells us the sequence is stupid.

No, under no circumstances!
Rulesets, general principles etc. must be able to handle supposedly nonsensical examples consistently.

However, as usual you are too impatient here. Honte cannot be everywhere at the same time. :razz:

Surely I am impatient Thomas, I agree. ;-)

My point is only to say that through all your districts (4, 6, 8 etc.) you will encounter more and more cooperative stupid loops, with or without ko
Here an example in district 6 with one ko and two pass

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

Click Here To Show Diagram Code: [go]$$W pass, pass $$ +-------------- $$ | 6 3 X O . . . $$ | 1 X X O . . . $$ | 5 X O O . . . $$ | X X O O . . . $$ | O O O . . . . $$ | . . . . . . . $$ | . . . . . . .[/go]

Cassandra · **#37**

Gérard TAILLE wrote:

Click Here To Show Diagram Code: [go]$$W pass, pass $$ +-------------- $$ | 6 3 X O . . . $$ | 1 X X O . . . $$ | 5 X O O . . . $$ | X X O O . . . $$ | O O O . . . . $$ | . . . . . . . $$ | . . . . . . .[/go]

I'm not as sure about that as you are.

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

A Black move at the shadowed point is forbidden by the rules!

Gérard TAILLE · **#38**

Cassandra wrote:

Gérard TAILLE wrote:

Click Here To Show Diagram Code: [go]$$W pass, pass $$ +-------------- $$ | 6 3 X O . . . $$ | 1 X X O . . . $$ | 5 X O O . . . $$ | X X O O . . . $$ | O O O . . . . $$ | . . . . . . . $$ | . . . . . . .[/go]

I'm not as sure about that as you are.

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

A Black move at the shadowed point is forbidden by the rules!

Oops, I have to add one liberty:

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

That's better isn't it?

Cassandra · **#39**

Gérard TAILLE wrote:

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

That's better isn't it?

NO.

The sequence you used during status confirmation to prove that Black will be unable to establish a PERMANENT "two-eye-formation", is NOT a FORCING one. Black might find a variation that suits him much more.

In the "two-eyed alive" world, the last move of an uninterrupted cycle is forbidden (better at the moment: "is likely to become forbidden for EVERY kind of cycle"). Therefore, all of Black's stones will become captured by White. Same, but much more obvious, effective result as within your "GT territory rules" world.

Cassandra · **#40**

About compositions of three ko-shapes (contd)

##### ASYMMETRICAL triple-ko cycles #1 #####

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

Let's add ONE EYE to ONLE ONE of the GENUINE triple-ko's groups.

Click Here To Show Diagram Code: [go]$$B Status assessment for BLACK groups $$ +---------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . ? ? ? ? S . . . . . . . | $$ | . . . . . . . ? O W . ? . . . . . . . | $$ | . . . , . . . ? . . X ? . . . , . . . | $$ | . ? ? ? ? S . ? ? ? ? ? . ? ? ? ? S . | $$ | . ? O . . ? . . . . . . . ? . O . ? . | $$ | . ? . X B ? . M M M M M . ? B . X ? . | $$ | . ? ? ? ? ? . M . . . M . ? ? ? ? ? . | $$ | . . . . . . . M X X X M . . . . . . . | $$ | . . . , . . . M M M M M . . . , . . . | $$ | . ? ? ? ? S . . . . . . . ? ? ? ? S . | $$ | . ? W . O ? . . . Q . . . ? . O W ? . | $$ | . ? . X . ? . . . . . . . ? X . . ? . | $$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . | $$ | . . . . . . . ? ? ? ? S . . . . . . . | $$ | . . . , . . . ? . . O ? . . . , . . . | $$ | . . . . . . . ? X B . ? . . . . . . . | $$ | . . . . . . . ? ? ? ? ? . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ +---------------------------------------+ $$ {AR M17 Q15} $$ {AR Q12 Q9} $$ {AR Q6 M3} $$ {AR H3 D6} $$ {AR D9 D12} $$ {AR D15 H17} $$ {AR E12 J8} $$ {AR K5 K7} $$ {AR P12 L8} $$ {AR E11 F10} $$ {AR F12 G11} $$ {AR J5 J6} $$ {AR L5 L6} $$ {AR O12 N11} $$ {AR P11 O10} $$ {AR K9 K10}[/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, WHITE is unable to leave the cycle shown (symbolised by the "triple-arrows").

As you can probably imagine, Black's point of view will be shown in separate diagrams.

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

Click Here To Show Diagram Code: [go]$$B Status assessment for WHITE groups $$ +---------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . ? ? ? ? S . . . . . . . | $$ | . . . . . . . ? O W . ? . . . . . . . | $$ | M M M M . . . ? . . X ? . . . M M M M | $$ | M ? ? ? ? S M ? ? ? ? ? M ? ? ? ? S M | $$ | M ? O . . ? M . . . . . M ? . O . ? M | $$ | M ? . X B ? M . . Y . . M ? B . X ? M | $$ | M ? ? ? ? ? M . . . . . M ? ? ? ? ? M | $$ | M M M . M M . ? ? ? ? S . M M . M M M | $$ | . . . , . . . ? O O . ? . . . , . . . | $$ | . ? ? ? ? S . ? . . X ? . ? ? ? ? S . | $$ | . ? W . O ? . ? ? ? ? ? . ? . O W ? . | $$ | . ? . X . ? . c o n t d . ? X . . ? . | $$ | . ? ? ? ? ? . M M M M M . ? ? ? ? ? . | $$ | . . . . . . M ? ? ? ? S M . . . . . . | $$ | . . . , . . . ? . . O ? . . . , . . . | $$ | . . . . . . M ? X B . ? M . . . . . . | $$ | . . . . . . 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} $$ {AR J15 J14} $$ {AR K15 K14} $$ {AR L15 L14} $$ {AR K12 K11}[/go]

This diagram shows a triple-ko cycle that is similar to the GENUINE one.
Black already knows that White will be unable to leave the cycle.
The marked stones are those that have been played last.

Contrary to White, BLACK is free to leave the cycle shown (symbolised by the "triple-arrow").
This exit can be taken at every position of the cycle. We chose the upper one for an exemplary case.

Click Here To Show Diagram Code: [go]$$B Status assessment for WHITE groups $$ +---------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . . | $$ | . ? ? ? ? S . . . . . . . . . . . . . | $$ | . ? O O . ? . . . Y . . . . . . . . . | $$ | . ? . . X ? . . . , . . . . . , . . . | $$ | . ? ? ? ? ? . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . m i r r d . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . Q . . . . . . . . . . . . . . . | $$ | . . . , . . . . . Q . . . . . , . . . | $$ | . ? ? ? ? S . . . . . . . . . . . . . | $$ | . ? . O O ? . . . . . . . . . . . . . | $$ | . ? B . . ? . . . . . . . . . . . . . | $$ | . ? ? ? ? ? . . . . . . . . . . . . . | $$ | . ? ? ? ? S . . . . . . . . . . . . . | $$ | . ? O O W ? . M M M M M . . . , . . . | $$ | . ? . . . ? . M e n d M . . . . . . . | $$ | . ? ? ? ? ? . M M M M M . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ +---------------------------------------+ $$ {AR K16 F3} $$ {AR D5 D6} $$ {AR D9 D10} $$ {AR D12 D13} $$ {AR D14 D15} $$ {AR J19 J18} $$ {AR K19 K18} $$ {AR L19 L18} $$ {AR C18 C19} $$ {AR D18 D19} $$ {AR E18 E19} $$ {AR K16 K11} $$ {AR K9 K4}[/go]

Black plays :bt:

outside the cycle. White has two options now.

LEFT:
:wc:

captures into the remaining ko.
:bc:

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

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

MIDDLE:
:wt:

is played outside the triple-ko.
This is a clear sign that White 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.

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

The presentation of the entire ASYMMETRICAL triple-ko cycle #1 might look like the following diagram.

Click Here To Show Diagram Code: [go]$$Bc $$ +---------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . ? ? ? ? S . . . . . . . | $$ | . . . . . . . ? O W . ? . . . . . . . | $$ | M M M M . . . ? . . X ? . . . M M M M | $$ | M ? ? ? ? S M ? ? ? ? ? M ? ? ? ? S M | $$ | M ? O . . ? M . . . . . M ? . O . ? M | $$ | M ? . X B ? M . . . . . M ? B . X ? M | $$ | M ? ? ? ? ? M . ? ? ? . M ? ? ? ? ? M | $$ | M M M . M M . . ? ? ? . . M M . M M M | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . ? ? ? ? S . . . . . . . ? ? ? ? S . | $$ | . ? W . O ? . . . . . . . ? . O W ? . | $$ | . ? . X . ? . . . . . . . ? X . . ? . | $$ | . ? ? ? ? ? . M M M M M . ? ? ? ? ? . | $$ | . . . . . . M ? ? ? ? S M . . . . . . | $$ | . . . , . . . ? . . O ? . . . . . . . | $$ | . ? ? ? . . M ? X B . ? M . . ? ? ? . | $$ | . ? ? ? . . 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} $$ {AR J15 K12} $$ {AR D6 C3} $$ {AR C3 C6} $$ {AR R6 R3} $$ {AR R3 Q6} $$ {AR K12 L15}[/go]

You will easily realise that White is hindered to leave the cycle, while Black can do so whenever and as often as he likes.

GT territory rules:: Honte's loops and cycles

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