GT territory rules:: Honte's loops and cycles

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

Post by Gérard TAILLE »

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.
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Gérard TAILLE
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Re: GT territory rules:: Honte's loops and cycles

Post by Gérard TAILLE »

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

Post by Cassandra »

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]
:lol: :lol: :lol:

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?
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)
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Re: GT territory rules:: Honte's loops and cycles

Post by Cassandra »

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.
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:
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)
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Re: GT territory rules:: Honte's loops and cycles

Post by Cassandra »

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.
Last edited by Cassandra on Thu Aug 26, 2021 11:42 pm, edited 2 times in total.
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)
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Gérard TAILLE
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Re: GT territory rules:: Honte's loops and cycles

Post by Gérard TAILLE »

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.
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 :b2: pass, :b4: pass
$$ +--------------
$$ | 6 3 X O . . .
$$ | 1 X X O . . .
$$ | 5 X O O . . .
$$ | X X O O . . .
$$ | O O O . . . .
$$ | . . . . . . .
$$ | . . . . . . .[/go]
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Cassandra
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Re: GT territory rules:: Honte's loops and cycles

Post by Cassandra »

Gérard TAILLE wrote:
Click Here To Show Diagram Code
[go]$$W :b2: pass, :b4: pass
$$ +--------------
$$ | 6 3 X O . . .
$$ | 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 :b6: 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!
:D
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)
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Gérard TAILLE
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Re: GT territory rules:: Honte's loops and cycles

Post by Gérard TAILLE »

Cassandra wrote:
Gérard TAILLE wrote:
Click Here To Show Diagram Code
[go]$$W :b2: pass, :b4: pass
$$ +--------------
$$ | 6 3 X O . . .
$$ | 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 :b6: 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!
:D
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? :D :D :D
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Cassandra
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Re: GT territory rules:: Honte's loops and cycles

Post by Cassandra »

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? :D :D :D
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.
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)
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Re: GT territory rules:: Honte's loops and cycles

Post by Cassandra »

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.
[/color]
Last edited by Cassandra on Fri Aug 27, 2021 6:52 am, edited 1 time in total.
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)
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Re: GT territory rules:: Honte's loops and cycles

Post by Gérard TAILLE »

Cassandra wrote:
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? :D :D :D
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.
Yes, though this loop may be build in theory, I said myself this loop is quite stupid and I am confident that in your "two-eyed alive" world such loop will never take place.
By the way the sequence itself may be not stupid and might be good in normal play but only as a sequence played only one time (I mean not forever in a real loop).

When you say "the last move of an uninterrupted cycle is forbidden" does that mean that it is superko rule? You have first to identify that a loop occurs and then you forbid one move in the cycle. It is exactly the job of a superko rule isn't it?
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Re: GT territory rules:: Honte's loops and cycles

Post by Cassandra »

About compositions of three ko-shapes (contd)


##### ASYMMETRICAL 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 C ? ?
$$ ? ? O O O O O O O ? ? ?
$$ ? ? ? ? ? ? ? ? ? ? ? ?
$$ ? ? ? ? ? ? ? ? ? ? ? ?[/go]
Let's add ONE EYE to ONLE ONE of the GENUINE triple-ko's groups, as well as a SHARED liberty.
Click Here To Show Diagram Code
[go]$$B
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . ? ? ? ? S . . . . . . . |
$$ | . . . . . . . ? O W . ? . . . . . . . |
$$ | . . . , . . . ? . . X C . . . , . . . |
$$ | . ? ? ? ? S . ? ? ? ? ? . ? ? ? ? S . |
$$ | . ? O . . ? . . . . . . . ? . O . ? . |
$$ | . ? . X B C . . . . . . . ? B . X C . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . : . . . . . , . . . |
$$ | . ? ? ? ? S . . . . . . . ? ? ? ? S . |
$$ | . ? W . O ? . . . . . . . ? . O W ? . |
$$ | . ? . X . C . . . . . . . ? X . . C . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . . . . . . . ? ? ? ? S . . . . . . . |
$$ | . . . , . . . ? . . O ? . . . , . . . |
$$ | . . . . . . . ? X B . C . . . . . . . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+
$$ {AR M17 Q15}
$$ {AR Q12 Q9}
$$ {AR D9 D12}
$$ {AR D15 H17}
$$ {AR Q6 M3}
$$ {AR J2 J1}
$$ {AR K2 K1}
$$ {AR L2 L1}
$$ {AR H3 D6}[/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 of a status assessment for a Black group first.

--------------------------------------------
Click Here To Show Diagram Code
[go]$$B Status assessment for BLACK groups
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . Y . . . . . Q . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . ? ? ? ? S . . . . . . . ? ? ? ? S . |
$$ | . ? W . . ? . . . . . . . ? . . O ? . |
$$ | . ? . X X C . . . . . . . ? X X . B . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . Y . . . . . , . . . |
$$ | . ? ? ? ? S . . . . . . . ? ? ? ? S . |
$$ | . ? . . . ? . . . . . . . ? . . O ? . |
$$ | . ? X X B C . . . . . . . ? X X . ? . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . . . . . . . . . . . . . a s y m m . |
$$ | . . . , . . . M M M M M . . o n e . . |
$$ | . . . . . . . M e n d M . . . . . . . |
$$ | . . . . . . . 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}
$$ {AR F14 O13}
$$ {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:
-- option 1: is 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.
-- option 2: occupies the SHARED liberty, creating the MIRRORED version of RIGHT.
This option is the ADVISABLE one.

RIGHT:
:bc: occupies the SHARED liberty.
This exits to ASYMMETRICAL triple-ko cycles #1.
This option is the ADVISABLE one.

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.

--------------------------------------------
Click Here To Show Diagram Code
[go]$$Bc Status assessment for WHITE groups
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . ? ? ? ? S . . . . . . . |
$$ | . . . . . . . ? O W . ? . . . . . . . |
$$ | . . . . . . . ? . . X C . . . . . . . |
$$ | . ? ? ? ? S . ? ? ? ? ? . ? ? ? ? S . |
$$ | . ? O . . ? . ? ? ? ? S . ? . O . ? . |
$$ | . ? . X B C . ? O O . ? . ? B . X C . |
$$ | . ? ? ? ? ? . ? . . X B . ? ? ? ? ? . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . , . . . ? ? ? ? S . . . , . . . |
$$ | . ? ? ? ? S . ? O O . ? . ? ? ? ? S . |
$$ | . ? W . O ? . ? . . X ? . ? . O W ? . |
$$ | . ? . X . C . ? ? ? ? ? . ? X . . C . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . . . . . . . ? ? ? ? S . . . . . . . |
$$ | . . . , . . . ? . . O ? . . . , . . . |
$$ | . . . . . . . ? X B . ? . . . . . . . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+
$$ {AR M17 Q15}
$$ {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 K11 K10}
$$ {AR J11 J10}
$$ {AR L11 L10}[/go]
:bc:
-- option 1: occupies the SHARED liberty.
This exits to ASYMMETRICAL triple-ko cycles #1.
This option is the ADVISABLE one.
-- option 2: (not displayed in the diagram for the sake of clarity) is played outside the triple-ko cycle.
White will capture into the remaining ko-shape, effectively returning to the main diagram of ASYMMETRICAL triple-ko cycles #2, as is shown with LEFT for the status assessement for WHITE groups (with colours interchanged).

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

The presentation of the entire ASYMMETRICAL triple-ko cycle #2 might look like the following diagram.
Click Here To Show Diagram Code
[go]$$W
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . ? ? ? ? S . . . . . . . |
$$ | . . . . . . . ? O W . ? . . . . . . . |
$$ | M M M M . . . ? . . X ? . . . M M M M |
$$ | M ? ? ? ? S M ? ? ? ? ? M ? ? ? ? S M |
$$ | M ? O . . ? M . . . . . M ? . O . ? M |
$$ | M ? . X B ? 1 . . . . . 1 ? B . X ? M |
$$ | M ? ? ? ? ? . . ? ? ? . . ? ? ? ? ? M |
$$ | M M M . M M . . ? ? ? . . M M . M M M |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . ? ? ? ? S . . . . . . . ? ? ? ? S . |
$$ | . ? W . O ? . . . . . . . ? . O W ? . |
$$ | . ? . X . ? . . . . . . . ? X . . ? . |
$$ | . ? ? ? ? ? . M . 1 . 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}
$$ {AR F13 J11}
$$ {AR J11 F12}
$$ {AR O13 L11}
$$ {AR L11 O12}
$$ {AR J5 K11}
$$ {AR K11 L5}[/go]
You will easily have realised that White can leave the cycle ONLY ONCE, while Black can do so whenever and as often as he likes.
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)
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Re: GT territory rules:: Honte's loops and cycles

Post by Cassandra »

Gérard TAILLE wrote:When you say "the last move of an uninterrupted cycle is forbidden" does that mean that it is superko rule? You have first to identify that a loop occurs and then you forbid one move in the cycle. It is exactly the job of a superko rule isn't it?
You are free to name is as you like to do, especially if this aids your understanding.

A cycle is a cycle, regardless of whether a ko-shape is involved or a "pass" is played in it.

It's completely the same with your "GT territory rules".
You would have to play the cycle through (at least once) to realise that there had been a ko-capture before a "pass", won't you?
Additionally, you would have to realise (depends on the position in question), whether passing instead of continuing with the cycle forever (might be simpler at first sight) was a valid option for any of the players.
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)
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Re: GT territory rules:: Honte's loops and cycles

Post by Cassandra »

Honte's magic DOUBLE-KO spell


To introduce this topic, let's use a reminiscence of "Who Wants to Be a Billionaire?"

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

Question: What is a DOUBLE-KO during play?

Answer option A: A tool that aims to triple the remaining length of the game.
Answer option B: A tool that aims to significantly complicate the subsequent status confirmation.
Answer option C: A tool to prevent to opponent from closing another ko-shape on the board.
Answer option D: Simply nonsense.

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

Question: What is a DOUBLE-KO during status confirmation?

Answer option A: A tool to prevent to opponent from closing another ko-shape on the board.
Answer option B: Simply useless.
Answer option C: A position on the board that significantly complicates the matter.
Answer option D: A tool that aims to triple the remaining length of the status complication.

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

What do you choose?
(All of your jokers have already been used up.)
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)
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Re: GT territory rules:: Honte's loops and cycles

Post by Gérard TAILLE »

Cassandra wrote:Honte's magic DOUBLE-KO spell


To introduce this topic, let's use a reminiscence of "Who Wants to Be a Billionaire?"

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

Question: What is a DOUBLE-KO during play?

Answer option A: A tool that aims to triple the remaining length of the game.
Answer option B: A tool that aims to significantly complicate the subsequent status confirmation.
Answer option C: A tool to prevent to opponent from closing another ko-shape on the board.
Answer option D: Simply nonsense.

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

Question: What is a DOUBLE-KO during status confirmation?

Answer option A: A tool to prevent to opponent from closing another ko-shape on the board.
Answer option B: Simply useless.
Answer option C: A position on the board that significantly complicates the matter.
Answer option D: A tool that aims to triple the remaining length of the status complication.

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

What do you choose?
(All of your jokers have already been used up.)
:D :D :D
During play:
Option A is true ;-) Depending of the way time is handled it could be a way to gain time ;-)
Option B does not exist because it is already the option C listed under status confirmation phase
Option C is also true. Depending of the circumtances this double may also allow to reach a NO RESULT game
Option D is true if a player plays in the double ko though the opponent did not take a ko elsewhere.

Additionnal option: a tool allowing to request on infinite number of resumptions with each time a real play on the board!

For status confirmation it is highly dependant of this status confirmation : pass-ko used, independancy of the areas via local-2 or other means ...
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