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 Post subject: GT territory rules:: Honte's loops and cycles
Post #1 Posted: Mon Aug 23, 2021 1:25 pm 
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Gérard TAILLE wrote:
Cassandra wrote:
Gérard TAILLE wrote:
I understand Cassandra and I agree with you for "simple" 3 kos positions. I just try to be more general, including position with 4 kos in which it is difficult to identify what the length of a cycle could be. In my GT rule I would like to take into all types of loops and not only 3 kos positions.

If you had a concrete example with 4 ko available, we could discuss this issue deeper ...


Yes OC here is an example:

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


Oops it does not seem to be the best example, I will try to find another. At least you can just try to identify what you mean by length of a cycle.


This is a copy of Gérard's posting https://lifein19x19.com/viewtopic.php?p=266800#p266800 in his thread "GT territory rules".

I intend to use this seperate thread for presenting / discussing what I "feel" might be a potential simplification for Gérard's new concept of an "advantageous loop". It may help to keep track of the other issues in Gérard's rules thread if part of the discussion is separated.
These ideas will be also valuable for the "two-eyed alive" world.

You may be wondering why the title of this thread mentions "Honte".
Honte is my labrador, four years old.
Going for a walk with Honte is not a special mental effort, as he is allowed to decide for himself how it goes. I'm sure his nose is way better than mine :razz:
As a rule, I'm only the one who holds the other end of the dog leash in my hands.
The biggest advantage of this approach: Honte can't complain to me after the walk, it would have been boring. :razz:

Another advantage: Unfinished thoughts can circulate freely and easily.

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The really most difficult Go problem ever: http://igohatsuyoron120.de/index.htm
Igo Hatsuyoron #120 (still unresolved by professionals, maybe solved by four amateurs)

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 Post subject: Re: GT territory rules:: Honte's loops and cycles
Post #2 Posted: Mon Aug 23, 2021 11:35 pm 
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Let's try to clarify some technical terms first.


Technical term "Loop"

Click Here To Show Diagram Code
[go]$$B Loop
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . X . . . . |
$$ | . O . . . . . O . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . X . . . . . X . |
$$ | . . . . O . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ +-------------------+
$$ {AR F8 G7}
$$ {AR H6 H5}
$$ {AR G4 F3}
$$ {AR D3 C4}
$$ {AR B5 B6}
$$ {AR C7 D8}[/go]

A loop of moves, once started, has no end. It's like walking on the circumference of a circle.


Technical term "Cycle"

Click Here To Show Diagram Code
[go]$$B Cycle #1
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . 1 . . . . |
$$ | . 6 . . . . . 2 . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . 5 . . . . . 3 . |
$$ | . . . . 4 . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ +-------------------+
$$ {AR F8 G7}
$$ {AR H6 H5}
$$ {AR G4 F3}
$$ {AR D3 C4}
$$ {AR B5 B6}[/go]

A cycle is one complete run through the loop.
The diagram shows the first walk on the complete circumference of a circle. We get infinitely close to the starting point without reaching it.

Click Here To Show Diagram Code
[go]$$Bm7 Cycle #2
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . 1 . . . . |
$$ | . 6 . . . . . 2 . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . 5 . . . . . 3 . |
$$ | . . . . 4 . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ +-------------------+
$$ {AR F8 G7}
$$ {AR H6 H5}
$$ {AR G4 F3}
$$ {AR D3 C4}
$$ {AR B5 B6}[/go]

A tiny additional jump brought us to the initial starting point. It follows the second walk on the complete cirumfence.
Ad infinitum ...


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

In addition, we need to be aware that we are in the STATUS CONFIRMATION phase.

In Gérard's territorial rules, the status confirmation is a two-step procedure that is a composition of
-- identifying the inside and outside borders of a specific area of the board, and
-- trying to establish a group with two eyes inside the borders of the area (of the colour of the inside border) in order to determine "territory".

In my (still incomplete) "two-eyed alive" world, the status confirmation is also a two-step procedure, but which is the composition of
-- identifying the life-and-death status of every single group individually (being able to achieve two eyes is also the decicive criterion here)
-- combining the results of these status confirmations in order to determine "territory".

The results (measured in "is territory") of both procedures will be identical in the overwhelming majority of cases. But there remain a few (very) exotic exceptions.


Please remember that status confirmation is a "YES / NO" issue only. NO enclosed points on the board are counted (but to identify eye points), as well as captured stones of the opponent.

Thus, while walking through the loop, the number of captured stones is IRRELEVANT.

Quite the contrary during ACTUAL PLAY, when captured stones have a value, of course.
During actual play, ...

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

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

:b2: captures TWO stones

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

:w3: captures ONE stone

Click Here To Show Diagram Code
[go]$$W :b4: pass
$$ +---------------+
$$ | . X X O . O X |
$$ | X . O . O O X |
$$ | X X X O O X X |
$$ | O O O X X X . |
$$ | . . O . . X . |
$$ | O O O . . X . |
$$ | . . O . . X . |
$$ +---------------+[/go]

... would be NO loop, but an (did not find another wording) "isomorphic repetition".
The position on the board is the same as four moves before, but the status of the entire game is NOT identical, as the difference of the prisoner counts has changed.
It's similar to observing the walk on the line of a car's shock absorber from above. Looks the same like walking on a circle first, but at a forthcoming moment in time, the wanderer will fall down.

Such "isomorphic repetitions" would NOT be performed forever during actual play, while GENUINE loops (like a solidly connected triple-ko) are likely to result in "no result" for the game.

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The really most difficult Go problem ever: http://igohatsuyoron120.de/index.htm
Igo Hatsuyoron #120 (still unresolved by professionals, maybe solved by four amateurs)

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 Post subject: Re: GT territory rules:: Honte's loops and cycles
Post #3 Posted: Tue Aug 24, 2021 2:45 am 
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Honte just returned from a walk ... :razz:


Loops with a cycle-length of 2

Let's put the basic-ko rule (which per se is a rule for actual play, by the way) aside for a while, and try to find out whether the systematic is consistent.

Basically, I will leave GT's border issue aside as well as the question of which single group the life-and-death status is currently examined.

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

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

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

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

We have reached the starting position. The cycle has a length of 2.


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

Click Here To Show Diagram Code
[go]$$W :w3: :b4: pass
$$ +---------------+
$$ | . O . X X O . |
$$ | O O O X X O . |
$$ | X O X 5 X O . |
$$ | X O O X X O . |
$$ | X X X O O O O |
$$ | . . X X X X X |
$$ | . . . . . . . |
$$ +---------------+[/go]

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

Click Here To Show Diagram Code
[go]$$W :w7: :b8: pass
$$ +---------------+
$$ | . O . X X O . |
$$ | O O O X X O . |
$$ | X O X . X O . |
$$ | X O O X X O . |
$$ | X X X O O O O |
$$ | . . X X X X X |
$$ | . . . . . . . |
$$ +---------------+[/go]

Ad infinitum...
=> White can pass forever.


Variation:

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

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

Black cannot prevent this.
=> White has a loop.


Next run:

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

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

A Black move at the shadowed point is forbidden, as White would pass thereafter.

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

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

White created a two-eye formation in the upper part of the board.
=> NO Black territory

For the status assessment of White's group, Black can only pass for his first move, as he does not want to play a self-atari.
Thereafter, the same sequences as above would apply.
=> White's territory


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

The cycle-length 2 fulfills the condition

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

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


Next run:

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

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

A Black move at the shadowed point is forbidden, as this was the move that completed the cycle.

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

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

White captured all of Black's stones permanently.
=> Black's group is neither "two-eyed alive" nor "in-seki alive".

For the status assessment of White's group, Black can only pass for his first move, as he does not want to play a self-atari.
Thereafter, the same sequences as above would apply.
White created a two-eye formation.
=> White's group is "two-eyed alive".


After the status assessment for all groups has been completed:

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

There is no Black "two-eyed alive" group inside the (upper) part of the board, which is fully enclosed by White's "two-eyed alive" group.
=> White's territory.

_________________
The really most difficult Go problem ever: http://igohatsuyoron120.de/index.htm
Igo Hatsuyoron #120 (still unresolved by professionals, maybe solved by four amateurs)


Last edited by Cassandra on Thu Aug 26, 2021 12:22 pm, edited 1 time in total.
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 Post subject: Re: GT territory rules:: Honte's loops and cycles
Post #4 Posted: Tue Aug 24, 2021 6:18 am 
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Loops with a cycle-length of 2 (contd)


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 |
$$ | X O X 1 X O O |
$$ | X O O X X O . |
$$ | X X X O O O O |
$$ | . . X X X O . |
$$ | . . X . X O . |
$$ +---------------+[/go]

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

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]

We have reached the starting position. The cycle has a length of 2.


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

Click Here To Show Diagram Code
[go]$$W :w3: :b4: pass
$$ +---------------+
$$ | . O . X . X O |
$$ | O O O X X X O |
$$ | X O X 5 X O O |
$$ | 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 |
$$ | X O 6 . X O O |
$$ | 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]$$W :w7: :b8: pass
$$ +---------------+
$$ | . O . X . X O |
$$ | O O O X X X O |
$$ | X O X 9 X O O |
$$ | X O O X X O . |
$$ | X X X O O O O |
$$ | . . X X X O . |
$$ | . . X . X O . |
$$ +---------------+[/go]

Ad infinitum...
=> White can pass forever.


Variation #1:

Click Here To Show Diagram Code
[go]$$W
$$ +---------------+
$$ | . O 6 X . X O |
$$ | 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]

Click Here To Show Diagram Code
[go]$$W
$$ +---------------+
$$ | . O X X 7 X O |
$$ | 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]

Black cannot prevent this.
=> White has a loop.


Variation #2:

Click Here To Show Diagram Code
[go]$$W :b6: pass
$$ +---------------+
$$ | . O . X . X O |
$$ | 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]

Click Here To Show Diagram Code
[go]$$W :w7: :b8: pass
$$ +---------------+
$$ | . O . X . X O |
$$ | 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]

If might be a good practical idea to have the status assessment ending here.

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


But let's continue for the sake of completeness, and clarity.

Click Here To Show Diagram Code
[go]$$W :w9: :b10: pass
$$ +---------------+
$$ | . O . X . X O |
$$ | 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]

Ad infinitum...
Black cannot prevent this.
=> White has a loop.


Next run:

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]

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 forever, as White would pass after its very first appearance.

Click Here To Show Diagram Code
[go]$$W :b4: pass
$$ +---------------+
$$ | . O 3 X 5 X O |
$$ | 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]

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

White created a two-eye formation in the upper part of the board.
=> NO Black territory

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

The position is symmetrical, so there will be
=> NO White territory
in the upper part of the board as well.


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

The cycle-length 2 fulfills the condition

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

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


Next run:

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]

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.

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.

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 position is symmetrical, so the result of the status assessment of White's group at the top will also be
=> White's group is "in-seki alive".

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

After the status assessment for all groups has been completed:

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

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

_________________
The really most difficult Go problem ever: http://igohatsuyoron120.de/index.htm
Igo Hatsuyoron #120 (still unresolved by professionals, maybe solved by four amateurs)


Last edited by Cassandra on Thu Aug 26, 2021 12:23 pm, edited 1 time in total.
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 Post subject: Re: GT territory rules:: Honte's loops and cycles
Post #5 Posted: Tue Aug 24, 2021 8:00 am 
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Cassandra wrote:
Let's try to clarify some technical terms first.


Technical term "Loop"

Click Here To Show Diagram Code
[go]$$B Loop
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . X . . . . |
$$ | . O . . . . . O . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . X . . . . . X . |
$$ | . . . . O . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ +-------------------+
$$ {AR F8 G7}
$$ {AR H6 H5}
$$ {AR G4 F3}
$$ {AR D3 C4}
$$ {AR B5 B6}
$$ {AR C7 D8}[/go]

A loop of moves, once started, has no end. It's like walking on the circumference of a circle.


Technical term "Cycle"

Click Here To Show Diagram Code
[go]$$B Cycle #1
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . 1 . . . . |
$$ | . 6 . . . . . 2 . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . 5 . . . . . 3 . |
$$ | . . . . 4 . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ +-------------------+
$$ {AR F8 G7}
$$ {AR H6 H5}
$$ {AR G4 F3}
$$ {AR D3 C4}
$$ {AR B5 B6}[/go]

A cycle is one complete run through the loop.
The diagram shows the first walk on the complete circumference of a circle. We get infinitely close to the starting point without reaching it.

Click Here To Show Diagram Code
[go]$$Bm7 Cycle #2
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . 1 . . . . |
$$ | . 6 . . . . . 2 . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . 5 . . . . . 3 . |
$$ | . . . . 4 . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ +-------------------+
$$ {AR F8 G7}
$$ {AR H6 H5}
$$ {AR G4 F3}
$$ {AR D3 C4}
$$ {AR B5 B6}[/go]

A tiny additional jump brought us to the initial starting point. It follows the second walk on the complete cirumfence.
Ad infinitum ...


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

In addition, we need to be aware that we are in the STATUS CONFIRMATION phase.

In Gérard's territorial rules, the status confirmation is a two-step procedure that is a composition of
-- identifying the inside and outside borders of a specific area of the board, and
-- trying to establish a group with two eyes inside the borders of the area (of the colour of the inside border) in order to determine "territory".

In my (still incomplete) "two-eyed alive" world, the status confirmation is also a two-step procedure, but which is the composition of
-- identifying the life-and-death status of every single group individually (being able to achieve two eyes is also the decicive criterion here)
-- combining the results of these status confirmations in order to determine "territory".

The results (measured in "is territory") of both procedures will be identical in the overwhelming majority of cases. But there remain a few (very) exotic exceptions.


Please remember that status confirmation is a "YES / NO" issue only. NO enclosed points on the board are counted (but to identify eye points), as well as captured stones of the opponent.

Thus, while walking through the loop, the number of captured stones is IRRELEVANT.

Quite the contrary during ACTUAL PLAY, when captured stones have a value, of course.
During actual play, ...

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

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

:b2: captures TWO stones

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

:w3: captures ONE stone

Click Here To Show Diagram Code
[go]$$W :b4: pass
$$ +---------------+
$$ | . X X O . O X |
$$ | X . O . O O X |
$$ | X X X O O X X |
$$ | O O O X X X . |
$$ | . . O . . X . |
$$ | O O O . . X . |
$$ | . . O . . X . |
$$ +---------------+[/go]

... would be NO loop, but an (did not find another wording) "isomorphic repetition".
The position on the board is the same as four moves before, but the status of the entire game is NOT identical, as the difference of the prisoner counts has changed.
It's similar to observing the walk on the line of a car's shock absorber from above. Looks the same like walking on a circle first, but at a forthcoming moment in time, the wanderer will fall down.

Such "isomorphic repetitions" would NOT be performed forever during actual play, while GENUINE loops (like a solidly connected triple-ko) are likely to result in "no result" for the game.


Dear Thomas,

This new thread is very interesting ideed. We will see that a great variety of loops may exist and, as a consequence, we have a lack of word: the word "loop" may quite restricted or quite large, the words "cycle" and "isomorphic repetitions" may also be quite unclear.
So let's try to discuss.

Let's take first your definition of a loop. The wording you propose is the following:
A loop of moves, once started, has no end.
This wording seems not that clear.

First of all you use the word "move" but a "move" may be either a "play" or a "pass".
=> it is not quite clear if your definition exclude a sequence of three successive passes in the loop.
OC I understand that "has no end" means probably "no three successive passes" but it could not be clear for all readers.

Click Here To Show Diagram Code
[go]$$W :b4: pass
$$ +---------------+
$$ | . X X O . O X |
$$ | X 1 3 2 O O X |
$$ | X X X O O X X |
$$ | O O O X X X . |
$$ | . . O . . X . |
$$ | O O O . . X . |
$$ | . . O . . X . |
$$ +---------------+[/go]

Secondly the sequence [ :w1: :b2: :w3: :b4: pass]* repeated ad infinitum is a "loop" according strictly to your definition (no end). You prefer saying that it is not a loop but an "isomorphic repetition". Fine but that means that the wording
A loop of moves, once started, has no end.
is not quite clear.
As fas as I am concerned I do not have really a problem with the wording "loop" also in this case.

BTW do you suggest a defintion of a "loop" in normal play (taking into account the prisoners?) and another defintion of a loop in confirmation phase?

Thirdly, taking a basic ko and the basic corresponding ko ban, is the sequence
[ :b1: capture ko, :w2: pass, :b3: pass, :w4: capture ko, :b5: pass, :w6: pass]* ad infinitum a loop?

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 Post subject: Re: GT territory rules:: Honte's loops and cycles
Post #6 Posted: Tue Aug 24, 2021 9:52 am 
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Gérard TAILLE wrote:
Dear Thomas,

This new thread is very interesting ideed. We will see that a great variety of loops may exist and, as a consequence, we have a lack of word: the word "loop" may quite restricted or quite large, the words "cycle" and "isomorphic repetitions" may also be quite unclear.
So let's try to discuss.

Let's take first your definition of a loop. The wording you propose is the following:
A loop of moves, once started, has no end.
This wording seems not that clear.

First of all you use the word "move" but a "move" may be either a "play" or a "pass".
=> it is not quite clear if your definition exclude a sequence of three successive passes in the loop.
OC I understand that "has no end" means probably "no three successive passes" but it could not be clear for all readers.

Click Here To Show Diagram Code
[go]$$W :b4: pass
$$ +---------------+
$$ | . X X O . O X |
$$ | X 1 3 2 O O X |
$$ | X X X O O X X |
$$ | O O O X X X . |
$$ | . . O . . X . |
$$ | O O O . . X . |
$$ | . . O . . X . |
$$ +---------------+[/go]

Secondly the sequence [ :w1: :b2: :w3: :b4: pass]* repeated ad infinitum is a "loop" according strictly to your definition (no end). You prefer saying that it is not a loop but an "isomorphic repetition". Fine but that means that the wording
A loop of moves, once started, has no end.
is not quite clear.
As fas as I am concerned I do not have really a problem with the wording "loop" also in this case.

BTW do you suggest a defintion of a "loop" in normal play (taking into account the prisoners?) and another defintion of a loop in confirmation phase?

Thirdly, taking a basic ko and the basic corresponding ko ban, is the sequence
[ :b1: capture ko, :w2: pass, :b3: pass, :w4: capture ko, :b5: pass, :w6: pass]* ad infinitum a loop?

Dear Gérard,

It is a bit early, isn't it?

Honte has just finished exploring District #2.
By the way, it seems that someone missed starting the numbering with #1. :D

Nevertheless, thanks to Honte's good nose, we were able to take the basic-ko rule back home with us.

Let me answer your questions for the time being...

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

Technical term "loop"

We will see in the further course of the journey to what extent another term (e.g. "circle", "ring"?) would be more appropriate.


Technical term "move"

Currently, "move" has the usual meaning either to occupy an empty intersection of the board ("GENUINE move") or to waive this right (i.e. "pass").


Three successive "pass"

There is no way that only three successive "pass" will ever be seen in District #2. :D

In general, three successive "pass" are nonsens, if they are embedded by two genuine moves. This is because (1 or 2) + 2n "pass" have the same effect as (1 or 2) "pass".
Currently, three successive "pass" can only be the appetiser for consuming many, many more.

We will see in the further course of the journey to what extent a specific "pass for ending the status confirmation" would be needed.
In principle, I am no friend of using the same technical term for two different pairs of shoes. This would run into similar problems as we have already encountered with "DAME".


Sending two, returning one

During actual play, any repeated sequence that affects the difference of prisoners in only one direction will not last forever. Therefore, is cannot be a "loop". If you ever wanted to maintain "loop", this would be a "temporary loop" in my understanding.
On the surface it looks like you are going to end up in the same place over and over again, but in fact that is not the case. Just because "position" during actual play is a compound of "board position" and "difference of prisoners".

During status confirmation, captured stones do not matter. Therefore, such a repeated sequence is a "loop".


:b1: capture ko, :w2: pass, :b3: pass, :w4: capture ko, :b5: pass, :w6: pass

We will have to wait and see if Honte finds something like this in District #6.

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 Post subject: Re: GT territory rules:: Honte's loops and cycles
Post #7 Posted: Tue Aug 24, 2021 10:43 am 
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Gérard TAILLE wrote:
Yes OC here is an example:

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

Oops it does not seem to be the best example, I will try to find another. At least you can just try to identify what you mean by length of a cycle

As promissed here is the new position I found, with only 3 kos :)

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

Sure it is good challenge for defining "loop", cycle" or whatever you want for the subject of this thread.
BTW with "GT territory rule" all the board is white territory, except OC the bottom left corner which is black territory.

How can you define here a cycle and its length?

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 Post subject: Re: GT territory rules:: Honte's loops and cycles
Post #8 Posted: Tue Aug 24, 2021 11:08 am 
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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.

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Post #9 Posted: Tue Aug 24, 2021 11:03 pm 
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Excursus: "HIGHLANDER - There can be only one"

I went to the cinema with Honte yesterday. We watched the famous film "Highlander". You will surely also remember the scene in the first flashback in which the hero rides through a beautiful landscape ...

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

... while "Queen" perform their well-known hit "White waaaaaaants to paaaaaaaas foreveeeeeeer".

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


During the commercial at the beginning, a short film about an accident during the shooting was shown:

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

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

Click Here To Show Diagram Code
[go]$$Bm5
$$ +-----------------------+
$$ | 2 X 4 X 6 X O . O . O |
$$ | O O X X X X O O O O X |
$$ | O O O O X O O X O X X |
$$ | O O O O O X X . X X . |
$$ | . 1 O O X O X X X X X |
$$ | 3 X 5 O X O O O O O O |
$$ | O . . O X O O O O O O |
$$ | O O O O X O O O O O O |
$$ | X X X X X X X X O O O |
$$ | X . X X X X X X O O . |
$$ | . X X X X X X X O . O |
$$ +-----------------------+[/go]

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

THREE immortals survived unbeheaded.

Thank goodness this accident had no effect on the completion of the film.

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


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

Click Here To Show Diagram Code
[go]$$Bm7 :w6: pass
$$ +-----------------------+
$$ | 2 X . X . X O . O 3 O |
$$ | X O X X X X O O O O X |
$$ | O O O O X O O X O X X |
$$ | O O O O O X X 4 X X . |
$$ | . 1 O O X O X X X X X |
$$ | . X . O X O O O O O O |
$$ | O . . O X O O O O O O |
$$ | O O O O X O O O O O O |
$$ | X X X X X X X X O O O |
$$ | X . X X X X X X O O . |
$$ | . X X X X X X X O . O |
$$ +-----------------------+[/go]

Click Here To Show Diagram Code
[go]$$Bm7
$$ +-----------------------+
$$ | O X . X . X O . O X . |
$$ | 5 O X X X X O O O O X |
$$ | O O O O X O O . O X X |
$$ | O O O O O X X O X X . |
$$ | . X O O X O X X X X X |
$$ | . X . O X O O O O O O |
$$ | O . . O X O O O O O O |
$$ | O O O O X O O O O O O |
$$ | X X X X X X X X O O O |
$$ | X . X X X X X X O O . |
$$ | . X X X X X X X O . O |
$$ +-----------------------+[/go]

Click Here To Show Diagram Code
[go]$$Bm13 :w12: pass
$$ +-----------------------+
$$ | 2 X . X . X O . O X 4 |
$$ | X O X X X X O O O O X |
$$ | O O O O X O O 3 O X X |
$$ | O O O O O X X O X X . |
$$ | . 1 O O X O X X X X X |
$$ | . X . O X O O O O O O |
$$ | O . . O X O O O O O O |
$$ | O O O O X O O O O O O |
$$ | X X X X X X X X O O O |
$$ | X . X X X X X X O O . |
$$ | . X X X X X X X O . O |
$$ +-----------------------+[/go]

Click Here To Show Diagram Code
[go]$$Bm13
$$ +-----------------------+
$$ | O X . X . X O . O . O |
$$ | 5 O X X X X O O O O X |
$$ | O O O O X O O X O X X |
$$ | O O O O O X X . X X . |
$$ | . X O O X O X X X X X |
$$ | . X . O X O O O O O O |
$$ | O . . O X O O O O O O |
$$ | O O O O X O O O O O O |
$$ | X X X X X X X X O O O |
$$ | X . X X X X X X O O . |
$$ | . X X X X X X X O . O |
$$ +-----------------------+[/go]


...

We are now approaching the last 10 minutes of the film -- SHOWDOWN!

Click Here To Show Diagram Code
[go]$$Bm99 :w98: pass
$$ +-----------------------+
$$ | 2 X . X . X O . O 3 O |
$$ | X O X X X X O O O O X |
$$ | O O O O X O O X O X X |
$$ | O O O O O X X 4 X X . |
$$ | 1 . O O X O X X X X X |
$$ | . O O O X O O O O O O |
$$ | O O O O X O O O O O O |
$$ | O O O O X O O O O O O |
$$ | X X X X X X X X O O O |
$$ | X . X X X X X X O O . |
$$ | . X X X X X X X O . O |
$$ +-----------------------+[/go]

Click Here To Show Diagram Code
[go]$$Bm3
$$ +-----------------------+
$$ | O X . X . X O . O X . |
$$ | 1 O X X X X O O O O X |
$$ | O O O O X O O . O X X |
$$ | O O O O O X X O X X . |
$$ | X . O O X O X X X X X |
$$ | . O O O X O O O O O O |
$$ | O O O O X O O O O O O |
$$ | O O O O X O O O O O O |
$$ | X X X X X X X X O O O |
$$ | X . X X X X X X O O . |
$$ | . X X X X X X X O . O |
$$ +-----------------------+[/go]

Click Here To Show Diagram Code
[go]$$Bm5 :w4: pass
$$ +-----------------------+
$$ | 2 X . X . X O . O X 4 |
$$ | X O X X X X O O O O X |
$$ | O O O O X O O 3 O X X |
$$ | O O O O O X X O X X . |
$$ | X 1 O O X O X X X X X |
$$ | . O O O X O O O O O O |
$$ | O O O O X O O O O O O |
$$ | O O O O X O O O O O O |
$$ | X X X X X X X X O O O |
$$ | X . X X X X X X O O . |
$$ | . X X X X X X X O . O |
$$ +-----------------------+[/go]

Click Here To Show Diagram Code
[go]$$Bm5
$$ +-----------------------+
$$ | O X . X . X O . O . O |
$$ | 5 O X X X X O O O O X |
$$ | O O O O X O O X O X X |
$$ | O O O O O X X . X X . |
$$ | X X O O X O X X X X X |
$$ | 6 O O O X O O O O O O |
$$ | O O O O X O O O O O O |
$$ | O O O O X O O O O O O |
$$ | X X X X X X X X O O O |
$$ | X . X X X X X X O O . |
$$ | . X X X X X X X O . O |
$$ +-----------------------+[/go]

Click Here To Show Diagram Code
[go]$$Bm11
$$ +-----------------------+
$$ | 2 X . X . X O . O 3 O |
$$ | X O X X X X O O O O X |
$$ | O O O O X O O X O X X |
$$ | O O O O O X X 4 X X . |
$$ | 1 . O O X O X X X X X |
$$ | O O O O X O O O O O O |
$$ | O O O O X O O O O O O |
$$ | O O O O X O O O O O O |
$$ | X X X X X X X X O O O |
$$ | X . X X X X X X O O . |
$$ | . X X X X X X X O . O |
$$ +-----------------------+[/go]

Click Here To Show Diagram Code
[go]$$Bm11
$$ +-----------------------+
$$ | O X . X . X O . O X 6 |
$$ | 5 O X X X X O O O O X |
$$ | O O O O X O O . O X X |
$$ | O O O O O X X O X X . |
$$ | X 7 O O X O X X X X X |
$$ | O O O O X O O O O O O |
$$ | O O O O X O O O O O O |
$$ | O O O O X O O O O O O |
$$ | X X X X X X X X O O O |
$$ | X . X X X X X X O O . |
$$ | . X X X X X X X O . O |
$$ +-----------------------+[/go]

Click Here To Show Diagram Code
[go]$$Bm11
$$ +-----------------------+
$$ | . X . X . X O . O . O |
$$ | X . X X X X O O O O X |
$$ | . . . . X O O . O X X |
$$ | . . . . . X X O X X . |
$$ | X X . . X W X X X X X |
$$ | . . . . X W W W W W W |
$$ | . . . . X W W W W W W |
$$ | . . . . X W W W W W W |
$$ | X X X X X X X X W W W |
$$ | X . X X X X X X W W . |
$$ | . X X X X X X X W . W |
$$ +-----------------------+[/go]

THE END -- There can be only one!

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


After the end credits, an extended version with longer sword fights was announced. One exemplary szene is shown below.

Click Here To Show Diagram Code
[go]$$Bm5
$$ +-----------------------+
$$ | 4 X . X . X O . O 3 O |
$$ | X O X X X X O O O O X |
$$ | O O O O X O O X O X X |
$$ | O O O O O X X 2 X X . |
$$ | . 1 O O X O X X X X X |
$$ | . X . O X O O O O O O |
$$ | O . . O X O O O O O O |
$$ | O O O O X O O O O O O |
$$ | X X X X X X X X O O O |
$$ | X . X X X X X X O O . |
$$ | . X X X X X X X O . O |
$$ +-----------------------+[/go]

Click Here To Show Diagram Code
[go]$$Bm5 :w12: pass
$$ +-----------------------+
$$ | O X . X . X O . O X 6 |
$$ | 7 O X X X X O O O O X |
$$ | O O O O X O O 5 O X X |
$$ | O O O O O X X O X X . |
$$ | . X O O X O X X X X X |
$$ | . X . O X O O O O O O |
$$ | O . . O X O O O O O O |
$$ | O O O O X O O O O O O |
$$ | X X X X X X X X O O O |
$$ | X . X X X X X X O O . |
$$ | . X X X X X X X O . O |
$$ +-----------------------+[/go]

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Igo Hatsuyoron #120 (still unresolved by professionals, maybe solved by four amateurs)

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 Post subject: Re: GT territory rules:: Honte's loops and cycles
Post #10 Posted: Wed Aug 25, 2021 1:04 am 
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Oops, I could I have been so blind and stupid to not see the following sequence after the :b1: ;-) ;-) ;-)

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

Click Here To Show Diagram Code
[go]$$B
$$ ---------------------
$$ | 4 X . X . X O . O |
$$ | 5 O X X X X O O O |
$$ | O O X O O O O O O |
$$ | 1 O O X X O X O . |
$$ | . O X O X X . X O |
$$ | O O X O O X X X X |
$$ | X X X O O O O X . |
$$ | X . X O . O O X X |
$$ | . X X O O . O O O |[/go]

Sorry Thomas. Take this position for a good challenge for defining loop or cycle but not for GT rule (no territory at top of the board)

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



BTW didn't you miss the following possibility:
Click Here To Show Diagram Code
[go]$$B
$$ +-----------------------+
$$ | X X . X . X O . O . O |
$$ | X O X X X X O O O O X |
$$ | O O O O X O O X O X X |
$$ | O O O O O X X . X X . |
$$ | . 3 O O X O X X X X X |
$$ | 2 1 4 O X O O O O O O |
$$ | O 5 . O X O O O O O O |
$$ | O O O O X O O O O O O |
$$ | X X X X X X X X O O O |
$$ | X . X X X X X X O O . |
$$ | . X X X X X X X O . O |
$$ +-----------------------+[/go]

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 Post subject: Re: GT territory rules:: Honte's loops and cycles
Post #11 Posted: Wed Aug 25, 2021 1:36 am 
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Gérard TAILLE wrote:
Sorry Thomas. Take this position for a good challenge for defining loop or cycle but not for GT rule (no territory at top of the board)

There is no need to apologize. It's an example of an interesting class of positions, isn't it?

However, your :b5: is an atari, so there will be NO loop at all.
Please be patient, Honte will be sniffing out sufficient study material for this topic, which you are so very interested in, in District #6 (latest in District #8).
We might even come back to this kind of position then.


Quote:
BTW didn't you miss the following possibility:
Click Here To Show Diagram Code
[go]$$B
$$ +-----------------------+
$$ | X X . X . X O . O . O |
$$ | X O X X X X O O O O X |
$$ | O O O O X O O X O X X |
$$ | O O O O O X X . X X . |
$$ | . 3 O O X O X X X X X |
$$ | 2 1 4 O X O O O O O O |
$$ | O 5 . O X O O O O O O |
$$ | O O O O X O O O O O O |
$$ | X X X X X X X X O O O |
$$ | X . X X X X X X O O . |
$$ | . X X X X X X X O . O |
$$ +-----------------------+[/go]

:D :D :D

It's similar here as with Igo Hatsuyôron 120:
-- Amateurs are good at tracking down other people's (even professional's) mistakes.
-- Finding a (/ the) correct solution is much more difficult for them.
-- If an attempted solution is incorrect, there is an easy way to correct it.


It seems that someone responsible for this classified the beginning of the first fight scene in "HIGHLANDER" as "not suitable for minors". From now on the movie will have to be shown without these 30 seconds. :razz:

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Last edited by Cassandra on Wed Aug 25, 2021 1:42 am, edited 1 time in total.
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Post #12 Posted: Wed Aug 25, 2021 1:41 am 
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Gérard TAILLE wrote:
Oops, I could I have been so blind and stupid to not see the following sequence after the :b1: ;-) ;-) ;-)

The hint chosen was a lot more entertaining than a bone-dry "Haven't you missed an obvious :b1:?", wasn't it?

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 Post subject: Re: GT territory rules:: Honte's loops and cycles
Post #13 Posted: Wed Aug 25, 2021 1:58 pm 
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Loops with a cycle-length of pseudo 4


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]

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

Click Here To Show Diagram Code
[go]$$B :w4: pass
$$ +---------------+
$$ | . O . X O . . |
$$ | 3 O X X O . . |
$$ | O X X O O . . |
$$ | X X O , . . . |
$$ | O O O . O . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ +---------------+[/go]

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]

We have reached the starting position. The cycle has a length of pseudo 4.
"Pseudo 4" is the length of a cycle that consist of 3 GENUINE moves and 1 pass at its end.


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

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

Click Here To Show Diagram Code
[go]$$Bm5 :w8: pass
$$ +---------------+
$$ | . O . X O . . |
$$ | 3 O X X O . . |
$$ | O X X O O . . |
$$ | X X O , . . . |
$$ | O O O . O . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ +---------------+[/go]

Click Here To Show Diagram Code
[go]$$Bm9
$$ +---------------+
$$ | 1 O . X O . . |
$$ | X O X X O . . |
$$ | 2 X X O O . . |
$$ | X X O , . . . |
$$ | O O O . O . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ +---------------+[/go]

Click Here To Show Diagram Code
[go]$$m9 :w12: pass
$$ +---------------+
$$ | . O . X O . . |
$$ | 3 O X X O . . |
$$ | O X X O O . . |
$$ | X X O , . . . |
$$ | O O O . O . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ +---------------+[/go]

Ad infinitum...
=> White can pass forever.


Variation #1:

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.


Variation #2:

Click Here To Show Diagram Code
[go]$$Bm5 :b7: pass
$$ +---------------+
$$ | . O 4 X O . . |
$$ | . O X X O . . |
$$ | O X X O O . . |
$$ | X X O , . . . |
$$ | O O O . O . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ +---------------+[/go]

Black cannot prevent this. All his stones become captured.
=> NO Black territory.


Next run:

There was not any ko capture, so this will follow the course shown above.
Black is unable to create a two-eye formation in the upper part of the board.
=> NO Black territory

For the status assessment of White's group, Black can only pass for his first move, as he does not want to play a self-atari.
Thereafter, the same sequences as above would apply.
White is unable to create a two-eye formation in the upper part of the board.
=> NO White territory


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

The cycle-length pseudo 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 are "seki-alive".
=> White's stones are "seki-alive".

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

After the status assessment for all groups has been completed:

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

=> The upper left corner 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 GENUINE move.

Next run:

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

Click Here To Show Diagram Code
[go]$$Bm5 :b7: pass
$$ +---------------+
$$ | . O 4 X O . . |
$$ | ? O X X O . . |
$$ | O X X O O . . |
$$ | X X O , . . . |
$$ | O O O . O . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ +---------------+[/go]

Capturing at the shadowed point is forbidden, as this was the cycle's last GENUINE move.

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

Same result as above.

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Last edited by Cassandra on Thu Aug 26, 2021 12:24 pm, edited 1 time in total.
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 Post subject: Re: GT territory rules:: Honte's loops and cycles
Post #14 Posted: Wed Aug 25, 2021 2:47 pm 
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Cassandra wrote:
Loops with a cycle-length of pseudo 4

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]

There are some misunderstanding here concerning GT territory rule.
Remember that the "permanently prohibited ko" I have in mind for my rule requires the existence of a ko (I know that in the rule you study yourself you may prohibit any move but that is another rule isn't it). I think it was clear in my first version and in the wording of my second version it is even much clearer (see "critical positions").
In the sending two return one loop there are neither "critical positions nor ko! => no "permanently prohibited ko" can be created => only normal play can be used => no territory because neither player is able to control all the corner.

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Post #15 Posted: Wed Aug 25, 2021 8:05 pm 
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Gérard TAILLE wrote:
There are some misunderstanding here concerning GT territory rule.
Remember that the "permanently prohibited ko" I have in mind for my rule requires the existence of a ko (I know that in the rule you study yourself you may prohibit any move but that is another rule isn't it). I think it was clear in my first version and in the wording of my second version it is even much clearer (see "critical positions").
In the sending two return one loop there are neither "critical positions nor ko! => no "permanently prohibited ko" can be created => only normal play can be used => no territory because neither player is able to control all the corner.

I intend to keep my postings in this thread consistent and comparable.

Dogs are creatures of habit who love fixed procedures.
I am afraid that Honte will be unable to always keeping track with each and every edit in your rules' draft.

I am sure that the sequences shown are displayed in extreme detail. Per se, and compared to what is common here in the forum, anyway.
So you will be in the best possible position to alert me to potential mistakes that would lead to a different result than what you intended.

What has been done with "sending two, returning one"?

-- It was shown that there is a sequence that results in the same position(s) becoming repeated over and over again.
-- This sequence includes a White "pass".
-- It was shown that Black is unable to stop White from playing this "pass" over and over again.
-- It was concluded that Black will be unable to establish a "two-eye-formation", and so will be unable to claim "territory".
-- It was concluded that White will be unable to establish a "two-eye-formation" as well, and so will be unable to claim "territory", too.

What do you consider the step(s) that would be superfluous in the case that a "ko-capture" was involved?

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

BTW, one of my superiors during my active career once said that although some things could be deleted from my reports, nothing could be added. It should be the same here.

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Post #16 Posted: Thu Aug 26, 2021 12:21 am 
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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 :w6:


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 :w8:


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.

_________________
The really most difficult Go problem ever: http://igohatsuyoron120.de/index.htm
Igo Hatsuyoron #120 (still unresolved by professionals, maybe solved by four amateurs)


Last edited by Cassandra on Thu Aug 26, 2021 12:25 pm, edited 1 time in total.
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 Post subject: Re: GT territory rules:: Honte's loops and cycles
Post #17 Posted: Thu Aug 26, 2021 2:09 am 
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Cassandra wrote:
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.

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 Post subject: Re: GT territory rules:: Honte's loops and cycles
Post #18 Posted: Thu Aug 26, 2021 2:19 am 
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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").

_________________
The really most difficult Go problem ever: http://igohatsuyoron120.de/index.htm
Igo Hatsuyoron #120 (still unresolved by professionals, maybe solved by four amateurs)

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 Post subject: Re: GT territory rules:: Honte's loops and cycles
Post #19 Posted: Thu Aug 26, 2021 3:05 am 
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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]

_________________
The really most difficult Go problem ever: http://igohatsuyoron120.de/index.htm
Igo Hatsuyoron #120 (still unresolved by professionals, maybe solved by four amateurs)


Last edited by Cassandra on Fri Aug 27, 2021 2:27 am, edited 2 times in total.
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 Post subject: Re: GT territory rules:: Honte's loops and cycles
Post #20 Posted: Thu Aug 26, 2021 6:32 am 
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Cassandra wrote:
Next run:

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]

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.

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.

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 :bc: stone ?
2) the :bt: stones ?
3) both :bc: in :bt: ? (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" ?

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