GT territory rule

Gérard TAILLE · Post by **Gérard TAILLE** » Sun Aug 22, 2021 2:54 pm

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

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

Is the marked set of location white territory?

No problem with the inside or outside border.
White has obviously a loop because even after

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

white can force black to always play a move => white has a loop. In addition white can make an infinite number of pass by keeping the loop => white has a advantageous loop => white can request a permanent prohibited ko on

=> white will able to capture all black stones at the top => white will able to build a two eye formation covering all the set of location => it white territory.

Gérard TAILLE · Post by **Gérard TAILLE** » Sun Aug 22, 2021 3:02 pm

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

Black cannot claim for having a territory including both white groups because she cannot captured the two white groups at the same time
Black cannot claim either for a territory with only one white group because of border problem
=> no territorry arround the two white groups.

Cassandra · Post by **Cassandra** » Sun Aug 22, 2021 8:06 pm

Gérard TAILLE wrote:Has black a advantageous loop?
$$W :w1: pass
$$ -----------------
$$ | . X X X X X X |
$$ | X X 3 X O X X |
$$ | O O X O 4 O O |
$$ | 2 O O O O O O |
$$ | 5 X X X X X X |
$$ | X X . . . X . |
$$ | . . . . . X . |
$$ -----------------
Click Here To Show Diagram Code
[go]$$W :w1: pass $$ ----------------- $$ | . X X X X X X | $$ | X X 3 X O X X | $$ | O O X O 4 O O | $$ | 2 O O O O O O | $$ | 5 X X X X X X | $$ | X X . . . X . | $$ | . . . . . X . | $$ -----------------[/go]
with black can now pass and whatever the answer of white you can see that black has still a loop and black can also make another pass etc. etc. for ever.
OC you can try other variation for white but it is quite obvious that, in any case, black can make an infinite number of pass without losing the fact that black has a loop!
As a consequence black is allowed to use permanent prohibited ko and it follows for example:

$$B
$$ -----------------
$$ | . X X X X X X |
$$ | X X 2 X O X X |
$$ | O O X O 3 O O |
$$ | 1 O O O O O O |
$$ | 4 X X X X X X |
$$ | X X . . . X . |
$$ | . . . . . X . |
$$ -----------------
Click Here To Show Diagram Code
[go]$$B $$ ----------------- $$ | . X X X X X X | $$ | X X 2 X O X X | $$ | O O X O 3 O O | $$ | 1 O O O O O O | $$ | 4 X X X X X X | $$ | X X . . . X . | $$ | . . . . . X . | $$ -----------------[/go]
and now with pass black request a permanent prohibited ko for the ko in . Now because white will not be allowed to capture this ko in it is clear that white will be quickly captured.

=>all board is black territory.

This two-step procedure after having identified a loop as "advantageous" looks too complicated in my eyes. There is a much easier option:

BLACK's advantageous loop has a length of a 6, which fulfills the condition x = (2 + 2n) with n = 1, 2, 3, ...
Therefore, simply prohibit the terminating move of an uninterrupted cycle (which would be a WHITE ko capture).

Cassandra · Post by **Cassandra** » Sun Aug 22, 2021 8:13 pm

Gérard TAILLE wrote:White has obviously a loop because even after
$$B
$$ -----------------
$$ | 4 3 2 X . X O |
$$ | 5 O X X X X O |
$$ | O O O O O O O |
$$ | 1 O X X X X X |
$$ | X O X . . X . |
$$ | 6 O X . . X X |
$$ | O O X . . X . |
$$ -----------------
Click Here To Show Diagram Code
[go]$$B $$ ----------------- $$ | 4 3 2 X . X O | $$ | 5 O X X X X O | $$ | O O O O O O O | $$ | 1 O X X X X X | $$ | X O X . . X . | $$ | 6 O X . . X X | $$ | O O X . . X . | $$ -----------------[/go]
white can force black to always play a move => white has a loop. In addition white can make an infinite number of pass by keeping the loop => white has a advantageous loop => white can request a permanent prohibited ko on => white will able to capture all black stones at the top => white will able to build a two eye formation covering all the set of location => it white territory.

Here, it is WHITE, who has an advantageous loop of the length 6.

Same principle as above:
Simply prohibit the terminating move of an uninterrupted cycle, which is Black's connection at 4 with

Cassandra · Post by **Cassandra** » Sun Aug 22, 2021 8:44 pm

Gérard TAILLE wrote:With a little practice the concept of "loop" and "advantageous loop" is quite obvious:

$$B
$$ +---------------------------------------+
$$ | a O O . O . O X O X X . . . . . . . . |
$$ | O X X O O O O X O O X X . . . . . . . |
$$ | X X X X X X O X X O O X X . . . . . . |
$$ | . . . , X O X X . X O O X . . , . . . |
$$ | . . . . X O X . X O . O X . . . . . . |
$$ | . . . . X O X X O . O O X . . . . . . |
$$ | . . . . X O O X X O O X X . . . . . . |
$$ | . . . . . . O O O X X X . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
Click Here To Show Diagram Code
[go]$$B $$ +---------------------------------------+ $$ | a O O . O . O X O X X . . . . . . . . | $$ | O X X O O O O X O O X X . . . . . . . | $$ | X X X X X X O X X O O X X . . . . . . | $$ | . . . , X O X X . X O O X . . , . . . | $$ | . . . . X O X . X O . O X . . . . . . | $$ | . . . . X O X X O . O O X . . . . . . | $$ | . . . . X O O X X O O X X . . . . . . | $$ | . . . . . . O O O X X X . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . |[/go]
Even if it is black to play, white will surely be able to play at "a" and after this move white can force black to answer endlessly with a play (I mean no pass) => white has a loop.
In addition it is also quite easy to see that white will always be able to pass after black takes the ko in the corner and, after such a black pass, black obviously has alway a loop => black will be able request a "permanent prohibited" ko in order to progress in the corner => the 10 white stones in the corner will be captured and then white stones involved in the double ko will be also captured.

You should not fall into the same trap J89's authors are already sitting in:
-- Choose a level of detail that is inversely proportional to the difficulty of the example.

Your comment on this example just doesn't match. I leave it up to you to find a consistent version of it.

jann · Post by **jann** » Mon Aug 23, 2021 1:32 am

These "have a loop" and "have an advantageous loop" doesn't seem clear enough. Do sequences with double passes count as loop? If no, how to "have advantageous loop" if opponent passes (once) after my pass? If yes, would a sole double ko seki make a loop? Maybe an advantageous loop even, breaking it?

Cassandra · Post by **Cassandra** » Mon Aug 23, 2021 2:03 am

viewtopic.php?p=266763#p266763

Gérard TAILLE wrote: variation
$$W :w1: pass
$$ -----------------
$$ | X X X X X X X |
$$ | d X 1 X 3 X O |
$$ | O O 4 O X O 2 |
$$ | O O O O O O O |
$$ | X X X X X X X |
$$ | . . . . . X . |
$$ | . . . . . X . |
$$ -----------------
Click Here To Show Diagram Code
[go]$$W :w1: pass $$ ----------------- $$ | X X X X X X X | $$ | d X 1 X 3 X O | $$ | O O 4 O X O 2 | $$ | O O O O O O O | $$ | X X X X X X X | $$ | . . . . . X . | $$ | . . . . . X . | $$ -----------------[/go]

Needs some editing.

is utilised twice.

Cassandra · Post by **Cassandra** » Mon Aug 23, 2021 3:51 am

viewtopic.php?p=266754#p266754

Gérard TAILLE wrote:
$$B
$$ -----------------
$$ | . O B . . O X |
$$ | X X O B . O X |
$$ | X X O B B O X |
$$ | O O O O O B X |
$$ | . O . . O B . |
$$ | O O . . O B X |
$$ | . O . . O B . |
$$ | . O . . O B X |
$$ -----------------
Click Here To Show Diagram Code
[go]$$B $$ ----------------- $$ | . O B . . O X | $$ | X X O B . O X | $$ | X X O B B O X | $$ | O O O O O B X | $$ | . O . . O B . | $$ | O O . . O B X | $$ | . O . . O B . | $$ | . O . . O B X | $$ -----------------[/go]
1)The inside border is made of only black stones

Needs some editing. One Black stone is missing.

Gérard TAILLE · Post by **Gérard TAILLE** » Mon Aug 23, 2021 6:57 am

jann wrote:These "have a loop" and "have an advantageous loop" doesn't seem clear enough. Do sequences with double passes count as loop? If no, how to "have advantageous loop" if opponent passes (once) after my pass? If yes, would a sole double ko seki make a loop? Maybe an advantageous loop even, breaking it?

I like such questions Jann because they adresse directly my ideas rather then a formal text on which I need help to find the best english wording.
So let's consider my ideas and I will see later how to improve my formal text, maybe with your help.

The only basic question you have to answer is the following : can a player prevents her opponent to make infinite passes? If the answer is YES it looks an advantage for the player doesn't it? Surprisingly a go player is generally able to answer this question very quickly and may even consider such question as obvious

Let's take the simple double ko

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

Can white prevents black to make infinite passes? Obviously the answer is NO isn't it?
Can black prevents white to make infinite passes? Obviously the answer is still NO?
The situation appears symmetrical => no advantageous loop.

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

Can white prevents black to make infinite passes? Obviously the answer is NO?
Can black prevents white to make infinite passes? This time the answer is YES, isn't it?
The situation is not symmetrical => black has an advantageous loop.

Considering your questions the point is to avoid mixing the two questions above. It is true that if black plays a sequence showing infinite passes for black then white would have also infinite passes. But that was not the questions above.

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

Can white prevents black to make infinite passes? Obviously the answer is YES?
Can black prevents white to make infinite passes? the answer is still YES?
The situation appears symmetrical => no advantageous loop.

Additonnal comment on these three examples:
In the first one the answers to the two basic questions are NO, NO => generally seki in common GO language or NO TERRITORY in my langage
In the second example the answers to the two basic questions are NO, YES => generally alive stones against dead stones in common GO language or TERRITORY in my langage
In the third example the answer to the two basic questions are YES, YES => generally seki in common GO language or NO TERRITORY in my langage. BTW in normal play this situation is a NO RESULT game.

Let's try to apply this stuff to monshine life:

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

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

Assume black claims for a black territory for the marked set of locations above then it follows:

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

=> it is black territory

Now assume black is more greedy and claim a black territory covering all the board. What will happen?

Click Here To Show Diagram Code: [go]$$W :w3: pass $$ --------------------- $$ | . . . X O 6 1 X . | $$ | . . . X O O X X X | $$ | . . . X O . O X 5 | $$ | . . . X O O O O 2 | $$ | . . . X X X X O O | $$ | . . . . . . X X X | $$ | X X X X . . . . . | $$ | O O O X X . . . . | $$ | . O 4 7 X . . . . | $$ ---------------------[/go]

white, showing the loop above ask the two basic questions:
Can white prevents black to make infinite passes? Obviously the answer is NO?
Can black prevents white to make infinite passes? The answer is YES, isn't it?
The situation is not symmetrical => black has an advantageous loop.
=> black is allowed to request "permenantly prohibited" ko. The game continue by

Click Here To Show Diagram Code: [go]$$Wm9 :b8: pass :w9: pass $$ --------------------- $$ | . . . X O X 3 X . | $$ | . . . X O O X X X | $$ | . . . X O . O X O | $$ | . . . X O O O O 2 | $$ | . . . X X X X O O | $$ | . . . . . . X X X | $$ | X X X X . . . . . | $$ | O O O X X . . . . | $$ | . O . O X . . . . | $$ ---------------------[/go]

and now

pass and at the same time black requests the previous white ko capture at

becomes a permanently prohibited ko. As a consequence you see white can capture all white stones => all the board is black territory.

OC this result is wrong but where is the mistake?
In fact white appears to be herself to greedy by trying to save all her stones. The mistaken move is

(trying to save white stones at the bottom though they cannot be saved). Instead white should simply pass. That way the answer to the question
can black prevents white to make infinite passes?
is now NO and there are no advantageous loop!
Surely black can capture white stone at the bottom but not the white stones in the double ko
=> the all board is not black territory.
As usual everything must be made during confirmation phase to find the perfect play.

Gérard TAILLE · Post by **Gérard TAILLE** » Mon Aug 23, 2021 7:02 am

Cassandra wrote:https://lifein19x19.com/viewtopic.php?p=266754#p266754

Gérard TAILLE wrote:
$$B
$$ -----------------
$$ | . O B . . O X |
$$ | X X O B . O X |
$$ | X X O B B O X |
$$ | O O O O O B X |
$$ | . O . . O B . |
$$ | O O . . O B X |
$$ | . O . . O B . |
$$ | . O . . O B X |
$$ -----------------
Click Here To Show Diagram Code
[go]$$B $$ ----------------- $$ | . O B . . O X | $$ | X X O B . O X | $$ | X X O B B O X | $$ | O O O O O B X | $$ | . O . . O B . | $$ | O O . . O B X | $$ | . O . . O B . | $$ | . O . . O B X | $$ -----------------[/go]
1)The inside border is made of only black stones
Needs some editing. One Black stone is missing.

yes Cassandra, thank you. It's done.

Gérard TAILLE · Post by **Gérard TAILLE** » Mon Aug 23, 2021 7:04 am

Cassandra wrote:https://lifein19x19.com/viewtopic.php?p=266763#p266763

Gérard TAILLE wrote: variation
$$W :w1: pass
$$ -----------------
$$ | X X X X X X X |
$$ | d X 1 X 3 X O |
$$ | O O 4 O X O 2 |
$$ | O O O O O O O |
$$ | X X X X X X X |
$$ | . . . . . X . |
$$ | . . . . . X . |
$$ -----------------
Click Here To Show Diagram Code
[go]$$W :w1: pass $$ ----------------- $$ | X X X X X X X | $$ | d X 1 X 3 X O | $$ | O O 4 O X O 2 | $$ | O O O O O O O | $$ | X X X X X X X | $$ | . . . . . X . | $$ | . . . . . X . | $$ -----------------[/go]
Needs some editing. is utilised twice.

Thank you again Cassandra. It is true. It's done now.

Gérard TAILLE · Post by **Gérard TAILLE** » Mon Aug 23, 2021 7:13 am

Cassandra wrote:
Gérard TAILLE wrote:Has black a advantageous loop?
$$W :w1: pass
$$ -----------------
$$ | . X X X X X X |
$$ | X X 3 X O X X |
$$ | O O X O 4 O O |
$$ | 2 O O O O O O |
$$ | 5 X X X X X X |
$$ | X X . . . X . |
$$ | . . . . . X . |
$$ -----------------
Click Here To Show Diagram Code
[go]$$W :w1: pass $$ ----------------- $$ | . X X X X X X | $$ | X X 3 X O X X | $$ | O O X O 4 O O | $$ | 2 O O O O O O | $$ | 5 X X X X X X | $$ | X X . . . X . | $$ | . . . . . X . | $$ -----------------[/go]
with black can now pass and whatever the answer of white you can see that black has still a loop and black can also make another pass etc. etc. for ever.
OC you can try other variation for white but it is quite obvious that, in any case, black can make an infinite number of pass without losing the fact that black has a loop!
As a consequence black is allowed to use permanent prohibited ko and it follows for example:

$$B
$$ -----------------
$$ | . X X X X X X |
$$ | X X 2 X O X X |
$$ | O O X O 3 O O |
$$ | 1 O O O O O O |
$$ | 4 X X X X X X |
$$ | X X . . . X . |
$$ | . . . . . X . |
$$ -----------------
Click Here To Show Diagram Code
[go]$$B $$ ----------------- $$ | . X X X X X X | $$ | X X 2 X O X X | $$ | O O X O 3 O O | $$ | 1 O O O O O O | $$ | 4 X X X X X X | $$ | X X . . . X . | $$ | . . . . . X . | $$ -----------------[/go]
and now with pass black request a permanent prohibited ko for the ko in . Now because white will not be allowed to capture this ko in it is clear that white will be quickly captured.

=>all board is black territory.
This two-step procedure after having identified a loop as "advantageous" looks too complicated in my eyes. There is a much easier option:

BLACK's advantageous loop has a length of a 6, which fulfills the condition x = (2 + 2n) with n = 1, 2, 3, ...
Therefore, simply prohibit the terminating move of an uninterrupted cycle (which would be a WHITE ko capture).

Is it simply a wording problem or it is a problem on the procedure itself?
BTW I did not use the wording "cycle" because for me a cycle is a sequence which is repeat indefinitly without any change. In that sense a cycle is only a particular case of loop.

jmeinh · Post by **jmeinh** » Mon Aug 23, 2021 8:29 am

Interesting project.

I'm not sure if
"2) the outside border of this set is only made of stones of the opponent or is empty"
really does what it's supposed to do (or if I don't quite understand it yet).

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

Is the marked set of locations a black territory?
if so, with what score?

Cassandra · Post by **Cassandra** » Mon Aug 23, 2021 8:30 am

Gérard TAILLE wrote:Is it simply a wording problem or it is a problem on the procedure itself?
BTW I did not use the wording "cycle" because for me a cycle is a sequence which is repeat indefinitly without any change. In that sense a cycle is only a particular case of loop.

In my understanding (visualise a solidly connected triple-ko, for example):

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

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]

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 ...

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

Just looked at your posting again. Probably I found the reason for our misunderstanding:

Cassandra wrote:BLACK's advantageous loop has a cycle-length of a 6, which fulfills the condition x = (2 + 2n) with n = 1, 2, 3, ...
Therefore, simply prohibit the terminating move of an uninterrupted cycle (which would be a WHITE ko capture).

This is what I intended (

) to write. Seems that it was too deep in the night...

RobertJasiek · Post by **RobertJasiek** » Mon Aug 23, 2021 9:03 am

Gérard TAILLE wrote:
$$W
$$ -----------------
$$ | . X X X X X X |
$$ | X X . X O X X |
$$ | O O X O . O O |
$$ | . O O O O O O |
$$ | O X X X X X X |
$$ | X X . . . X . |
$$ | . . . . . X . |
$$ -----------------
Click Here To Show Diagram Code
[go]$$W $$ ----------------- $$ | . X X X X X X | $$ | X X . X O X X | $$ | O O X O . O O | $$ | . O O O O O O | $$ | O X X X X X X | $$ | X X . . . X . | $$ | . . . . . X . | $$ -----------------[/go]
Can white prevents black to make infinite passes? Obviously the answer is NO?
Can black prevents white to make infinite passes? This time the answer is YES, isn't it?
The situation is not symmetrical => black has an advantageous loop.

Considering your questions the point is to avoid mixing the two questions above. It is true that if black plays a sequence showing infinite passes for black then white would have also infinite passes. But that was not the questions above.

$$W
$$ -----------------
$$ | X X X X X X X |
$$ | . X . X . X O |
$$ | O O X O X O . |
$$ | O O O O O O O |
$$ | X X X X X X X |
$$ | . . . . . X . |
$$ | . . . . . X . |
$$ -----------------
Click Here To Show Diagram Code
[go]$$W $$ ----------------- $$ | X X X X X X X | $$ | . X . X . X O | $$ | O O X O X O . | $$ | O O O O O O O | $$ | X X X X X X X | $$ | . . . . . X . | $$ | . . . . . X . | $$ -----------------[/go]
Can white prevents black to make infinite passes? Obviously the answer is YES?
Can black prevents white to make infinite passes? the answer is still YES?
The situation appears symmetrical => no advantageous loop.

I do not understand what you are trying to say. Please explain!

Life In 19x19

GT territory rule

Re: GT territory rule

Re: GT territory rule

Re: GT territory rule

Re: GT territory rule

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Re: GT territory rule

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Re: GT territory rule

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