It is currently Tue Oct 19, 2021 8:58 am

All times are UTC - 8 hours [ DST ]




Post new topic Reply to topic  [ 146 posts ]  Go to page 1, 2, 3, 4, 5 ... 8  Next
Author Message
Offline
 Post subject: GT territory rule
Post #1 Posted: Sun Aug 22, 2021 9:38 am 
Lives in sente

Posts: 821
Liked others: 14
Was liked: 37
Rank: 1er dan
After a lot of research and some verifications I am now able to show you my ideas for what I call a "GT territory rule" to not confuse with "Ikeda territory rules"
First of all what is the goal? The goal is to respect as far as possible the traditionnal japonese rule. In that sense it is the same goal as J2003 but it is a completly different approach I hope to be easier to understand.

This "GT territory rule" does not change the normal play (in particular no superko, and I keep NO RESULT game) but bring a new approach for the confirmation phase.
The most visible particularity is to have no need at all for a status of the different group of stones. A territory is defined directly without knowing if stones are alive, dead, unsettled, in-seki or whatever you want.

Four concepts are the key points for this confirmation phase:
1) the use of "two-eye-formation" concept well defined in the "Simplified Japanese Rules" by Robert
2) the use of "border of a set of locations" concept you can find in Robert M. Pauli article
and two new concepts I saw nowhere:
3) the "advantageous loop"
4) the "permanent prohibited" ko

Here is my proposal :

First of all already known definitions:

A "two-eye-formation" is a set of one or several strings of the same player and exactly two empty intersections so that each of the strings is adjacent to each of the two intersections, none of the strings is adjacent to another empty intersection, and each of the two intersections is adjacent only to the strings.

The "inside border" of a set of locations is all the locations in the set which are adjacent to a location not in the set

The "outside border" of a set of locations is all the locations outside the set which are adjacent to a location in the set


and now my confirmation phase:

A set of locations is a "territory" for a player if:
1) the inside border of this set is only made of stones of the player
2) the outside border of this set is only made of stones of the opponent
3) the set of location can be entirely covered by a "two-eye formation" even if the opponent plays first in an alternation game using normal play and the "permanently prohibited" ko (see here after)

A player is said to have a "loop" if she can prove that, after a finite number of moves, then her opponent would never stop to play (to put a stone on the board)
A player is said to have a "advantageous loop" if she can prove she can make an infinite number of pass moves and still having a loop after each pass

When a player has an advantageous loop then, if that player is able to pass after a ko capture by the opponent, the player can request that this ko capture by the opponent is permanently prohibited, even if this ko disappears and reappears later.


Examples analysis will soon follow

Edit: my updated draft version is here : https://lifein19x19.com/viewtopic.php?p=267160#p267160


Last edited by Gérard TAILLE on Sat Sep 04, 2021 6:59 am, edited 3 times in total.
Top
 Profile  
 
Offline
 Post subject: Re: GT territory rule
Post #2 Posted: Sun Aug 22, 2021 9:57 am 
Lives in sente

Posts: 821
Liked others: 14
Was liked: 37
Rank: 1er dan
Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . . . . X O . |
$$ | X X X X X X X |
$$ | O O O O O O O |
$$ | . . . . . O . |
$$ | . . . . . O O |
$$ | . . . . . O . |
$$ | . . . . . O . |
$$ -----------------[/go]

Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | C C C C B W C |
$$ | B B B B B B B |
$$ | O O O O O O O |
$$ | . . . . . O . |
$$ | . . . . . O O |
$$ | . . . . . O . |
$$ | . . . . . O . |
$$ -----------------[/go]
is the marked set of locations a black territory?

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

Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . . . . X O . |
$$ | X X X X X X X |
$$ | W W W W W W W |
$$ | . . . . . O . |
$$ | . . . . . O O |
$$ | . . . . . O . |
$$ | . . . . . O . |
$$ -----------------[/go]
2)The outside border is made of only white stones

Click Here To Show Diagram Code
[go]$$W
$$ -----------------
$$ | 8 1 2 4 X O 6 |
$$ | X X X X X X X |
$$ | W W W W W W W |
$$ | . . . 5 . O . |
$$ | . 3 . 7 . O O |
$$ | . . . . . O . |
$$ | . . . . . O . |
$$ -----------------[/go]
3)Black can easily prove she build a two eye formation covering completly the set of locations

=> it is black territory

Top
 Profile  
 
Offline
 Post subject: Re: GT territory rule
Post #3 Posted: Sun Aug 22, 2021 10:06 am 
Lives in sente

Posts: 821
Liked others: 14
Was liked: 37
Rank: 1er dan
Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | O . X . X . O |
$$ | O . X X X O O |
$$ | O O X O O O O |
$$ | X O X O O O O |
$$ | X O X O O . O |
$$ | X O X O X X O |
$$ | . O X O X X O |
$$ -----------------[/go]


Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | W . X . X . O |
$$ | W . X X X O O |
$$ | W W X O O O O |
$$ | B W X O O O O |
$$ | B W X O O . O |
$$ | B W X O X X O |
$$ | . W X O X X O |
$$ -----------------[/go]
is the marked set of locations a white territory?

Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | W . X . X . O |
$$ | W . X X X O O |
$$ | W W X O O O O |
$$ | X W X O O O O |
$$ | X W X O O . O |
$$ | X W X O X X O |
$$ | . W X O X X O |
$$ -----------------[/go]
1)The inside border is made of only white stones

Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | O C X . X . O |
$$ | O C X X X O O |
$$ | O O B O O O O |
$$ | X O B O O O O |
$$ | X O B O O . O |
$$ | X O B O X X O |
$$ | . O B O X X O |
$$ -----------------[/go]
2)The outside border is not made of only black stones

It is not territory (BTW you do not need to analyse any sequence :) )

Top
 Profile  
 
Offline
 Post subject: Re: GT territory rule
Post #4 Posted: Sun Aug 22, 2021 10:24 am 
Lives in sente

Posts: 821
Liked others: 14
Was liked: 37
Rank: 1er dan
Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . X O . O X . |
$$ | X . O . O X X |
$$ | O O O O X X . |
$$ | X X X X X X X |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ -----------------[/go]


Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | C B W C W X . |
$$ | B C W C W X X |
$$ | W W W W X X . |
$$ | X X X X X X X |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ -----------------[/go]
is the marked set of locations a white territory?

Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . X O . W X . |
$$ | X . O . W X X |
$$ | W W W W X X . |
$$ | X X X X X X X |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ -----------------[/go]
1)The inside border is made of only white stones

Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . X O . O B . |
$$ | X . O . O B X |
$$ | O O O O B X . |
$$ | B B B B X X X |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ -----------------[/go]
2)The outside border is made of only black stones

but even (!) if black passes white cannot build a two eye formation covering completly the set of locations:
Click Here To Show Diagram Code
[go]$$B :b1: pass
$$ -----------------
$$ | 4 X O 5 O X . |
$$ | X 2 O 3 O X X |
$$ | O O O O X X . |
$$ | X X X X X X X |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ -----------------[/go]

=> the set of location considered is not white territory.

What about this another set of locations:

Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | C B W . O X . |
$$ | B C W . O X X |
$$ | W W W W X X . |
$$ | X X X X X X X |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ -----------------[/go]
is the marked set of locations a white territory?

Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . X W . O X . |
$$ | X . W . O X X |
$$ | W W W W X X . |
$$ | X X X X X X X |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ -----------------[/go]
1)The inside border is made of only white stones

Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . X O C O X . |
$$ | X . O C O X X |
$$ | O O O O B X . |
$$ | B B B B X X X |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ -----------------[/go]
2)The outside border is not made of only black stones
=> it is not territory

Top
 Profile  
 
Offline
 Post subject: Re: GT territory rule
Post #5 Posted: Sun Aug 22, 2021 10:47 am 
Lives in sente

Posts: 821
Liked others: 14
Was liked: 37
Rank: 1er dan
Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . O X X . O X |
$$ | X X O X . O X |
$$ | X X O X X O X |
$$ | O O O O O X X |
$$ | . O . . O X . |
$$ | O O . . O X X |
$$ | . O . . O X . |
$$ | . O . . O X X |
$$ -----------------[/go]


Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . O B B C W B |
$$ | X X O B C W B |
$$ | X X O B B W B |
$$ | O O O O O B B |
$$ | . O . . O B C |
$$ | O O . . O B B |
$$ | . O . . O B C |
$$ | . O . . O B B |
$$ -----------------[/go]
is the marked set of locations a black territory?

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

Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . W X X . O X |
$$ | X X W X . O X |
$$ | X X W X X O X |
$$ | O O O W W X X |
$$ | . O . . W X . |
$$ | O O . . W X X |
$$ | . O . . W X . |
$$ | . O . . W X X |
$$ -----------------[/go]
2)The outside border is made of only white stones

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

and you can easily prove that black, even without the move, is able to capture the three marked white stones and to build a two eye formation.

=> this set of locations is black territory


Last edited by Gérard TAILLE on Mon Aug 23, 2021 7:00 am, edited 1 time in total.
Top
 Profile  
 
Offline
 Post subject: Re: GT territory rule
Post #6 Posted: Sun Aug 22, 2021 11:56 am 
Lives in gote

Posts: 430
Location: Netherlands
Liked others: 231
Was liked: 123
Rank: EGF 3d
Universal go server handle: gennan
Do I understand correctly that to properly score a game, it would require filling all neutral points before passing?
If you don't fill all neutral points outside your prospective territory before passing, there are no points inside?

Top
 Profile  
 
Offline
 Post subject: Re: GT territory rule
Post #7 Posted: Sun Aug 22, 2021 12:01 pm 
Lives in sente

Posts: 821
Liked others: 14
Was liked: 37
Rank: 1er dan
gennan wrote:
Do I understand correctly that to properly score a game, it would require filling all neutral points before passing?
If you don't fill all neutral points outside your prospective territory before passing, there are no points inside?

Yes Gennan your are completly right. BTW it is exactly the same in J89 and J2003 where all dame should be played in normal play (I mean before the confirmation phase).

Top
 Profile  
 
Offline
 Post subject: Re: GT territory rule
Post #8 Posted: Sun Aug 22, 2021 12:22 pm 
Lives in sente

Posts: 821
Liked others: 14
Was liked: 37
Rank: 1er dan
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]
is the marked set of locations a black territory?

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

Click Here To Show Diagram Code
[go]$$B
$$ ---------------------
$$ | . . . X W X . X . |
$$ | . . . X W O X X X |
$$ | . . . X W . O X O |
$$ | . . . X W W W O . |
$$ | . . . X X X X W W |
$$ | . . . . . . X X X |
$$ | X X X X . . . . . |
$$ | O O O X X . . . . |
$$ | . O . O X . . . . |
$$ ---------------------[/go]
2)The outside border is made of only white stones
BTW do you recognise in J2003 the barrier of the local2 area associated to the white group in the bottom left corner?

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]

And it is quite easy for black to continue until building a two eye formation covering all the set of location

=> it is black territory

Top
 Profile  
 
Offline
 Post subject: Re: GT territory rule
Post #9 Posted: Sun Aug 22, 2021 12:39 pm 
Tengen

Posts: 5492
Liked others: 0
Was liked: 744
Click Here To Show Diagram Code
[go]$$c
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . X . . . . . . . . . |
$$ | . . . , X . . . . X . . . . X , X . . |
$$ | . . . X . . . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . X . . . . . . . . . |
$$ | . . X X . . . . X X X . . . . X X . . |
$$ | . . . . . . . . . X . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . X . . . |
$$ | . . . , X . . . . X . . . . X , . . . |
$$ | . . . X . . . . . X . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


No black territory because outside border is not white.

Please exemplify the ko rules!

Top
 Profile  
 
Offline
 Post subject: Re: GT territory rule
Post #10 Posted: Sun Aug 22, 2021 12:58 pm 
Lives in sente

Posts: 821
Liked others: 14
Was liked: 37
Rank: 1er dan
RobertJasiek wrote:
Click Here To Show Diagram Code
[go]$$c
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . X . . . . . . . . . |
$$ | . . . , X . . . . X . . . . X , X . . |
$$ | . . . X . . . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . X . . . . . . . . . |
$$ | . . X X . . . . X X X . . . . X X . . |
$$ | . . . . . . . . . X . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . X . . . |
$$ | . . . , X . . . . X . . . . X , . . . |
$$ | . . . X . . . . . X . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


No black territory because outside border is not white.

Please exemplify the ko rules!


Click Here To Show Diagram Code
[go]$$c
$$ -----------------------------------------
$$ | C C C C C C C C C C C C C C C C C C C |
$$ | C C C C C C C C C C C C C C C C C C C |
$$ | C C C B C C C C C B C C C C C C C C C |
$$ | C C C C B C C C C B C C C C B C B C C |
$$ | C C C B C C C C C C C C C C C B C C C |
$$ | C C C C C C C C C C C C C C C C C C C |
$$ | C C C C C C C C C C C C C C C C C C C |
$$ | C C C C C C C C C C C C C C C C C C C |
$$ | C C C B C C C C C B C C C C C C C C C |
$$ | C C B B C C C C B B B C C C C B B C C |
$$ | C C C B C C C C C B C C C C C C C C C |
$$ | C C C C C C C C C C C C C C C C C C C |
$$ | C C C C C C C C C C C C C C C C C C C |
$$ | C C C C C C C C C C C C C C C C C C C |
$$ | C C C B C C C C C C C C C C C B C C C |
$$ | C C C C B C C C C B C C C C B C C C C |
$$ | C C C B C C C C C C C C C C C B C C C |
$$ | C C C C C C C C C C C C C C C C C C C |
$$ | C C C C C C C C C C C C C C C C C C C |
$$ ---------------------------------------[/go]
Is the entire board black territory?

The inside boarder is empty => it is only made of black stone because it is made of only n black stones with n = 0 (maybe my wording is not correct but it is what I mean)
The outside boarder is empty => it is only made of white stones (same comment as above)
I do not know if black can kill all white stones if it is white to play. If it is the case then the entire board is black territory. If not there no territory.

Top
 Profile  
 
Offline
 Post subject: Re: GT territory rule
Post #11 Posted: Sun Aug 22, 2021 1:38 pm 
Lives in sente

Posts: 821
Liked others: 14
Was liked: 37
Rank: 1er dan
Solid triple ko
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]
Is all the board black territory?
1) The inside border is OK (it is empty)
2) The outside border is OK (it is empty)
3) I black able to build a two eye formation?
Has black a loop?
Click Here To Show Diagram Code
[go]$$W :w1: pass
$$ -----------------
$$ | X X X X X X X |
$$ | 2 X 3 X 5 X O |
$$ | O O 6 O X O 4 |
$$ | O O O O O O O |
$$ | X X X X X X X |
$$ | . . . . . X . |
$$ | . . . . . X . |
$$ -----------------[/go]

and it is clear black can force white to answer for ever by a play (I mean not a pass) => black has a loop.

variation
Click Here To Show Diagram Code
[go]$$W
$$ -----------------
$$ | X X X X X X X |
$$ | 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]

If white never pass then that means that black has a loop
and as soon as white makes a pass then black plays at "d" and white will not be able to play another pass => black has loop.

Has black an advantageous loop? No because if black tries to make an infinite number of pass then white will have the opportunity to play at "d" and then black will not be able to make another pass.
=> no "permanent prohibited" ko can be used => no territory because black will never be able to build an eye formation covering all the board.


Last edited by Gérard TAILLE on Mon Aug 23, 2021 7:03 am, edited 1 time in total.
Top
 Profile  
 
Offline
 Post subject: Re: GT territory rule
Post #12 Posted: Sun Aug 22, 2021 1:59 pm 
Lives in sente
User avatar

Posts: 1192
Liked others: 11
Was liked: 136
Rank: German 1 Kyu
Gérard TAILLE wrote:
The inside boarder is empty => it is only made of black stone because it is made of only n black stones with n = 0 (maybe my wording is not correct but it is what I mean)
The outside boarder is empty => it is only made of white stones (same comment as above)

You will need an adjustment ...

A set of locations is a "territory" for a player if:
1) the inside border of this set is only made of stones of the player or is empty
2) the outside border of this set is only made of stones of the opponent or is empty

...

In Robert's full-board example, you are unable to occupy all virtual border points outside the edge of the board with WHITE stones, as this would massively affect the sequences for creating a potential White two-eye-formation inside.

The same is true for any territory that is connected to the edges of the board. All virtual border points beyond the edge of the board must be empty, as you will have difficulties to find an occupation with virtual stones that keeps the life-and-death balance inside intact. There is NO simple way to expand a 19x19-board into a 21x21-board with maintaining the 19x19-properties :D

In principle, you must not assume the border beyond the edges of the board being a compound of virtual board points.
It's more like a virtual line, marking the end of the rectangular world. It runs close to the edge of the wooden Go board that you can clearly see from above.

-----------------
EDITED

_________________
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 Sun Aug 22, 2021 2:21 pm, edited 2 times in total.
Top
 Profile  
 
Offline
 Post subject: Re: GT territory rule
Post #13 Posted: Sun Aug 22, 2021 2:10 pm 
Lives in sente

Posts: 821
Liked others: 14
Was liked: 37
Rank: 1er dan
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]
Is all the board black territory?

No problem with the empty borders.

Has black a loop?
Click Here To Show Diagram Code
[go]$$W :w1: pass
$$ -----------------
$$ | . X X X X X X |
$$ | X X 3 X 7 X X |
$$ | O O 6 O 4 O O |
$$ | 2 O O O O O O |
$$ | 5 X X X X X X |
$$ | X X . . . X . |
$$ | . . . . . X . |
$$ -----------------[/go]

it is clear that white will never pass => black has a loop

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

and it is clear that white will never pass => black has a loop

Has black a advantageous loop?
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 :b6: 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:

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 :b5: pass black request a permanent prohibited ko for the ko in :w4:. Now because white will not be allowed to capture this ko in :w4: it is clear that white will be quickly captured.

=>all board is black territory.

Top
 Profile  
 
Offline
 Post subject: Re: GT territory rule
Post #14 Posted: Sun Aug 22, 2021 2:15 pm 
Lives in sente

Posts: 821
Liked others: 14
Was liked: 37
Rank: 1er dan
Cassandra wrote:
Gérard TAILLE wrote:
The inside boarder is empty => it is only made of black stone because it is made of only n black stones with n = 0 (maybe my wording is not correct but it is what I mean)
The outside boarder is empty => it is only made of white stones (same comment as above)

You will need an adjustment ...

A set of locations is a "territory" for a player if:
1) the inside border of this set is only made of stones of the player or is empty
2) the outside border of this set is only made of stones of the opponent or is empty

...

In Robert's full-board example, you are unable to occupy all virtual border points outside the edge of the board with WHITE stones, as this would massively affect the sequences for creating a potential White two-eye-formation inside.

The same is true for any territory that is connected to the edges of the board. All virtual border points beyond the edge of the board must be empty, as you will have difficulties to find an occupation with virtual stones that keeps the life-and-death balance inside intact. There is NO simple way to expand a 19x19-board into a 21x21-board with maintaining the 19x19-properties :D


Thank you Cassandra for this adjustment, I take it OC.

Top
 Profile  
 
Offline
 Post subject: Re: GT territory rule
Post #15 Posted: Sun Aug 22, 2021 2:39 pm 
Lives in sente

Posts: 821
Liked others: 14
Was liked: 37
Rank: 1er dan
With a little practice the concept of "loop" and "advantageous loop" is quite obvious:

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.

Top
 Profile  
 
Offline
 Post subject: Re: GT territory rule
Post #16 Posted: Sun Aug 22, 2021 2:54 pm 
Lives in sente

Posts: 821
Liked others: 14
Was liked: 37
Rank: 1er dan
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 :w5: => 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.

Top
 Profile  
 
Offline
 Post subject: Re: GT territory rule
Post #17 Posted: Sun Aug 22, 2021 3:02 pm 
Lives in sente

Posts: 821
Liked others: 14
Was liked: 37
Rank: 1er dan
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.

Top
 Profile  
 
Offline
 Post subject: Re: GT territory rule
Post #18 Posted: Sun Aug 22, 2021 8:06 pm 
Lives in sente
User avatar

Posts: 1192
Liked others: 11
Was liked: 136
Rank: German 1 Kyu
Gérard TAILLE wrote:
Has black a advantageous loop?
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 :b6: 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:

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 :b5: pass black request a permanent prohibited ko for the ko in :w4:. Now because white will not be allowed to capture this ko in :w4: 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).

_________________
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 Sun Aug 22, 2021 8:14 pm, edited 2 times in total.
Top
 Profile  
 
Offline
 Post subject: Re: GT territory rule
Post #19 Posted: Sun Aug 22, 2021 8:13 pm 
Lives in sente
User avatar

Posts: 1192
Liked others: 11
Was liked: 136
Rank: German 1 Kyu
Gérard TAILLE wrote:
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 :w5: => 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 :b7:

_________________
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 Sun Aug 22, 2021 8:49 pm, edited 1 time in total.
Top
 Profile  
 
Offline
 Post subject: Re: GT territory rule
Post #20 Posted: Sun Aug 22, 2021 8:44 pm 
Lives in sente
User avatar

Posts: 1192
Liked others: 11
Was liked: 136
Rank: German 1 Kyu
Gérard TAILLE wrote:
With a little practice the concept of "loop" and "advantageous loop" is quite obvious:

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.

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

Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 146 posts ]  Go to page 1, 2, 3, 4, 5 ... 8  Next

All times are UTC - 8 hours [ DST ]


Who is online

Users browsing this forum: No registered users and 1 guest


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group