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 Post subject: Problem with the formal definition of territory in AGA rule.
Post #1 Posted: Fri Feb 12, 2016 11:31 am 
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My English is very bad, sorry in advance.
I'm reading official AGA (link) go rules and I have a problem with the formal definition of territory.
Please see the diagram and follow my deliriums.

Click Here To Show Diagram Code
[go]$$
$$ ------------------
$$ | ? ? ? ? X . . . .
$$ | ? ? ? ? X . . . .
$$ | ? ? ? ? X . . . .
$$ | ? ? ? ? X . . . .
$$ | X X X X a : . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | X X X X . : . . .
$$ | W W W W 1 . . . .
$$ | W W W W X . . . .
$$ | W W W W X . . . .
$$ | W W W W X . . . .
$$ ------------------[/go]


Rule 5:
Quote:
Capture: Stones of the same color are said to be connected if they are adjacent
along horizontal or vertical--not diagonal--lines on the board. A string of
connected stones consists of those stones which can be reached from a given
stone by moving only to adjacent stones of the same color. A string of connected
stones is surrounded by stones of the opposite color if it has no empty points
horizontally or vertically--not diagonally--adjacent
to any of its member stones.
(Such adjacent empty points are known as liberties of the string.)
After a player moves, any stone or string of stones belonging to the opponent
which is completely surrounded by the player's own stones is captured, and
removed from the board. Such stones become prisoners of the capturing player.


According to this rule, after the move 1, the white stones marked with the red circles have no liberties therefore they are surrounded and I can remove them. So far so good.

Rule 9:
Quote:
Ending the Game: Two consecutive passes signal the end of the game. After
two passes, the players must attempt to agree on the status of all groups of
stones remaining on the board. Any stones which the players agree could not
escape capture if the game continued, but which have not yet been captured and
removed, are termed dead stones. If the players agree on the status of all such
groups, they are removed from the board as prisoners of the player who could
capture, and the game is scored as in Rule 12. If there is a disagreement over the
status of some group or groups, play is resumed as specified in Rule 10.


Rule 12:
Quote:
Counting: There are two methods for counting the score at the end of the
game. One is based on territory, the other on area. The players should agree in
advance of play which method they will use. If there is no agreement, territory
counting shall be used.
(Although players' scores may differ under the two methods, the difference in their
scores, and hence the game result, will be the same.)
Territory: Those empty points on the board which are entirely surrounded by live
stones of a single color are considered the territory of the player of that color.
(At the end of the game, the empty points remaining on the board fall into regions. A
region is the smallest set of empty points containing a given empty point and any empty
points adjacent to any empty point in the set. That is, a region consists of those empty
points which can be reached from a given empty point by moving only to adjacent
empty points. A region is entirely surrounded by stones of a single color if the only
stones adjacent to empty points in the region are of that color.


Now watch the shaded zone of the first diagram, according to my interpretation of the rules, after the agreement phase, it is black territory because it is totally surrounded (horizontally or vertically not diagonally) by black stones. This is the problem. Now I thought that to totally surround the zone and to do territory playing in the point a (is it a teire right?) was required.

Is my interpretation of the rule right? Which of the following zones are formally surrounded and therefore territories?
Click Here To Show Diagram Code
[go]$$.
$$ ---------------------------------------
$$ | ? X . . . . . . . . . . . . . . . X ? |
$$ | X . . . . . . . . . . . . . . . . X X |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . X X X . . . . . . . X X X X X . . |
$$ | . X ? ? ? X . . . . . . X ? ? ? X . . |
$$ | . X ? ? ? X . . . . . . X ? ? ? X . . |
$$ | . X ? ? ? X . . . . . . X ? ? ? X . . |
$$ | . . X X X . . . . . . . X X X X X . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


What is the state in japanese and chinese rules?

Thank you. Have a nice day and sorry for bad English.

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 Post subject: Re: Problem with the formal definition of territory in AGA r
Post #2 Posted: Fri Feb 12, 2016 11:47 am 
Oza

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Phobos wrote:
Click Here To Show Diagram Code
[go]$$.
$$ ---------------------------------------
$$ | ? X . . . . . . . . . . . . . . . X ? |
$$ | X . . . . . . . . . . . . . . . . X X |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . X X X . . . . . . . X X X X X . . |
$$ | . X ? ? ? X . . . . . . X ? ? ? X . . |
$$ | . X ? ? ? X . . . . . . X ? ? ? X . . |
$$ | . X ? ? ? X . . . . . . X ? ? ? X . . |
$$ | . . X X X . . . . . . . X X X X X . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


What is the state in japanese and chinese rules?

Thank you. Have a nice day and sorry for bad English.


By the rules, each of the shaded areas is territory, because as you move around it, the only stones adjacent to them are black stones. That is, you can't get to a white stone from any of the given points without crossing through a black stone. Note that this assumes that all of the black stones have been agreed to be alive by both players.

Technically, all the other empty points on the board would count as black territory too, because they are only in contact with black stones, empty spaces, and empty spaces in contact with black stones. If there were a white group on the board somewhere, this would not be the case.

This is exactly the same as in japanese rules in these cases, though there is a special case in japanese rules (eyes in seki) which are counted as territory by the AGA rules but not by japanese rules.

Chinese rules are rather different, in that the score is never counted with territory, so you can't make a direct comparison in this way. For your purposes however, all of the shaded points, INCLUDING the black stones surrounding them, would each be counted a point for scoring.

Edit: To clarify what you seem to be asking, a territory doesn't have to be surrounded by one and only one string of stones, provided that you can't access stones of the opposite colour from within the territory.

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 Post subject: Re: Problem with the formal definition of territory in AGA r
Post #3 Posted: Fri Feb 12, 2016 12:39 pm 
Judan

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Phobos wrote:
My English is very bad, sorry in advance.
I'm reading official AGA (link) go rules and I have a problem with the formal definition of territory.


Rules are written in ordinary language. Don't expect formal definitions. :)

AGA Rules wrote:
Rule 5:
Capture: Stones of the same color are said to be connected if they are adjacent along horizontal or vertical--not diagonal--lines on the board. A string of connected stones consists of those stones which can be reached from a given stone by moving only to adjacent stones of the same color. A string of connected stones is surrounded by stones of the opposite color if it has no empty points horizontally or vertically--not diagonally--adjacent to any of its member stones. (Such adjacent empty points are known as liberties of the string.) After a player moves, any stone or string of stones belonging to the opponent which is completely surrounded by the player's own stones is captured, and removed from the board. Such stones become prisoners of the capturing player.


Emphasis mine.

Quote:
Rule 12:
Territory: Those empty points on the board which are entirely surrounded by live stones of a single color are considered the territory of the player of that color.
(At the end of the game, the empty points remaining on the board fall into regions. A region is the smallest set of empty points containing a given empty point and any empty points adjacent to any empty point in the set. That is, a region consists of those empty points which can be reached from a given empty point by moving only to adjacent empty points. A region is entirely surrounded by stones of a single color if the only stones adjacent to empty points in the region are of that color.


Emphasis mine.

Note that the definition of "surrounded" in each rule is slightly different. But what about "adjacent"? The capture rule specifies "horizontally or vertically--not diagonally--adjacent" a number of times, but the territory rule does not. By normal pragmatics of language, since the territory rule does not restrict adjacent to rookwise adjacent (another way of saying horizontally or vertically adjacent), we would expect that the territory rule does not intend to restrict the meaning of adjacent, and requires territory to be diagonally surrounded, as well as rookwise surrounded. This is a slip on the part of the rules writers. Adjacent in the rules of go always means rookwise adjacent.

Good catch, BTW. :) :clap:

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Post #4 Posted: Fri Feb 12, 2016 12:55 pm 
Judan
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Bill, nice to learn a new term: rookwise ; thanks. :)

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Post #5 Posted: Fri Feb 12, 2016 5:07 pm 
Judan

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EdLee wrote:
Bill, nice to learn a new term: rookwise ; thanks. :)


Hi, Ed!

Some years ago I was dissatisfied with how various go rules in English defined connected groups of stones. I thought that they were awkward and not all that easy for non-players to understand. Then I realized that the problem had probably already been solved, since polyominoes are connected the same way. I looked up polyominoes and they are rookwise connected. That is what the mathematicians who study polyominoes say. If it’s good enough for them, it’s good enough for me. :D

So in go, stones may be rookwise connected, dame are rookwise adjacent, and territory is rookwise surrounded. :D

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 Post subject: Re: Problem with the formal definition of territory in AGA r
Post #6 Posted: Fri Feb 12, 2016 5:28 pm 
Lives with ko

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Phobos wrote:
Click Here To Show Diagram Code
[go]$$
$$ ------------------
$$ | ? ? ? ? X . . . .
$$ | ? ? ? ? X . . . .
$$ | ? ? ? ? X . . . .
$$ | ? ? ? ? X . . . .
$$ | X X X X a : . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | X X X X . : . . .
$$ | W W W W 1 . . . .
$$ | W W W W X . . . .
$$ | W W W W X . . . .
$$ | W W W W X . . . .
$$ ------------------[/go]


Now I thought that to totally surround the zone and to do territory playing in the point a (is it a teire right?) was required.


Hi,
No, teire points are inside territories. a is a dame (granted that there are invisible white stones somewhere).
The old japanese rule, still in use at the world amateur championship, requires that a is filled before counting.
Under AGA rules, or any other area scoring rules (chinese, Ing...), the players had better fill it before passing, because it is worth one point.
In the modern professional japanese rule, it is not mandatory to fill it, but if the players don't do it, they have no points !

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 Post subject: Re: Problem with the formal definition of territory in AGA r
Post #7 Posted: Fri Feb 12, 2016 6:39 pm 
Judan

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Pio2001 wrote:
Phobos wrote:
Click Here To Show Diagram Code
[go]$$
$$ ------------------
$$ | ? ? ? ? X . . . .
$$ | ? ? ? ? X . . . .
$$ | ? ? ? ? X . . . .
$$ | ? ? ? ? X . . . .
$$ | X X X X a : . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | X X X X . : . . .
$$ | W W W W 1 . . . .
$$ | W W W W X . . . .
$$ | W W W W X . . . .
$$ | W W W W X . . . .
$$ ------------------[/go]


Now I thought that to totally surround the zone and to do territory playing in the point a (is it a teire right?) was required.


Hi,
No, teire points are inside territories. a is a dame (granted that there are invisible white stones somewhere).
The old japanese rule, still in use at the world amateur championship, requires that a is filled before counting.


To be clear, if "a" is a neutral point, it may be filled by either a Black or a White stone. :)

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Post #8 Posted: Fri Feb 12, 2016 8:27 pm 
Judan
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Bill, Thanks.

Polyomino and the obligatory Tetris .
Quote:
That is what the mathematicians who study polyominoes say.
That's what they said after chess was born. :)
( The wikipedia page references Go in its footnote [1] -- The circle is now complete. :mrgreen: )


This post by EdLee was liked by: Bill Spight
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 Post subject: Re: Problem with the formal definition of territory in AGA r
Post #9 Posted: Sat Feb 13, 2016 2:49 am 
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Now I understand. Thank you very much to all of you.

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