RobertJasiek wrote:
How / with which principles have you derived / created the German version?
Continued.
Approach #3: Topology of "useless points".
- Click Here To Show Diagram Code
[go]$$B
$$ +------------------------
$$ | . O . O . O . O X . . |
$$ | O X O O O O O O X . . |
$$ | X X X . X O X X X . . |
$$ | X . X X X O X . . . . |
$$ | . X O O O X X . . . . |
$$ | . X O . . . . . . . . |
$$ | X X O . . . . . . . . |
$$ | O O O . . . . . . . . |
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . . . . |[/go]
This is J89's L&D Example 24, which comment explains the effect of "useless points" on the determination of "territory", using a two-stage ko as an examplary case.
We will limit ourselves here on "useless points", and therefore neither discuss L&D, nor "territory", nor two-step ko.
There are three different types of "useless points":
![white 1 :w1:](./images/smilies/w1.gif)
"Two-sided boundary points"
![white 2 :w2:](./images/smilies/w2.gif)
"One-sided boundary points"
![black 3 :b3:](./images/smilies/b3.gif)
"Unplayable useless points"
Please note that these three types can NOT be handled DIFFERENTLY in J89, as the same technical term is used to identify them.
I refrained from adjusting the interpretations, so as not to make things too confusing.
----------
"Two-sided boundary points"
- Click Here To Show Diagram Code
[go]$$B
$$ +------------------------
$$ | . O . W . W . W X . . |
$$ | O B W W W W W W X . . |
$$ | B B B M B W X X X . . |
$$ | B . B B B W X . . . . |
$$ | . X O O O X X . . . . |
$$ | . X O . . . . . . . . |
$$ | X X O . . . . . . . . |
$$ | O O O . . . . . . . . |
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . . . . |[/go]
The "useless point"
![x :ex:](./images/smilies/ex.gif)
is RIGHT NEXT to the marked stones
![black with circle :bc:](./images/smilies/bc.gif)
of both sides, which are "
independently alive".
- Click Here To Show Diagram Code
[go]$$B
$$ +------------------------
$$ | , , , , , , , , X . . |
$$ | , X , , , , , , X . . |
$$ | X X X M X , X X X . . |
$$ | X . X X X , X . . . . |
$$ | . X O O O X X . . . . |
$$ | . X O . . . . . . . . |
$$ | X X O . . . . . . . . |
$$ | O O O . . . . . . . . |
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . . . . |[/go]
J89 mentiones something like '"useless points" next to them "ALONG THE LINES OF THE BOARD"'. What does "along the lines of the board" mean?
The diagram above shows the region doomed worthless by the marked "useless point" from White's point of view.
- Click Here To Show Diagram Code
[go]$$B
$$ +------------------------
$$ | . O . O . O . O X . . |
$$ | O , O O O O O O X . . |
$$ | , , , M , O X X X . . |
$$ | , , , , , O X . . . . |
$$ | , , O O O X X . . . . |
$$ | , , O . . . . . . . . |
$$ | , , O . . . . . . . . |
$$ | O O O . . . . . . . . |
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . . . . |[/go]
This diagram displays the region doomed worthless by the marked "useless point" from Black's point of view.
- Click Here To Show Diagram Code
[go]$$B
$$ +------------------------------------------------------------------------------------------------------------------------
$$ | . O . O . O . O X . . | . O . O . O . O X . . | . O . O . O . O X . . | . O . O . O . O X . . | . O . O . O . O X . . |
$$ | O X O O O O O O X . . | O # O O O O O O X . . | O # O O O O O O X . . | O X O O O O O O X . . | O X O O O O O O X . . |
$$ | X X X M X O X X X . . | # # # M # O X X X . . | # # # . # O X X X . . | X X X . X O X X X . . | X X X . X O X X X . . |
$$ | X . X X X O X . . . . | # . # # # O X . . . . | # M # # # O X . . . . | X T X X X O X . . . . | X . X X X O X . . . . |
$$ | . X O O O X X . . . . | . X O O O X X . . . . | M X O O O X X . . . . | T # O O O X X . . . . | . # O O O X X . . . . |
$$ | . X O . . . . . . . . | . X O . . . . . . . . | . X O . . . . . . . . | M # O . . . . . . . . | M # O . . . . . . . . |
$$ | X X O . . . . . . . . | X X O . . . . . . . . | X X O . . . . . . . . | # # O . . . . . . . . | # # O . . . . . . . . |
$$ | O O O . . . . . . . . | O O O . . . . . . . . | O O O . . . . . . . . | O O O . . . . . . . . | O O O . . . . . . . . |
$$ | . . . . . . . . . . . | . . . . . . . . . . . | . . . . . . . . . . . | . . . . . . . . . . . | . . . . . . . . . . . |
$$ | . . . . . . . . . . . | . . . . . . . . . . . | . . . . . . . . . . . | . . . . . . . . . . . | . . . . . . . . . . . |[/go]
You can also utilise an iterative method for identifying worthless regions on the board, here displayed for such a Black region:
![black 1 :b1:](./images/smilies/b1.gif)
Mark the solidly connected Black stones that are RIGHT NEXT to
![x :ex:](./images/smilies/ex.gif)
(with
![black with square :bs:](./images/smilies/bs.gif)
here).
![black 2 :b2:](./images/smilies/b2.gif)
Mark the (previously unmarked) empty board points RIGHT NEXT to
![black with square :bs:](./images/smilies/bs.gif)
with
![x :ex:](./images/smilies/ex.gif)
.
![black 3 :b3:](./images/smilies/b3.gif)
Mark the solidly connected Black stones, as well as the previously unmarked empty points, that are RIGHT NEXT to
![triangle :et:](./images/smilies/et.gif)
(=
![x :ex:](./images/smilies/ex.gif)
from
![black 2 :b2:](./images/smilies/b2.gif)
).
![black 4 :b4:](./images/smilies/b4.gif)
If no stones / empty points were marked, then stop, else continue with
![black 2 :b2:](./images/smilies/b2.gif)
.
- Click Here To Show Diagram Code
[go]$$B
$$ +------------------------
$$ | . O . O . O . O X . . |
$$ | O X O O O O O O X . . |
$$ | X X X * X O X X X . . |
$$ | X . X X X O X . . . . |
$$ | . X O O O X X . . . . |
$$ | . X O . . . . . . . . |
$$ | X X O . . . . . . . . |
$$ | O O O . . . . . . . . |
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . . . . |[/go]
This "useless point" situated at the boundary between "
independently alive" stones of both players can be filled by either player.
Thus, this type of "useless point" will be called "two-sided boundary point" hereafter.
Please note that -- in principle -- IMPLICITLY enforcing the occupation of "two-sided boundary points" (as is done in J89) is nothing more than a means to make the scoring less prone to error. "Two-sided boundary points" have nothing to do with "territory"!
----------
"One-sided boundary points"
- Click Here To Show Diagram Code
[go]$$B
$$ +------------------------
$$ | M O . O . O . O X . . |
$$ | P X O O O O O O X . . |
$$ | X X X * X O X X X . . |
$$ | X . X X X O X . . . . |
$$ | . X O O O X X . . . . |
$$ | . X O . . . . . . . . |
$$ | X X O . . . . . . . . |
$$ | O O O . . . . . . . . |
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . . . . |[/go]
The "useless point"
![x :ex:](./images/smilies/ex.gif)
is RIGHT NEXT to the marked White stone, which is a "death stone".
- Click Here To Show Diagram Code
[go]$$B
$$ +------------------------
$$ | M , , , , , , , X . . |
$$ | , X , , , , , , X . . |
$$ | X X X * X , X X X . . |
$$ | X . X X X , X . . . . |
$$ | . X O O O X X . . . . |
$$ | . X O . . . . . . . . |
$$ | X X O . . . . . . . . |
$$ | O O O . . . . . . . . |
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . . . . |[/go]
The diagram above shows the region doomed worthless by the marked "useless point". As a matter of course, it's a White region only.
- Click Here To Show Diagram Code
[go]$$B
$$ +------------------------------------------------------------------------------------------------------------------------
$$ | M O . O . O . O X . . | M @ . O . O . O X . . | . @ M O . O . O X . . | . O T @ . @ . @ X . . | . O . @ M @ M @ X . . |
$$ | O X O O O O O O X . . | @ X O O O O O O X . . | @ X O O O O O O X . . | O X @ @ @ @ @ @ X . . | O X @ @ @ @ @ @ X . . |
$$ | X X X * X O X X X . . | X X X * X O X X X . . | X X X * X O X X X . . | X X X * X @ X X X . . | X X X * X @ X X X . . |
$$ | X . X X X O X . . . . | X . X X X O X . . . . | X . X X X O X . . . . | X . X X X @ X . . . . | X . X X X @ X . . . . |
$$ | . X O O O X X . . . . | . X O O O X X . . . . | . X O O O X X . . . . | . X O O O X X . . . . | . X O O O X X . . . . |
$$ | . X O . . . . . . . . | . X O . . . . . . . . | . X O . . . . . . . . | . X O . . . . . . . . | . X O . . . . . . . . |
$$ | X X O . . . . . . . . | X X O . . . . . . . . | X X O . . . . . . . . | X X O . . . . . . . . | X X O . . . . . . . . |
$$ | O O O . . . . . . . . | O O O . . . . . . . . | O O O . . . . . . . . | O O O . . . . . . . . | O O O . . . . . . . . |
$$ | . . . . . . . . . . . | . . . . . . . . . . . | . . . . . . . . . . . | . . . . . . . . . . . | . . . . . . . . . . . |
$$ | . . . . . . . . . . . | . . . . . . . . . . . | . . . . . . . . . . . | . . . . . . . . . . . | . . . . . . . . . . . |[/go]
The iterative method again.
- Click Here To Show Diagram Code
[go]$$B
$$ +------------------------
$$ | Q O Q O . O . O X . . |
$$ | O X O O O O O O X . . |
$$ | X X X * X O X X X . . |
$$ | X . X X X O X . . . . |
$$ | . X O O O X X . . . . |
$$ | . X O . . . . . . . . |
$$ | X X O . . . . . . . . |
$$ | O O O . . . . . . . . |
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . . . . |[/go]
This "useless point" can be filled by only one player (White here).
The two-stage ko makes another White move necessary, but this issue will not be discussed here.Thus, this type of "useless point" will be called "one-sided boundary point" hereafter.
Please note that -- in principle -- IMPLICITLY enforcing the occupation of "one-sided boundary points" (as is done in J89) is nothing more than a means to make the scoring less prone to error. "One-sided boundary points" have nothing to do with "territory"!
----------
"Unplayable useless points"
- Click Here To Show Diagram Code
[go]$$B
$$ +--------------------
$$ | . O O O . X O . . |
$$ | X X X X X X O . . |
$$ | O O O O O O O . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |[/go]
This is a position being part of Diagram 6 of J89's Commentary.
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[go]$$B
$$ +--------------------
$$ | M W W W M B O . . |
$$ | B B B B B B O . . |
$$ | O O O O O O O . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |[/go]
There are two "useless points"
![x :ex:](./images/smilies/ex.gif)
, which both are RIGHT NEXT to White's "life-stones"
![white with circle :wc:](./images/smilies/wc.gif)
and to Black's "life-stones"
![black with circle :bc:](./images/smilies/bc.gif)
.
- Click Here To Show Diagram Code
[go]$$B
$$ +--------------------
$$ | M O O O M , O . . |
$$ | , , , , , , O . . |
$$ | O O O O O O O . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |[/go]
The diagram above shows the region doomed worthless by the marked "useless points" from White's point of view.
- Click Here To Show Diagram Code
[go]$$B
$$ +--------------------
$$ | M , , , M X O . . |
$$ | X X X X X X O . . |
$$ | O O O O O O O . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |[/go]
This diagram displays the region doomed worthless by the marked "useless points" from Black's point of view.
- Click Here To Show Diagram Code
[go]$$B
$$ +--------------------
$$ | M O O O M X O . . |
$$ | X X X X X X O . . |
$$ | O O O O O O O . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |[/go]
Neither side will play at any of the marked points.
Thus, this type of "useless point" will be called "unplayable useless point" hereafter.
Please note that the determination of "terriory" is ONLY affected by these "unplayable useless points".
----------
- Click Here To Show Diagram Code
[go]$$B
$$ +--------------------
$$ | . O . X . X O . . |
$$ | O O O X X X O . . |
$$ | X X X X O O O . . |
$$ | O O O O O . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |[/go]
This position is displayed in Diagram 13 of J89's Commentary (original version).
- Click Here To Show Diagram Code
[go]$$B
$$ +--------------------
$$ | . W M B . B O . . |
$$ | W W W B B B O . . |
$$ | B B B B O O O . . |
$$ | O O O O O . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |[/go]
The "useless point"
![x :ex:](./images/smilies/ex.gif)
is RIGHT NEXT to White's "life-stones"
![white with circle :wc:](./images/smilies/wc.gif)
, as well as to Black's "life-stones"
![black with circle :bc:](./images/smilies/bc.gif)
.
- Click Here To Show Diagram Code
[go]$$B
$$ +--------------------
$$ | , , M X . X O . . |
$$ | , , , X X X O . . |
$$ | X X X X O O O . . |
$$ | O O O O O . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |[/go]
The diagram above shows the region doomed worthless by the marked "useless point" from White's point of view.
- Click Here To Show Diagram Code
[go]$$B
$$ +--------------------
$$ | . O M , , , O . . |
$$ | O O O , , , O . . |
$$ | , , , , O O O . . |
$$ | O O O O O . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |[/go]
This diagram displays the region doomed worthless by the marked "useless point" from Black's point of view.
- Click Here To Show Diagram Code
[go]$$B
$$ +--------------------
$$ | . O M X . X O . . |
$$ | O O O X X X O . . |
$$ | X X X X O O O . . |
$$ | O O O O O . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |[/go]
Neither side will play at the marked point, which therefore is an "unplayable useless point".
The determination of "territory" is affected by this "unplayable useless point".
----------
- Click Here To Show Diagram Code
[go]$$B
$$ +------------------
$$ | . O . O X O . . |
$$ | O O O X X O . . |
$$ | X O X . X O . . |
$$ | . X X X X O . . |
$$ | X X O O O O . . |
$$ | O O O . . . . . |
$$ | . . . . . . . . |
$$ | . . . . . . . . |[/go]
This diagram shows J89's Commentary's Diagram 14 / J89's L&D Example 25, with colours reversed.
- Click Here To Show Diagram Code
[go]$$B
$$ +------------------
$$ | . W M P B O . . |
$$ | W W W B B O . . |
$$ | Z W B . B O . . |
$$ | M B B B B O . . |
$$ | B B O O O O . . |
$$ | O O O . . . . . |
$$ | . . . . . . . . |
$$ | . . . . . . . . |[/go]
The "useless point"
![x :ex:](./images/smilies/ex.gif)
at the upper edge is RIGHT NEXT to White's "life-stones"
![white with circle :wc:](./images/smilies/wc.gif)
, as well as to White's "
dead"
(according to J89) stone
![white with x :wx:](./images/smilies/wx.gif)
.
The "useless point"
![x :ex:](./images/smilies/ex.gif)
at the left edge is RIGHT NEXT to Black's "life-stones"
![black with circle :bc:](./images/smilies/bc.gif)
, as well as to Black's "
dead"
(according to J89) stone
![black with x :bx:](./images/smilies/bx.gif)
.
- Click Here To Show Diagram Code
[go]$$B
$$ +------------------
$$ | , , M , X O . . |
$$ | , , , X X O . . |
$$ | X , X . X O . . |
$$ | . X X X X O . . |
$$ | X X O O O O . . |
$$ | O O O . . . . . |
$$ | . . . . . . . . |
$$ | . . . . . . . . |[/go]
The diagram above shows the region doomed worthless by the marked "useless point" from White's point of view.
- Click Here To Show Diagram Code
[go]$$B
$$ +------------------
$$ | . O . O , O . . |
$$ | O O O , , O . . |
$$ | , O , , , O . . |
$$ | M , , , , O . . |
$$ | , , O O O O . . |
$$ | O O O . . . . . |
$$ | . . . . . . . . |
$$ | . . . . . . . . |[/go]
This diagram displays the region doomed worthless by the marked "useless point" from Black's point of view.
- Click Here To Show Diagram Code
[go]$$B
$$ +------------------
$$ | . O M O X O . . |
$$ | O O O X X O . . |
$$ | X O X . X O . . |
$$ | M X X X X O . . |
$$ | X X O O O O . . |
$$ | O O O . . . . . |
$$ | . . . . . . . . |
$$ | . . . . . . . . |[/go]
Neither side will play at any of the marked "useless points", which therefore are "unplayable useless points".
The determination of "terriory" is affected by these "unplayable useless points".
----------
- Click Here To Show Diagram Code
[go]$$B
$$ +--------------------
$$ | . O X . X X O . . |
$$ | O . X . X X O . . |
$$ | X X X X O O O . . |
$$ | O O O O O . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |[/go]
This is J89's L&D Example 2.
I have modified it slightly so as not to distract from the actual topic.
- Click Here To Show Diagram Code
[go]$$B
$$ +--------------------
$$ | . @ B . X X O . . |
$$ | @ M B . X X O . . |
$$ | B B B B O O O . . |
$$ | O O O O O . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |[/go]
The "useless point"
![x :ex:](./images/smilies/ex.gif)
is RIGHT NEXT to White's "seki-stones"
![white with square :ws:](./images/smilies/ws.gif)
, as well as to Black's "life-stones"
![black with circle :bc:](./images/smilies/bc.gif)
.
- Click Here To Show Diagram Code
[go]$$B
$$ +--------------------
$$ | , , X . X X O . . |
$$ | , M X . X X O . . |
$$ | X X X X O O O . . |
$$ | O O O O O . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |[/go]
The diagram above shows the region doomed worthless by the marked "useless point" from White's point of view.
- Click Here To Show Diagram Code
[go]$$B
$$ +--------------------
$$ | . O , , , , O . . |
$$ | O M , , , , O . . |
$$ | , , , , O O O . . |
$$ | O O O O O . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |[/go]
This diagram displays the region doomed worthless by the marked "useless point" from Black's point of view.
- - - - -
The iterative method should be clear now, so let us discuss the board's topology a bit further, instead.
- Click Here To Show Diagram Code
[go]$$B
$$ +--------------------
$$ | . O Y . Y X O . . |
$$ | O . Y . X X O . . |
$$ | X X X X O O O . . |
$$ | O O O O O . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |[/go]
As a matter of course, Black stones cannot surround Black stones, as "Black stone" is the material the fences are made of.
Black's marked stones simply disappear in Black's topological view on the board.
- Click Here To Show Diagram Code
[go]$$B
$$ +--------------------
$$ | . W ? . ? X O . . |
$$ | W . ? . X X O . . |
$$ | X X X X O O O . . |
$$ | O O O O O . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |[/go]
Neither can Black stones effectively surround "
alive" White stones.
White's marked stones simply disappear in Black's topoligical view on the baord, as well as everything these stones surround.
- Click Here To Show Diagram Code
[go]$$B
$$ +--------------------
$$ | ? ? ? , ? X O . . |
$$ | ? , ? , X X O . . |
$$ | X X X X O O O . . |
$$ | O O O O O . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |[/go]
This diagram shows Black's resulting topological view on the board.
- Click Here To Show Diagram Code
[go]$$B
$$ +--------------------
$$ | , O ? ? ? ? O . . |
$$ | O , ? ? ? ? O . . |
$$ | ? ? ? ? O O O . . |
$$ | O O O O O . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |[/go]
This is the comparable topological White view.
You will easily realise that the empty point that exists in BOTH topological views is the "useless point".
- - - - -
- Click Here To Show Diagram Code
[go]$$B
$$ +--------------------
$$ | . O X . X X O . . |
$$ | O M X . X X O . . |
$$ | X X X X O O O . . |
$$ | O O O O O . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |[/go]
Neither side will play at the marked point, which therefore is an "unplayable useless point".
The determination of "territory" is affected by this "unplayable useless point".
----------
To be continued ... (simply follow the link)