Seki in territory scoring, area scoring and stone scoring

[Alcadeias]

Hello.

In my quest to find the ultimate scoring system, I found the following seki position, and I wondered how it was scored in each of the three scoring systems: territory scoring, area scoring, stone scoring.

$$c
$$ +-------------+
$$ | X X X O O . |
$$ | X X . X O . |
$$ | . O X X O . |
$$ | O . X X O . |
$$ +-------------+

Click Here To Show Diagram Code

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

With territory scoring we have:
B = 0
W = 4
Score = -4

Okay so this one is just stupid.
Black clearly has a lot of stones on the board, and White can’t kill those stones hence these stones are alive, so there’s no way that Black has zero point…
“Territory” is just a human invention. But stones on the other hand are something much more fundamental, they are two of the three possible states of every point: Black stone, White stone, or empty. Only these states should be taken into account for scoring, not “territory”.
That’s why I believe territory scoring is not logical, and the only natural scoring system is stone scoring, or area scoring with a group tax.

What’s also interesting is the score in the other two scoring systems.

With stone scoring we have:
B = 10
W = 9
Score = +1

With area scoring we have:
B = 11
W = 11
Score = 0

Incredible! They differ by 1. Mind blown. I thought that they could only differ by an even number of points.

I’ve read somewhere that:
SB = AB – 2*GB
SW = AW – 2*GW
SB – SW = (AB – 2*GB) – (AW – 2*GW)
StoneScoring = AreaScoring – 2*(GB-GW)

SB = Stone scoring for Black
SW = Stone scoring for White

AB = Area scoring for Black
AW = Area scoring for White

GB = Number of groups that Black has
GW = Number of groups that White has

But so apparently this formula is only an approximation that only works if there are no seki.

So what’s the general formula that is always true even when there is seki?

Maybe this:

SB = AB – 2*IAGB – SGB
SW = AW – 2*IAGW – SGW
SB – SW = (AB – AW) – 2*(IAGB – IAGW) – (SGB – SGW)
StoneScoring = AreaScoring – 2*(IAGB – IAGW) – (SGB – SGW)

IAGB = Number independently alive groups that Black has
IAGW = Number of independently alive groups that White has

SGB = Number of seki groups that Black has and which have precisely one eye
SGW = Number of seki groups that White has and which have precisely one eye

Basically the formula means that each color gets a tax of two points for each of their independently alive groups, a tax of one point for each of their seki groups which have precisely one eye, and there is no tax for seki groups which have zero eye.

I’m not even sure if it’s really the correct formula… It seems to be correct for almost every seki positions that I could find, but I’m not totally sure if it’s also correct for the position that I presented previously, it’s a really tricky position… The formula would work if we considered that all the Black stones are forming one single seki group which has precisely one eye, but it’s not clear if that’s really the case…
This is beginning to get too complicated for me, I’m only a 15 kyu patzer.

[Bill Spight]

You need to include other forms of territory scoring.

$$c
$$ +-------------+
$$ | X X X O O . |
$$ | X X . X O . |
$$ | . O X X O . |
$$ | O . X X O . |
$$ +-------------+

Click Here To Show Diagram Code

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

Lasker-Maas, Spight, and Ikeda (some number): Black has 1 point, White has 4. Net score = -3

Territory scoring with "group tax", No pass go with prisoner return: Black has no points, White has 2. Net score = -2

[RobertJasiek]

There are different kinds of territory scorings. Some score "territory" in seki.

Instead of considering only particular sekis, think in general and independently of the seki shapes. (You would not believe quite a few possible seki shapes.) Speak of numbers of empty intersections occupied or surrounded in specific manners.

[xed_over]

Hello.

With territory scoring we have:
B = 0
W = 4
Score = -4

With stone scoring we have:
B = 10
W = 9
Score = +1

I'm confused.
Assuming the players took turns, then there would either be at least two or three captured white stones, depending on whether or not black or white played last.

so if white played last and there were 3 captured stones, then the first example:
With territory scoring we have:
B = 0
W = 4 - 3
Score = W+1

Does Stone counting literally mean counting only the live stones on the board, and nothing else?
Then isn't W = 7 ? How did you get 9?
so
With stone scoring we have:
B = 10
W = 7
Score = B+3

Yes, seki can change things. You should first understand the basics, before trying to understand the more complicated situations.

And contrived unreachable positions seem pointless to me.

edit: corrected misspelling of life for live

[RobertJasiek]

Does Stone counting literally mean counting only the life stones on the board

No. It is "stone scoring" and means "stones on the board".

[Alcadeias]

I'm confused.
Assuming the players took turns, then there would either be at least two or three captured white stones, depending on whether or not black or white played last.

Not necessarily. Maybe from a practical point of view you are correct, I don't know. But from a theoretical point of view, any number of captured stones is possible.

Then isn't W = 7 ? How did you get 9?
so
With stone scoring we have:
B = 10
W = 7
Score = B+3

Currently White has 7 stones on the board, and he can play 2 more stones on the right like in the following diagram (but he must leave 2 empty points for his two eyes), so he has 7+2=9 points.

$$c
$$ +-------------+
$$ | X X X O O . |
$$ | X X . X O O |
$$ | . O X X O . |
$$ | O . X X O O |
$$ +-------------+

Click Here To Show Diagram Code

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

[xed_over]

Does Stone counting literally mean counting only the life stones on the board

No. It is "stone scoring" and means "stones on the board".

your words seems to say the same thing my words are saying (ignoring my misspelling of life for live), so I'm still confused by your no response.

Alcadeias and Sensei's has cleared it up for me, thanks
http://senseis.xmp.net/?StoneScoring

so Stone scoring is kinda like Ing fill-in counting, except for leaving two open points on the board for each group.

[RobertJasiek]

In the earlier thread context, we have not been speaking about counting procedures but scoring systems, so I presume you should say scoring in order to avoid unnecessary confusion about contents.

Please note that I have removed LIVE / LIFE because it does not belong the definition of stone scoring. Even your cited SL page gets it [almost] right: "the stones are simply counted." (It should say: "scored") The stones - not their life and death status.

http://home.snafu.de/jasiek/endrules.html
http://home.snafu.de/jasiek/e7.html
http://home.snafu.de/jasiek/int.html

[phillip1882]

in aga rules, in order to achieve that position, white would have had to pass and thus give up a stone 4 times. (one extra pass so he has last play.)
this gives territory score black 1 point, white 0 points and area score black 11 points white 11 points.
(i think in aga rules white gets 1 extra point komi for an even game in territory scoring. not sure though.)

[xed_over]

(i think in aga rules white gets 1 extra point komi for an even game in territory scoring. not sure though.)

not true. where did you hear such silly things?

white must play last, so if white passed first, then he will pass two stones to black's one. otherwise, if black passes first, then they each only pass one stone.
but that just makes sure that territory counting/scoring (I often use these terms synonymously, since one can't score without counting), is the same as area counting/scoring where its unnecessary to keep track of prisoners at all.

[phillip1882]

then why in my analysis does area and territory differ by 1 point?

[HermanHiddema]

then why in my analysis does area and territory differ by 1 point?

Because you had white pass four times instead of three times. Under AGA, both players must play the same number of moves (or pass stones). Black has 10 on the board, white has 7, so white has to give three pass stones to equalize.

[phillip1882]

okay let me run through my logic.
let's ignore this position for the moment and instead say we have a normal 19x19 game of go with 3 dame points, with it being blacks' move. there are no captures on the board.
white believes he will win by more than three points and decides to rub it in his opponents face by passing and giving up stones.
black plays 1 dame. white passes. black plays the second dame. white passes the second time. black takes the third dame. white passes, black passes, white passes again. ooooohhhh i see what i did wrong. i didn't count black's pass. so the score for territory under aga rules for that positon would be 0 - 0.

[skydyr]

okay let me run through my logic.
let's ignore this position for the moment and instead say we have a normal 19x19 game of go with 3 dame points, with it being blacks' move. there are no captures on the board.
white believes he will win by more than three points and decides to rub it in his opponents face by passing and giving up stones.
black plays 1 dame. white passes. black plays the second dame. white passes the second time. black takes the third dame. white passes, black passes, white passes again. ooooohhhh i see what i did wrong. i didn't count black's pass. so the score for territory under aga rules for that positon would be 0 - 0.

Yeah, the pass stones are a gimmick to ensure that both sides played an equal number of moves.

[doubleoverflow]

Black can fill in the false eye. White can fill at the right side to form two eyes. So stone scoring would be B11, W9.

Area scoring, B12, W12.

AGA territory scoring, suppose 10 turns for each player, B 1+3 pass stones = 4, W 4.