Hi,
I am wondering what would be the effect of using area counting while evaluating the size of endgame moves.

Click Here To Show Diagram Code

[go]$$Bc Endgame moves
$$ -------------------------------
$$ | . . . . b b . . . c c . . . .
$$ | . . . . X O O O O O X X X . .
$$ | . . . . X O . . . O X . . . .
$$ | . . . . X O . . . O X . . . .
$$ | a X X X X O . . . . . . . . .
$$ | a O O O O O . . . . . . . . .
$$ | . . . . . . . . . . . . . . .
$$ | . . . . . . . . . . . . . . .
$$ | . . . . . . . . . . . . . . .
$$[/go]

Here, closing the frontier at aa is worth 4 points double sente, while bb is 3 points sente/gote, and cc is 2 points double gote.

However, if we count stones + territory instead of territory + prisoners, then all three sequences are worth 4 points.

It comes from the fact that territory and area scoring are only equivalent as long as the two players play the same number of stones.

If the endgame moves have follow-ups, then the difference between their "territory" value and "area" value can be even bigger, because the same player may play several stones in a row locally while the opponent plays elsewhere.

What is the right explanation ?

a) The two methods are right. Any excess of points given by one of them in a local endgame sequence is necessarily cancelled by a shortage in another local endgame sequence.
b) The two methods don't give the same value to sente and gote.
c) Both methods are just approximations. The only exact value of a move is the best final score the player can get using global perfect play until the end of the game.

What is the right explanation?

d) With some exceptions, depending upon the rules, an area play gains 1 point more than a territory play. That is because the stone played counts as 1 point under area scoring, but 0 pointns under territory scoring. The exceptions mainly have to do with whether territory is scored in seki.

A reverse sente, gote, or ko may each have a different swing under area scoring and territory scoring, but the average gain for each will be one point more under area scoring than under territory scoring (with some exceptions, as noted).

For instance, a ko may have a swing of 4 points under area scoring, but only a swing of 1 point under territory scoring. The average gain per move in the ko is 4/3 under area scoring, 1/3 under territory scoring. 1/3 + 1 = 4/3 , as advertised.

A gote with a swing of 4 points under area scoring has a swing of 2 points under territory scoring. The average gain per move is 2 points under area scoring, 1 point under territory scoring.

A reverse sente with a swing of 4 points under area scoring has a swing of 3 points under territory scoring. The average gain per move is 4 points under area scoring, 3 points under territory scoring.

If you calculate the average gain per move the mystery disappears.

Edit: Here is a illustrative diagram.

Click Here To Show Diagram Code

[go]$$Bc Area 4 pt. swings
$$ -------------------------------
$$ | . . . . X W 7 O . . 6 4 5 . .
$$ | . . . . X X O O O O O X X X .
$$ | . . . . X O . . . O X . . . .
$$ | . . . . X O . . . O X . X . .
$$ | 3 X X X X O . . . . . . . . .
$$ | 1 O O O O O . . . . . . . . .
$$ | 2 . . . . . . . . . . . . . .
$$ | . O . . . . . . . . . . . . .
$$ | . . . . . . . . . . . . . . .
$$[/go]

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

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Thanks !

Is it possible to have a situation with two independent endgame sequences, where area counting would lead to A being worth more than B, while territory counting would tell the opposite ?

I don't think so, except unless by "area counting" you expand it to mean the typical area counting rules in which points in seki count whilst in "territory counting" they don't. Then you could have a move that makes a seki with some eye points which would be less by those number of eye points in area vs territory.

In my experience everyone, including Chinese players, calculates the sizes of moves during the game using territory swings (possible converting to miai values for comparisons) as it's simpler and more intuitive to not keep adding 1s all the time. The only time, afaik, area counting of the stones makes a difference to size of moves is when you are running out of dame (so tedomari is important) and the last ko.

That's interesting! I had been wondering for a while about using area counting to calculate endgame move values because it seemed like it would be simpler.

With territory counting you have to count White territory (generally with respect to some artificial boundary on the board) and Black territory for two different sequences. That means either

• Keeping two old numbers (White and Black territory) in your head for sequence A while you calculate two new numbers for sequence B, then doing some math
• Remembering just the difference between the two old numbers, but that always feels artificial
• Remembering the difference in White territory between sequences A and B, and then the same for Black, but this requires visualizing each sequence twice.

My hope was that with area counting all you have to do is look at how the border between the two colors has changed, which should be easier to do in one pass in your head. But if no one does this, then either it's not as easy I think, or everyone just learns to be efficient with the territory method so there's no point in switching.

It sounds like you are asking about final scores, not the average values of moves. If so, yes.

As Uberdude points out, the rules matter, such as whether territory is counted in seki or not, and AGA, Ing, and Chinese rules, all of which use area scoring, have positions that they evaluate differently. That aside, almost always correct play by territory scoring will also be correct play by area scoring. That is why, as Uberdude also points out, Chinese pros calculate territory.

One way to make the final score differ is to change who gets the last dame, since dame count as 0 in territory scoring, but as 1 pt. in area scoring. And one way to do that is to alter the parity of the number of dame in seki (odd or even). And that is possible. But then we simply have two different sequences that produce the same territory score, but one of them is better by area scoring.

Another way is with one way dame: that is, points in seki that only one player may fill, but are not territory. Those may give one player one or two more points by area scoring than by territory scoring.

In practice, as Uberdude also points out, having a final ko that does not have to be filled by area scoring is the main way (aside from points in seki) that you can get correct play by territory scoring to be incorrect by area scoring. (In the early 20th century there were disagreements about counting territory in unfilled kos, but now all professional territory rules do not do so.) Also, there is no single way to evaluate kos. I developed a theory of ko evaluation that would evaluate such kos differently, and thus indicate different lines of play under territory scoring and area scoring. See forum/viewtopic.php?p=193996#p193996 .

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

IMO there are some positions that are easier to evaluate by area scoring, and some that are easier to evaluate by territory scoring. Back in the early '80s I wrote an article about that, which was never published. I suppose that Chinese pros calculate by territory because territory is easier to count, in general. There is less of it.

Short story. The original environmental go game, between Jiang Jujo and Rui Naiwei, was to be played under Ing rules, which use area scoring. In fact, it took place at the Ing Center. At the end of play, however, Berlekamp and I got a different winner than Jujo and Naiwei. The reason was that they were counting territory. That meant that the coupons were each worth 1 pt. more for them. We had thought that the 1 pt. coupon was equivalent to a Japanese dame, but that was not how they had viewed it. So when we published the results we said that it was played under territory scoring. Which, in effect, it was. That was when they told us that Chinese pros normally calculate territory, not area.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

No, I was just thinking about pure territory (like in the Simplified Japanese rule, with points in seki, and in the last ko).

Something like this, for example :

Click Here To Show Diagram Code

[go]$$B
$$ ------------------
$$ | O O O . . a a . .
$$ | b X O . . O X . X
$$ | b X O . . O X . .
$$ | b X O , . O X . .
$$ | b X O . . O X . .
$$ | b X O O O O X . .
$$ | X X X X X X X . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

Here, the double gote AA is worth 2 points in territory counting, and 4 points in area counting.

I suppose that BB can be seen as 1 point sente, or 1.875 points double gote (1 + 1/2 + 1/4 + 1/8). Let's see it as gote.
In area counting, it will be 2 + 2/2 + 2/4 + 2/8 + 2/16 = 3.875 points.

With both methods, AA is worth a bit more than BB.

For AA, the values given by area scoring are two points more, because for White being gote, we count one more stone, and for Black being gote, we count also one more stone.

I was wondering if these two extra points being applied to some endgame sequences only, and not to other ones, could lead A > B to become A < B. But I couldn't find any example.

It seems that the area values are always superior or equal to the territory values. Is that so ?

If we sum many follow-up moves like in the BB example, can it lead to more than 2 points of difference between area and territory values ?

OK. You are using swing counting. So far, so good.



You can't apply those two extra points to any endgame sequence. For that you have to use how much a play gains. The hane-tsugi at "a" gains 1 point by territory scoring, not 2, and 2 points by area scoring, not 4. Similarly, the play at the mouth of the corridor gains 0.9375 by territory scoring, not 1.875, and 1.9375 by area scoring, not 3.875.



A play by area scoring gains 1 point more than a play by territory scoring, because the stone played counts as 1 point by area scoring.



No. You can get more than 2 points difference with kos, however.

Here is an example where equivalent territory plays make a difference by area scoring.

Click Here To Show Diagram Code

[go]$$B 1 point swing by area scoring. Outer stones alive.
$$ ------------------------
$$ . X 2 X . X a O . O 1 O .
$$ . X O X X X X O O O X O .
$$ . X O O O O O X X O X O .
$$ . . . . . . O . X X X . .
$$ . . . . . . . . . . . . .[/go]

When plays elsewhere gain less than 8.5 points for either player by area scoring, the player with the move may be able to get the last dame with double sente. For instance, with 7.5 komi, if Black would get 7 more points of territory on the board than White, thus losing by 0.5 when White gets the last dame, she could arrange to get the last dame by playing with sente and win by 0.5, instead. Conversely, if White had the move he could connect at 1 with sente and hold Black to a lead of 7 points on the board. OC, none of this would affect the territory score.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

How to calculate the local area count of a local gote endgame?

Click Here To Show Diagram Code

[go]$$B Initial position
$$ ------------------
$$ | O O . O . . . . .
$$ | X X X O O . . . .
$$ | . . X X O . . . .
$$ | . . . X . . . . .
$$ | . . . . . . . . .[/go]

Click Here To Show Diagram Code

[go]$$B Locale
$$ ------------------
$$ | W W C O . . . . .
$$ | X X X O O . . . .
$$ | . . X X O . . . .
$$ | . . . X . . . . .
$$ | . . . . . . . . .[/go]

Click Here To Show Diagram Code

[go]$$B Black starts
$$ ------------------
$$ | O O 1 O . . . . .
$$ | X X X O O . . . .
$$ | . . X X O . . . .
$$ | . . . X . . . . .
$$ | . . . . . . . . .[/go]

Click Here To Show Diagram Code

[go]$$B Black follower, local area count B = 3
$$ ------------------
$$ | C C B O . . . . .
$$ | X X X O O . . . .
$$ | . . X X O . . . .
$$ | . . . X . . . . .
$$ | . . . . . . . . .[/go]

Click Here To Show Diagram Code

[go]$$W White starts
$$ ------------------
$$ | O O 1 O . . . . .
$$ | X X X O O . . . .
$$ | . . X X O . . . .
$$ | . . . X . . . . .
$$ | . . . . . . . . .[/go]

Click Here To Show Diagram Code

[go]$$B White follower, local area count W = -3
$$ ------------------
$$ | W W W O . . . . .
$$ | X X X O O . . . .
$$ | . . X X O . . . .
$$ | . . . X . . . . .
$$ | . . . . . . . . .[/go]

We have the followers' local area counts B = 3 and W = -3.

The local area count in the initial position is C = (B + W) / 2 = (3 + (-3)) / 2 = (3 - 3) / 2 = 0/2 = 0.

What does this value mean for positional judgement?!

For comparison, the local territory count in the initial position is Ct = 2. It is easy to understand this for positional judgement.

How to derive meaning for positional judgement from the local area count?

Let me try. In the initial position, locally, White has played an excess of 2 stones. Therefore, assuming alternation, Black has played 2 stones elsewhere. If we also take them into account, we get the modified C + 2 = 0 + 2 = 2 points for the positional judgement from the local area count.

Is this interpretation right?

EDITS

Click Here To Show Diagram Code

[go]$$B Initial position
$$ ------------------
$$ | W W C O . . . . .
$$ | X X X O O . . . .
$$ | . . X X O . . . .
$$ | . . . X . . . . .
$$ | . . . . . . . . .[/go]

In the region of play, which is marked, the count is 0 by area scoring, +2 (for Black) by territory scoring. To convert between the two I just add a point for each White stone in the original position to the area count to get the territory count, or, equivalently subtract one point for each White stone from the territory count to get the area count. And, OC, I would do the opposite for each Black stone. This follows from the fact that area scoring counts stones but territory scoring does not. The corner region has a territory count of two points for Black, but there are two White stones there, so we count each stone as one point for White, yielding an area count of zero.

OC, when the stone difference is not the only difference between the scores, you have to take the other differences into account.

Edit:

Click Here To Show Diagram Code

[go]$$B Initial position
$$ ------------------
$$ | W W . W . . . . .
$$ | B B B W W . . . .
$$ | . . B B W . . . .
$$ | . . . B . . . . .
$$ | . . . . . . . . .[/go]

Note that in the larger region shown here each player has played the same number of stones, so the territory count and area count in the larger region are the same, with possible exceptions, as noted before.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

1 point for each white stone in the locale means calculating -1 for each because the area count is viewed from Black's value perspective so white stones must be subtracted.

EDIT: oops no. Added instead of subtracted. But what is the theoretical explanation for this arithmetic operation? I understand it with my earlier reason given: Black must have played 2 stones elsewhere, which we can add.

***

The other differences? Hm.
- the pass difference
- the difference of not recompensated handicap stones minus 1
- any pass stones if applicable
- komi
- for the global context, the prisoner difference to avoid counting all stones on the board and avoid accounting earlier removals per locale
Are these all?

Then, depending on study purposes, it can be useful to consider BoardParity and SekiParity. Not to mention any rules exceptions, of course.

EDITED

Well, if each player has played the same number of stones, then, barring exceptions, the territory count and area count are the same. You can start from there. But the simple point is that each stone played gains one point for the player who played it by area counting and zero territory counting. That holds for both final scores and counts before scoring. In the three point corner White has played two more stones than Black, so the local area count is worth two more points for White than the territory count.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.