Rubilia/ Normal Values Presentation Ways

The mean scores in the normal value analysis of a particular position can be based on several reference positions. Here is an example with the interesting variants.

Table of contents [1] Absolute score [2] Score referring to the statical "as is", with all stones considered alive [3] Score referring to the point assignment that matches the effective board constellation as closely as possible [4] "Normalized values" by Bill Spight

Table of diagrams (__1.00__, 0.50) (__1.00__, 0.50) (__-0.50__, 0.50) (__2.00__, 0.50) (__-0.50__, 0.50) (__4.00__, 0.50) (__0.00__, 0.50) (__3.50__, 0.50) (__0.50__, 0.50)

[1] Absolute score

referring to the natural zero, i. e. the empty (1a) or equally devided (1b, 1c) board

(1a) referring to the empty board of the given size

(1.00, 0.50)  

+ The most realistic view. No external reference, just the position as it is shown.

- Zi counting (score referring to neutral) may be more difficult to grasp hereby than it is with a reference shown.
- This doesn`t really help to understand the idea of zi visualisation.

(1b) with equally devided board of the given size shown as reference

(1.00, 0.50)  

- In general, the shape of this reference cannot visually correspond to the actual position.
- Boardsize parity may require a shared point in the reference

(1c) with the board padded until neutral and shown as reference

(-0.50, 0.50)  

+ Visual correspondence feasible
+ Helps to understand the idea of zi visualisation.

o Score always near zero

- Requires adjusting the board sizes
- Padding may be considered ugly

[2] Score referring to the statical "as is", with all stones considered alive

(2.00, 0.50)  

+ No reference needs to be shown.

- In open positions, relatively difficult to understand. Topic obfuscated.
- If absolute scores are desired, the implicit offset has to be taken into account.

[3] Score referring to the point assignment that matches the effective board constellation as closely as possible

This is the way currently used in the list - similar to variant (1c), but without padding.

(-0.50, 0.50)  

+ Visual correspondence feasible
+ Helps to understand the idea of zi visualisation.

o Score always near zero

- Requires paying attention to the reference
- If absolute scores are desired, the reference offset has to be taken into account.

                          (-1/2, 1/2)
                          /         \
                   (0, 1/2)          (-11/4, 9/4)
                   /      \         //          \
          (1/2, 1/2)      (-1/2, 1/2)           (-5, 0)
          /        \      /         \
     (1, 0)         (0, 0)          (-1, 0)

[4] "Normalized values" by Bill Spight

Bill: A way that I use, which gives what I call normalized values, is relative to the number of stones in the original position.

(4.00, 0.50)  

Reduced game tree:

                          (4, 0.5)
                          /       \
                     (5, 0)       (3, 0)

blubb: This case, if I understand you correctly, is the same as variant (2). The numbers differ because you are referring to moku rather than to zi - see also below. (Again, shouldn`t the root value be (4, 1)?)
But since you base this on the number of stones in the original position, how about positions with (single colored) eyes? Do you treat eye points as empty like the three shared ones here, or as colored? In variant (2) above, they are colored.

Bill: What makes area and territory scoring practically equivalent is that, as a rule, each player plays the same number of stones or Black plays one more. When you look at a region of the board, though, the number of stones played may not be the same or nearly so. So from the final scores I subtract the original number of stones to make the comparison between scoring methods clear. I do not treat eyes like stones.

blubb: Ah, that makes sense. So your score differs from variant (2) by the tally of eye points. Because eyes count the same under territory and area scoring, this doesn`t affect the scoring invariance. The scores you get feel more familiar than variant (2) though, particularly from the territory perspective.

One advantage of this way is that simple sekis have a count of zero. E. g,

(0.00, 0.50)  

Also, the count by area scoring and the count by territory scoring are typically the same (with White scores positive). This highlights the difference between the two forms of scoring when the count is different.

This way the score is the difference between the White score and the Black score.

blubb: The difference between the white score and the black score, in moku, is twice as big as the chinese score, in zi. The former obviously is more common in Go countries influenced by the Japanese mindset, including great parts of the west. The latter allows to see the empty board as equally devided, and to immediately visualise e. g. a 7.5 zi play as "shifting the borderline between the colors by 7.5 board points". This transparency is something I really like. Anyway, either way can be applied to all sorts of scoring. As far as I can see, variant (2) is equivalent to your suggestion except for the differing units. It also gives typically the same count under area scoring and territory scoring.

Bill: Perhaps the two are equivalent. But doesn't that mean deriving the zi by taking the final score as half the difference between the White and Black scores?

blubb: The score in zi can be derived from the white and black scores. Under chinese scoring and referring to neutral (the empty board), the traditional way to count the score of one color is enough. With a suitably chosen reference position though, not even that is necessary. (Variant (2) doesn`t really provide a well-suited reference for this, but variant (3) does.) It then suffices to determine the boarderline and see by how many board points it differs from the reference line.

We could simply take the White score.

(3.50, 0.50)  

Reduced game tree:

                          (3.5, 0.5)
                          /         \
                     (4, 0)         (3, 0)

But that does not keep the seki count at 0.

(0.50, 0.50)  

Game tree:

                          (0.5, 0.5)
                          /        \
                     (1, 0)        (0, 0)

And the comparison between the two scoring methods is obscure.

blubb: I agree.