Yesterday's rule dispute in Korea

[Pio2001]

On the other hand, the French rule forgets to tell that the dead stones must be removed if pass stones are used to count the game !
[...]
they forgot to reintroduce the part about removing dead stones there !

In fact, I'm wrong. I misunderstood the rule : there is no need to tell that dead stones must be removed, even counting territory + prisoners + pass stones, since, thanks to the pass stones, their capture costs nothing.
In the french rule, the removal of dead stones appears in the commentary, but is not part of the rule's statements.

[Bill Spight]

I realise that I do not know: what is the Capture Game?

The first player to capture one or more stones wins.

$$Wcm16 No Pass Baduk
$$ ----------
$$ | . O X X . |
$$ | 4 O O X 2 |
$$ | 5 O X X 1 |
$$ | 6 O O X 3 |
$$ | . O X X . |
$$ -----------

Click Here To Show Diagram Code

[go]$$Wcm16 No Pass Baduk
$$ ----------
$$ | . O X X . |
$$ | 4 O O X 2 |
$$ | 5 O X X 1 |
$$ | 6 O O X 3 |
$$ | . O X X . |
$$ -----------[/go]

Why is the lower right eye worth 2 points?

$$Wc No Pass Baduk
$$ ----------
$$ | . O X X . |
$$ | O O O X X |
$$ | . O X X O |
$$ | O O O X O |
$$ | . O X X . |
$$ -----------

Click Here To Show Diagram Code

[go]$$Wc No Pass Baduk
$$ ----------
$$ | . O X X . |
$$ | O O O X X |
$$ | . O X X O |
$$ | O O O X O |
$$ | . O X X . |
$$ -----------[/go]

The left side is worth -3 + 2 = -1, right? The right side, I claim, is worth 1 + 2 - 2 = 1. In which case the total score is 0, so whoever moves first loses.

$$Wc White first
$$ ----------
$$ | . O X X . |
$$ | O O O X X |
$$ | 1 O X X O |
$$ | O O O X O |
$$ | . O X X 2 |
$$ -----------

Click Here To Show Diagram Code

[go]$$Wc White first
$$ ----------
$$ | . O X X . |
$$ | O O O X X |
$$ | 1 O X X O |
$$ | O O O X O |
$$ | . O X X 2 |
$$ -----------[/go]

$$Wc White first, cont.
$$ ----------
$$ | . O X X . |
$$ | O O O X X |
$$ | O O X X 4 |
$$ | O O O X 3 |
$$ | . O X X X |
$$ -----------

Click Here To Show Diagram Code

[go]$$Wc White first, cont.
$$ ----------
$$ | . O X X . |
$$ | O O O X X |
$$ | O O X X 4 |
$$ | O O O X 3 |
$$ | . O X X X |
$$ -----------[/go]

White to play loses, as advertised.

$$Bc Black first
$$ ----------
$$ | . O X X . |
$$ | O O O X X |
$$ | . O X X O |
$$ | O O O X O |
$$ | . O X X 1 |
$$ -----------

Click Here To Show Diagram Code

[go]$$Bc Black first
$$ ----------
$$ | . O X X . |
$$ | O O O X X |
$$ | . O X X O |
$$ | O O O X O |
$$ | . O X X 1 |
$$ -----------[/go]

$$Bc Black first, cont.
$$ ----------
$$ | . O X X . |
$$ | O O O X X |
$$ | 4 O X X 2 |
$$ | O O O X 3 |
$$ | . O X X X |
$$ -----------

Click Here To Show Diagram Code

[go]$$Bc Black first, cont.
$$ ----------
$$ | . O X X . |
$$ | O O O X X |
$$ | 4 O X X 2 |
$$ | O O O X 3 |
$$ | . O X X X |
$$ -----------[/go]

Black to play loses, as advertised.

[RobertJasiek]

Oh. I expected an eye-local evaluation...!

[Bill Spight]

What is Bill Frazor's fractional territory position and your evaluation of it?

Fraser's position is a ko position, OC, since the ko takes place after the dame are filled. IIRC, each play loses ⅓ pt. on average. IOW, each play gains ⅔ pt. on average by area scoring. I'll see if I can dig it up.

[RobertJasiek]

"The result of this exchange is 16 - 10 = 6 pts. This is the result regardless of who plays first, and is therefore the value of the ko under these conditions. When Black is komaster and White's reply elsewhere gains 10 pts. the value of the ko is 6 pts. If White's reply gains 4 pts. the value of the ko is 12 pts. If White's reply gains 0 pts. (White fills a dame) the value of the ko is 16 pts. If White's reply loses 1 pt. (White fills in territory) the value of the ko is 17 pts. How the value of the ko changes with the value of plays elsewhere when one player is komaster"

Why do you call it the value of the ko and do not call it the value of the ko ensemble?

[Bill Spight]

Oh. I expected an eye-local evaluation...!

Well, it's there in the variations. In CGT terms, {1|2||} = 2.

[Bill Spight]

"The result of this exchange is 16 - 10 = 6 pts. This is the result regardless of who plays first, and is therefore the value of the ko under these conditions. When Black is komaster and White's reply elsewhere gains 10 pts. the value of the ko is 6 pts. If White's reply gains 4 pts. the value of the ko is 12 pts. If White's reply gains 0 pts. (White fills a dame) the value of the ko is 16 pts. If White's reply loses 1 pt. (White fills in territory) the value of the ko is 17 pts. How the value of the ko changes with the value of plays elsewhere when one player is komaster"

Why do you call it the value of the ko and do not call it the value of the ko ensemble?

I was explaining komaster values. Ko ensemble is a term from my theory before I learned Berlekamp's komaster theory.

[RobertJasiek]

Ok, but what then is a komaster value? A count? In which sense? Of what? How to interpret it in the global context?

[Bill Spight]

Ok, but what then is a komaster value? A count? In which sense? Of what? How to interpret it in the global context?

A komaster value is a count. In some cases it depends on the global temperature. At those temperatures the ko mast is not vertical, but inclined.

Example: Suppose we have a so-called half point ko where nothing else is left except many dame and Black is komaster. Black to play can fill the ko for 1 pt. The value of the ko is 1 pt. in that case.

Now, the mast value of the ko is the value above which the mast is vertical, and it is ⅔ in that case. Sometimes people informally refer to the mast value simply as the value, which can be confusing.

[RobertJasiek]

I am afraid I understand nothing. Thermographs do not help my understanding at all.

[Bill Spight]

I am afraid I understand nothing. Thermographs do not help my understanding at all.

But you do understand how, in the example I gave, the result will be 1, regardless of who plays first, right?

[RobertJasiek]

Yes if territory scoring is used and the ko is a basic endgame ko (not a real half point ko).

[Bill Spight]

Yes if territory scoring is used and the ko is a basic endgame ko (not a real half point ko).

OK. Example 2: Suppose we have a ko with Black, komaster, where Black to play could win the ko in 1 move for 6 pts., and if White won the ko with two moves the local score would be 0. Suppose also that there are many plays that gain 1 pt. and nothing else that gains more, except the ko. How do we value the ko by komaster theory?

[RobertJasiek]

I would want it to be 6 but you will say 5.

[Bill Spight]

I would want it to be 6 but you will say 5.

Not just me, but Professor Berlekamp. You get it.

And if there are only dame left, the value is 6.

And after the dame stage, if Black has an unremovable ko threat but White has no threat, the value is 7. (Unless the rules require Black to win the ko at the dame stage, OC. )