Re: [gnugo-devel] safety_3_10.1

[bump]

> I like the idea, but have some doubts whether it can be made work well.
> I found at least 3 kind of situations where it would currently produce
> non-sense. I've appended them below. Also, I generally have some
> distrust towards valuations that cannot possibly be made continuous...

The condition of having 2 eyes cannot be made continuous!

I think the surround status is a potentially useful
measure, even though it is inherently discrete. There is a
*qualitative* difference between the situation where a
dragon is enclosed by the convex hull of its neighbors,
and when it is not. If it is not enclosed by the convex
hull of its neighbors, it is difficult to contain it
with a single move for purely geometrical reasons.

A picture is worth 1000 words. In nngs:8, the dragon at M7 is
surrounded by this criterion. Here is the expanded hull:

15 . . . . . . . . . . . . . . . . . . . 15
14 . . . . . . . . . . . . . . . . X . . 14
13 . . . . . . . . . . . . . . . O O . . 13
12 . . . . . . . . . . . . . . . . . . . 12
11 . . . . . . . . . . . . . . . . . . . 11
10 . . O . . . . . . * * * * * * * . . . 10
 9 . . . . . . . . * X * * * * * X * . . 9 
 8 . . . . . . . . * X O * * * * * * . . 8 
 7 . . . . . . . O X O * O * * * * * . . 7 
 6 . . . . . . . O X * * * * * * * * . . 6 
 5 . . . . . . * X X * * * * * * X * . . 5 
 4 . . O . O . . * O X X * * * * * * . . 4 
 3 . . . . . . . O . O * X * * * X * . . 3 
 2 . . . . . . . . . . O X * * * * . . . 2 
 1 . . . . . . . . . . . * . . . . . . . 1 
   A B C D E F G H J K L M N O P Q R S T

As soon as we add a stone at M10, it is only weakly
surrounded. As you can see, without the stone at M10,
it is very difficult to find a single move that stops
the dragon from escaping. This is a qualitative
difference, and as such is appropriately measured by
a criterion that is discrete, not continuous.

This criterion has to be used in conjunction with other
measures of course. One in particular would be small
effective size. In the 9 examples I looked at, 8 had
effective sizes of at 10 or 11, and only one (safety:5)
had effective size of as much as 15.

>    A B C D E F G H J K L M N O P Q R S T
> 19 . . . . . . . . . . . . . . . . . . . 19
> 18 . . . . . . . . . . . . . . . . . . . 18
> 17 . . . . . . . . . . . . . . . . . . . 17
> 16 . . . + . . . . . + . . . . . + . . . 16
> 15 . . . . . . . . . . . . . . . . . . . 15
> 14 . . . . . . . . . . . . . . . . . . . 14
> 13 . . . . . . . . . . . . . . . . . . . 13
> 12 . . . X . . . . . . . . . . . X X . . 12
> 11 . . . . . . . . O . . . . . . . . . . 11
> 10 . . . X . . . . . O . . . . . X . . . 10
>  9 . . . . . . . . . . . . . . . . . . . 9
>  8 . . . . . . . . . O . . . . . a . . . 8
>  7 . . . . . . . . . . . . . . . . . . . 7
>  6 . . . X . . . . . . . . . . . X . . . 6
>  5 . . . . . . . . . . . . . . . . . . . 5
>  4 . . X X . . . . . O . . . . . X X . . 4
>  3 . . . . . . . . . . . . . . . . . . . 3
>  2 . . . . . . . . . O . . . . . . . . . 2
>  1 . . . . . . . . . . . . . . . . . . . 1
>    A B C D E F G H J K L M N O P Q R S T
> 
> The stone at K2 means that K4 is not surrounded. If
> you remove it, K4 is surrounded. Now if you add a
> black stone at _a_, it is only weakly surrounded (it
> should be _not_ surrounded according to your
> explanations, but running your patch on it gives
> weakly surrounded).

About the stone at K2, some tweaking of the criterion
near the edge may be necessary. There's more to be said
about this but for the moment suffice it to say I don't
consider this a very serious problem.

The last point --- that adding to the enclosure makes
the dragon less surrounded --- is more disturbing.

Without the stone at 'a':

13 . . . . . . . . . . . . . . . . . . . 13
12 . . . X . . . . . . . . . . . X X . . 12
11 . . . . . . . . O . . . . . . . . . . 11
10 . . . X . . . . . O . . . . . X . . . 10
 9 . . . . . . . . . . . . . . . . . . . 9 
 8 . . . . . . . . . O . . . . . . . . . 8 
 7 . . . * * * * * * * * * * * * * . . . 7 
 6 . . * X * * * * * * * * * * * X * . . 6 
 5 . . * * * * * * * * * * * * * * * . . 5 
 4 . * X X * * * * * O * * * * * X X * . 4 
 3 . . * * * * * * * * * * * * * * * . . 3 
 2 . . . . . . . . . . . . . . . . . . . 2 
 1 . . . . . . . . . . . . . . . . . . . 1 
   A B C D E F G H J K L M N O P Q R S T

With the stone at 'a':

14 . . . . . . . . . . . . . . . . . . . 14
13 . . . . . . . . . . . . . . . * * . . 13
12 . . . X . . . . . . . . . * * X X * . 12
11 . . . . . . . . O . . * * * * * * * . 11
10 . . . X . . . . . O * * * * * X * * . 10
 9 . . . . . . . * * * * * * * * * * * . 9 
 8 . . . . . * * * * O * * * * * X * * . 8 
 7 . . . * * * * * * * * * * * * * * * . 7 
 6 . . * X * * * * * * * * * * * X * * . 6 
 5 . . * * * * * * * * * * * * * * * * . 5 
 4 . * X X * * * * * O * * * * * X X * . 4 
 3 . . * * * * * * * * * * * * * * * . . 3 
 2 . . . . . . . . . . . . . . . . . . . 2 
 1 . . . . . . . . . . . . . . . . . . . 1 
   A B C D E F G H J K L M N O P Q R S T

We see that enlarging the surrounding dragon has brought
allies into the hull, so that the dragon no longer
satisfies the definition of being surrounded.

> 12 . . . X . . . . . . . . . . . . . . . 12
> 11 . . . . . . . . . . . . . . . . O . . 11     WHITE has captured 0 stones
> 10 . . . X . . . . . + . . . . . + . . . 10     BLACK has captured 0 stones
>  9 . . . . . . . . . . . . . . . . . . . 9
>  8 . . . . . . . . . . . . . . . . O . . 8
>  7 . . . . . . . . . . . . . . . . O . . 7
>  6 . . . X . . . . . . . . . X . X . . . 6
>  5 . . . . . . . . . . . . . . . . O . . 5
>  4 . . X X . . . . . O . . X . . X O . . 4
>  3 . . . . . . . . . . . . . . . X O . . 3
>  2 . . . . . . . . . . . . . . . X X X . 2
>  1 . . . . . . . . . . . . . . . . . . . 1
>    A B C D E F G H J K L M N O P Q R S T
> 
> K4 is only weakly surrounded because of the white dragon at R5/R7.

This example can be fixed if we disregard friendly
dragons within the hull if they are not neighbors of
the dragon under attack. That does not help with the
first example, however, where the J11 dragon is a
neighbor of K4.

Dan