Re: computer-go: Evaluating positions

["Eric Boesch" <ericboesch@xxxxxxxxxxx>]

Nick Wedd wrote:
> Doesn't a quarter-alive group have _more_ influence than a three-
> quarter-alive one?
>
> If you thrash around near a live but weakish group, you risk weakening
> it further.  If you thrash around near a more-or-less-dead group, you
> have little downside risk, and have threats to resurrect it.
The fastest way to add an appearance of friendly influence to vacant or 
enemy-controlled parts of the board, is to drop a stone right in the middle 
of it.  The influence function, left alone, would advocate doing this 
consistently, and litter the board with aggressive but dead stones.

Here are the details of my program's influence function, if anyone cares.  I 
thought it performed well, but writing an adequate influence function is 
easy.  In constrast, the strength function (to use Vlad's terminology 
instead of "percent-alive") comes in two flavors:  awful or hypothetical.

Control of a point is a value between -1 and 1:

   C(x,y) = (w - b) / (k + w + b)

k is fixed for each point on the board; it is highest in the middle  and 
lowest in the corner.  w is the total white influence (with strength 
factored in) over point (x,y).  b is black influence.

Now I will define w more precisely.

 w = sum(over all paths P from all white stones s to point (x,y))
       of
   weight(length(P)) * strength(s) * crossover-penalties(P)

Duplicate paths between a stone and a point count, since the more open paths 
there are between two points, the greater the relationship between them.

weight(length(P)) decreases super-exponentially as length(P) increases, and 
drops to 0 beyond a certain point.

P incurs a (1-strength(worm)) crossover penalty for each worm (string) it 
passes over (discounting the source stone s).  So influence can radiate with 
diminished effect through another worm, but only if that other worm's 
strength is not 1, that is, only if it is conceivable that the other worm 
could be productively threatened (even if it could not be killed) sooner or 
later.

Maximizing influence alone (omitting strength(s)) strongly favors playing in 
empty or nearly-empty parts of the board, and especially disfavors playing 
near friendly stones, because of the diminishing returns represented by the 
(k + w + b) denominator.  Loose and aggressive play results.

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