Thanks again for your replies, and for inviting me to join this list.
Your comment about the current influence generator being multi-purpose and geared to "point counting" makes me think that a separate "strategic" influence mapping may be appropriate.
[PF]:
>> 1) Little consideration is paid to the concept of "aji." Stones which
>> are "effectively" dead, according to the criteria presented,
>> nonetheless contain the potential to "spring to life" and as such
>> continue to exert influence and deserve to be figured into strategic
>> calculations. (This perhaps explains some of the curious situations
>> where the program seems to "give up" during hand-to-hand combat.)
>
[GF]:
>Sure, handling aji is a weak point. I doubt making dead stones
>generate influence is an effective solution though. In particular when
>the influence is used to estimate territory it would seem
i>nappropriate.
[PF]:
A lot depends on how you define a "dead stone". I'm sure we have all had the experience of playing a stronger player and having stones we deemed dead suddenly seem to come alive or threaten to come alive out of nowhere.
So perhaps a distinction must be made between an influence map that counts territory, and an influence map that is used for strategic purposes. For the purpose of strategy, the "aji" of what might otherwise be considered dead stones becomes quite relevant. In particular, as long as ANY neighboring stones do not have two eyes or there remains the potential space to create or link to a live structure, I would not count that stone dead, and I would say it has some defineable amount of power (influence). In the case were it truly is doomed, I believe the opponent stones influence values would be so high as to swamp the influence around the "dead" stone and make it irrelevant. Of course, a linear declining function would show this better than an exponential declining. See next.
[PF]:
>> 2) No justification is given as to why the influence dropoff is
>> exponential rather than linear or even plausibly a curve that is the
>> reverse of exponential. Several "adjustments" to the Gnu Go algorithm
>> seem to address deficiencies of the exponential drop-off, for example,
>> the need to boost the influence of a wall as opposed to a single
>> stone, and the monkey-jump situation. I would like to revisit these
>> and other positions, presenting alternative dropoff formulations. My
>> intuition is that a linear dropoff will prove the most useful.
[GF]:
>Yes, the exponential dropoff is an ad hoc choice, as would any other
>choice have been. My intuition is that exponential dropoff is
>generally most useful.
[PF]:
Last night I was able to finish programming the ability to import and export positions as well as board diagrams (console-text mode) and influence maps. I have started to create a series of diagrams of various wall sizes and extensions. The point is that we know from experience what is over-concentrated and what is thin, and to see what sort of numbers are generated. I will send them to the list if there is any interest, once I have completed the set and polished up the document.
For a linear drop-off, there is somewhat more consistency, at first look, as to numbers that denote weak, invadeable points and what invasions might be considered hari-kari. With the exponential drop-off (I am simulating this with the sequence 100, 33, 11, 4, 1, 0), it seems that the numbers are less reliable in predicting this distinction.
An important quality of a STRATEGIC influence/power mapper (as opposed to point-counter) would be to be consistent in this regard.
I recall there being something said about the need to find moves that create multiple threats. This is the gist of what I am trying to create. For a strategic influence map to be useful in this regard, its projection of a stone's power has to be far enough to constitute a legitimate double threat. It seems to me that the point-counting 9exponential drop-off) influence map has such a steep drop-off that after 3 or 4 spaces, the numbers are so small as to be very difficult to interpret. Thus, by its nature, it is not a tool suitable to making double threat/dual purpose strategic moves. (As opposed to tactical double threats -- where I leave this an open question.)
[PF]:
>> 5) I would challenge the adjustment made to prevent the "bending"
>> influence. What justification is there for this?
[GF]:
>Just an intuition for what properties would be useful in an influence
>function.
[PF]:
>> A move is a move, there is no momentum from point to point in the
>> sense of physical bodies. If we were to consider a model, I would
>> say Influence is more like sound than light, or more like water in
>> its ability to flow around obstacles.
[GF]:
>Well, I think I have to counter with the question what justifications
>there are for that. :-)
[PF}:
Fair enough. I think that for strategic purposes, one wants to consider the potential that a play in enemy territory has link up to friendly stones. The ability to link up is most clearly defined by the number of spaces or plays required, not the direction of the play. Consider the following diagram:
. . . . . .
. X O . . .
. X O .(X).
. X O . . .
. . . . . .
If influence does not wrap, the play at (X) would be considered to have no support whatsoever from the three X's on the far side of the O's. But clearly, their presence adds to the power of (X).
>From an earlier email:
[PF]:
>> (5) Structures like eyes or moyos have defineable "influence"
>> generating characteristics that might prove useful.
[GF]:
>I'm not quite following you here. Please elaborate.
Stones with eyeshape will generate many differentiated local peaks, stones with bad shape will have less differentiation (single peaks of high influence). Areas with walls on one, two or three or four sides will have different types of tilt or curvature. If one can spot the state of a framework (how many sides), it would be useful in determining attack strategy.