Single Comment

George Duke:
| Has initial array positioning already entered discussion for 
| value determinations?

No, it hasn't, and I don't think it should, as this discussion is about
Piece Values, and not about positional play. Piece values are by
definition averages over all positions, and thus independent on the
placement of pieces on the board.

Note furthermore that the heuristic of evaluation is only useful for
strategic characteristics of a position, i.e. characteristics that tend to
be persistent, rather than volatile. Piece placement can be such a trait,
but not always. In particular, in the opening phase, pieces are not locked
in the places they start, but can find plenty better places to migrate to,
as the center of the board is still complete no-man's land. Therefore, in
the opening phase, the concept of 'tempo' becomes important: if you waste
too much time, the opponent gets the chance to conquer space, and prevent
your pieces that were badly positioned in the array to properly develop.

I did some asymmetric playtesting for positional values in normal Chess, swapping Knights and Bishops for one side, or Knights and Rooks. I was not able to detect any systematic advantage the engines might have been deriving from this. In my piece value testing I eliminate positionsal influences by playing from positions that are as symmetric as possible given the material imbalance. And the effect of starting the pieces involved in the imbalance in different places is averaged out by playing from shuffled arrays, so that each piece is tried in many different locations.