I think it would be helpful if people post their own values on the board for the pieces. Here are the ones I put in Gothic Vortex

Pawn = 100

Knight = 275 with 20 pawns, 255 with 0 pawns.
Exact value = 250 + pawns.

Bishop = 310

Rook = 530 with 0 pawns, 440 with 20 pawns.
Exact value = 530 - (pawns * 3).

Archbishop = 690 with 20 pawns, 650 with 0 pawns.
Exact value = 650 + (pawns * 2).

Chancellor = 860, unchanging

Queen = 900 with 20 pawns, 960 with 0 pawns.
Exact value = 960 - (pawns * 3).

These values were chosen carefully, but I still think they can be changed.

For example, compare how Rook + Pawn will be traded for Bishop + Knight as the pawn count varies. At the beginning of the game, R + P = 540, and B + N is 585. You don't want to give up a B + N for R + P early on, because your two minors are developed an in play, while the Rook is most likely just sitting there after having castled.

A Bishop will not trade itself for 3 pawns unless there is some other form of compensation. Notice a Knight will always trade iteself for 3 pawns, or 2 pawns + "heavy positional damage". Some of you may have seen Vortex tossing its Knight to do this already. So far, I think this is strong behavior.

Also, 2 Knights cannot mate a lone king in the absence of pawns. So, a Rook is more valuable than 2 Knights with pawns = 0 (530 for Rook, 510 for 2 Knights).

This "simple" approach makes the program appear to have endgame intelligence. It will prefer to have a Rook over 2 Knights heading into the endgame, and it can direct this play from a distance with the properly chosen values.

If others want to post their "ideal values" I would be happy to review them.