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M. Winther:
| Muller, I haven't bothered to figure out Zillions's piece evaluation
| method. Of course, in the initial position the knight is placed at the 
| rim and threatens only 3 squares. Closer to the centre it threatens 8 
| squares. I suppose this is why its value increases more than the
| bishop.

Ah, OK. You were speaking on the very short term, after development but
before material got traded. I consider that positional evaluation, not
part of the piece values. In the opening the positional evaluation is not
a strategic feature: all pieces are placed very poorly, but the opponent
does also have no means yet to prevent you from moving them to average
locations. A minimax search from the opning will thus be able to reach
leaves where the piece placement is more typical, and the score of such a
search does properly include the strategic part of the positional
evaluation, where the evaluation of the single position would not.

If you have not figured out Zillions evaluation, how did you obtain the
numbers you quote? Does Zillions print its total evaluation of the root
position, or can one specify a fixed search depth and print the score of
that? In that case you could simply delete a Knight from one side and a
Bishop from the other, and note the score imbalance this creates (in, say,
a 10-ply search), and then delete another Bishop on both sides and repeat
the experiment, to see if the the imbalance is affected. In case 1 you
would have BB-BN, which involves B-N difference plus B-pair bonus, while
in the second case it would be B vs N, only dependent on the B-N
difference.

| On 10x10 boards this is an even greater problem. The difference 
| between a bishop and a knight corresponds, perhaps, to a pawn. Of 
| course, there are important strategical aspects to this. One cannot 
| trade a bishop for a knight easily. 

Well, so you trade it for N+P. Pawns are abundant, and in the beginning
usually the sole defendants of Knights. So opportunities for trades like
that occur often enough. The situation is not worse as in Capablanca,
where you would effectively lose a full Pawn on trading your first Bishop
for a Knight. If the Bishop gets worth even more, trading B+P vs R (about
neutral in Capablanca, for the first Bishop) would be a natural channel.

Btw, I doubt that 10x10 would really affect the Bishop value so much. It
is mainly the increased width of the board, allowing the Bishop more
forward moves, that causes its value to increase.