Sam Trenholme:
| What is you experience with how being colorbound affects the value 
| of a short range leaper?

I never tried measuring heavily 'challenged' pieces like the Alfil or
Dabbaba. So I can only speak for color-bound pieces that can still access
50% of the board, like Bishop, Ferz, Camel, FD.

My experience is that, when I measure those in pairs of opposite color,
their value hardly suffers. A pair of FDs was worth almost as much as a
pair of Knights (580 vs 600). But in analogy to Bishops the value of such
a pair should be split in a base value and a pair bonus. A good way to
measure the pair bonus seems playing the two color-bound pieces on the
same color against a pair on different color. At least for the Bishops
this worked quite well, using Joker.

Problem is that Fairy-Max is really a bit too simple to measure a subtle
effect like this, as its evaluation does not include any pair bonuses. In
micro-Max, for orthodox Chess, I simply make the Bishop worth more than a
Knight, to bias it against B vs N trades. Although this makes it shy away
from B vs N trades even with only a single Bishop for no justifyable
reason, this is not very harmful. Unfortunately, this trick does not make
it avoid trading Bishops of unlike color against Bishops of like color.
And when tboth engines see these as perfectly equal trade, they become
very likely, wasting the advantage of the pair. I guess I could fix this
by programming the Bishops of either side as different pieces, and give
the Bishops of the side that has the pair a larger base value. (And
similar for other color-bound pieces.) I have not tried this yet.

Note that one should also expect cross-type pair bonuses, e.g. an FD plus
a Bishop are worth more if they are on unlike color. I am also not sure
how to calculate pair bonuses if there are more than 2 color-bound pieces
on the board foreach side. E.g. with 4 Bishops, two on white, two on
black, do I have two pairs, or four pairs?

I currently believe Betza's conjecture as a working hypothesis, that as
long as you have one piece of every color-class, the total value of the
set does not suffer from the color boundness. But I haven't tested 8
Alfils per side, and I have no idea how much the value of the set
decreases if you have only 4 left. There could be a term that is quadratic
in the number of Alfils in the evaluation. All this can in principle be
tested, but a piece with 4 targets, like Ferz, is not much worth to begin
with (~150 cP on 8x8). The Alfil is most likely not better, even in a
dense pack. And pair-bonus effects are usually again a small fraction of
the base value, and might be as low as 20 cP. It requires an enormous
number of games to get such small difference above the noise threshold.