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I was thinking about that, too and I think is probably more complicated. Having two different pieces bounded on two different colour is definetly better than bounding them on the same colur. That is really easy too see as material gets reduced. But I'm not sure if a simple "bonus" aproach is enoguh, just as a first glance (as I did not make any experiments) should not be.
Also there is a game named Dada I had noticed where all pieces are colourbound so as to white is the attacker on the white squares and black on the black squares (as kings are bounded to the reversed colour). But there is a matter more of attack and defence, you bassically have 2 different games rather than colour bounding. Point being extreme cases, as almost always, give wierd results. But maybe we are not tali=king about extreme cases here as good players/engines would work to avoid that :)!
H. G. Muller wrote on Sun, Dec 17, 2017 11:45 AM UTC:This is a very good question, and is already on my to-do list for many years. (Alas, never high enough.) It is in fact why I started the 'Pair-o-Max' fork of Fairy-Max; this gives a configured bonus on the victim value for indicated piece types on every capture that leaves an odd number of them. (And it can also be made aware of drawishness due to lack of mating potential.) I never found the time to lauch a systematic investigation on this issue, though,
One thing I did determine, though (although not with great precision): pairs should not be counted combinatorially. If you have 4 Bishops, distributed 2+2 over the square shades, they are worth as much as two pairs. They do not count as 2x2 = 4 pairs. With 2+1 Bishops you should count only 1 pair.
I am pretty sure that in the case of multiple color-bound piece types there must be 'cross bonuses', e.g. that F+B on the same color should be worse than F+B on different color. In end-games of Team-Mate Chess, which features two color-bound types (FA and AG), in 3+2-men end-games of FA+AG vs FA or AG it mattered whether the stronger piece (FA) was on the same shade or opposite shade as the opponent piece for the end-game to be a general win or a general draw. That raises the interesting question how to score 2B+F. So a lot of testing would have to be done. A good start would be to determine the pair bonus if individual isolated color-bound piece types. By playing pairs of F, FA, FD, FAD, BD, BDD on different shade against those on the same shade, in the presence of only pieces that can access the entire board (and Pawns).
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In Chess, the bishops are worth 325 centi-pawns plus an extra bonus of 50 if the player has one of each color-binding. Or you could consider them to be worth 350 each with a penalty of 50 for losing one of them.
In ChessV, I now want to generalize this... A simple approach would be to give a flat bonus of 50 for any player that has at least one colorbound piece on each color binding. (This would automatically not give any bonus for games that don't even have colorbound pieces.) But is this right? Consider the Colorbound Clobberers. It seems if they have only one BD and only one FAD and they are both on the same color, this is probably a huge disadvantage. The enemy can evade two pieces at once by staying on the other color.
Another question would be pieces with even stricter bindings like a Dabbabah which can only see 1/4 of the board. I'm probably not going to really consider this for the time being. I'm not sure it currently plays any games with 4 Dabbabahs on each of the four bindings. It will become a relevant question, however, when it plays Hexagonal where there are 3 different bishops...