For example, what about the Queen? The Queen is worth as much as a Rook, a Bishop, and a Pawn combined, but the "Average with Probability" figures will always err by showing the Queen as exactly equal to Rook plus Bishop.
We know that the Bishop must be ( at least potentially ) worth less than its mobility shows, because the Bishop is confined to squares of one color -- half the squares on the board it can never get to at all!
Could it be that the reason the Queen is worth more than Rook plus Bishop is that the Queen is NOT confined to one color?
Could it be that having two pieces instead of one gives the enemy more targets to attack?
Could it be that the Queen is more valuable because she moves in 8 different directions, and therefore the Queen may, in a single move, attack 6 squares that she did not previously attack ( a Rook or Bishop can only attack 2 new squares ).
Could it matter that the Queen can attack 3 new squares FORWARDS but the R or B can only attack 1?
Could it be that ALL of these causes contribute, in varying amounts, to the superiority of the Q over the separate Rook and Bishop?
Yes, it could. :-)
[November 1996] I should mention that my *opinion* is that forward forking power is the most important factor.
Now we're getting closer; but we're still a long way from being able to decide how much, for example, to subtract from the Alfil because it can only see one-eighth of the board, a long way from deciding how much more powerful is the King than the separate Wazir and Ferz, and nowhere near being able to calculate the true values of the Chancellor or KnightRider.
In order to try to assign reasonable numbers to some of the effects listed above, it would be helpful to have a better idea of the correct values of the basic set of unknown pieces -- Wazir, Ferz, Dabbaba, Alfil, and KnightRider.
Hey, wait! Isn't that what I want to calculate? Am I saying that I need the answers before I can figure out how to derive them?
Not exactly; there are millions of possible chess pieces, we know a little bit about the values of half a dozen of them, and I'm saying it would help to know more about another few in order to find out how to calculate the millions and millions that remain....