Comments/Ratings for a Single Item
Hi H.G.
For the Alibaba if I recall right I gave a considerable (x2) leaper bonus to both the A and D components, before primitively concluding AD (aka Spider)=A+D+P=2.25
Where A=D (roughly) = (N-P)/[2 times 2] (roughly) each (Why the N? - I treated an A or D leap as kind of similar enough to a N leap, except they each only go to half as many cells). Why the 'N-P'? Well, if Q=R+B+P then my imprecise way of guessing a piece half a Q's power would be (Q-P)/2, for example. Why '/[2 times 2]'? Well that's the final penalty factor, where one of the 2's means that an A (or D) only has half as many moves as a N.
If I also recall right, it's
Where A is binded 3 ways, and D is bound just 2 ways, but is often slower than an A (thus a penalty factor of /[2*8] should perhaps be used for each [rather than /4] I feel, but the leaper bonus I gave for the A and D each is a factor of x2, and I [perhaps generously] gave A and D each a x2 bonus for distance often covered faster by a series of leaps compared to a series of N leaps, so thus the final /4 penalty factor).
So, A+D+P (for AD, aka Spider) = (N-P)/4+(N-P)/4+P = 0.625+0.625+1 = 2.25
Kevin, I am adding the Dragon Horse or Crowned Bishop, worth six Pawns. Multiplying my previous list by 0.36 makes my combined value of Rook and Knight equal to yours, as follows:
Pawn = 1.08, Elephant = 1.44, Ferz = 1.80, Knight = 3.60, Rook = 5.40,
plus Alibaba (A+D) = 2.52, Commoner (F+W) = 4.32 and Dragon Horse (B+W) = 6.48.
I edited my previous comment, in case any missed that.
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This is why serious computer studies always use a number of different mixes of opponent pieces, and average over many shuffles of those as initial setup. E.g. if you want to compare the value of Queen, Archbishop and Chancellor, you don't just play these against each other (e.g. in a FIDE setup whetre one player starts with A or C instead of a Q), but also against, say, R+B, R+N, R+N+P, 2B+N, B+2N (deleting these for the player that has Q, C or A, and deleting Q of the other player), to see which of the super-pieces does better, and by how much.
To test an Alibaba (which I apparently did once), you would replace 2N, N+B, 2B or R for two Alibabas (and give the opponent Pawn odds to get closer to equality), and just a single N or B for one Alibaba.
How does your estimate take account of the severe color binding of the Alibaba? Because of that it seems a very weak piece to me. It can for instance not act against half the Pawns.
Ancient Shatranj theory indeed values different Pawns differently. In Shatranj an Alfil is considered slightly better than an average Pawn. But you should keep in mind that a FIDE Pawn is worth significantly more than a Shatranj Pawn, because it has a game-deciding promotion, while in Shatranj an extra Ferz is often not helpful at all. And I suspect a lot of the value of the Alfil is that, even if tactically worthless, it acts as insurance against loss by baring when only weak pieces are left.