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I believe the correct values for the Knight, Hawk, and Elephant to be 2.5, 4.5, and 5, respectively.
I think you should transfer the moving without capturing one square orthogonally from the Elephant to the Hawk to remove its colourboundness.
You might even underestimate them. A Crowned Bishop (B+W), which also has an enhancement of 4 target squares to an ordinary Bishop, tested as stronger than a Rook on 8x8 (say 5.25). I expect B+D (Hawk) to produce a similar enhancement. F+D (also color-bound), which is included in the Hawk, almost exactly balances a Knight on 8x8. In none of my tests so far color-boundedness seems to suppress the value of a piece very much. It probably just gives a larger pair bonus, which I could not measure well. Adding a single Wazir-like non-capture to a Bishop to break the color-boundedness upped its value by about 1/6, but adding it to a Knight upped its value by a very similar amount. So it is more likely that the enhancement is produced by the increased manoeuvrability than by lifting the color-boundedness. This seemed to be additive, so adding a full non-capture Wazir produced ~2/3, while adding an unrestricted Wazir (to make the Crowned Bishop) produced about 2. So captures seem to be worth about twice as much as non-captures. All this was on 8x8; the Bishop value seems to go up on wider boards. My guess is that the B-N difference, which is already 1/2 on a 10x8 board without the pair bonus, will be driven up to 1 on this large board. Say N=2.5 and B=3.5 excluding the pair bonus (when R=5). That might make the Hawk actually stronger than a Rook, ~5.5 + pair bonus. The Elephant has 12 capture targets, and short-range leapers with 12 moves usually are worth around 4.5, but might devaluate slightly on this big board. The Wazir non-captures will probably add 1.That would make 5.25. So my educated guess is that the Hawk is stronger than the Elephant, and that both are stronger than a Rook.
Please delete this file and then transfer all of these comments into a comment-only discussion file instead.
EDIT: Transfer is done; this is the comments' new home. --Ben Reiniger
EDIT: Transfer is done; this is the comments' new home. --Ben Reiniger
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