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John Smith wrote on Mon, Jan 12, 2009 11:58 PM UTC:
I believe the correct values for the Knight, Hawk, and Elephant to be 2.5, 4.5, and 5, respectively.

John Smith wrote on Tue, Jan 13, 2009 12:21 AM UTC:
I think you should transfer the moving without capturing one square orthogonally from the Elephant to the Hawk to remove its colourboundness.

H. G. Muller wrote on Tue, Jan 13, 2009 07:58 AM UTC:
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.

John Smith wrote on Tue, Jan 13, 2009 03:26 PM UTC:
I didn't get much sleep, so I'm probably wrong.

(zzo38) A. Black wrote on Mon, Apr 23, 2012 01:33 AM UTC:Poor ★
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

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