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Jeremy Lennert wrote on Tue, May 24, 2011 03:37 AM UTC:
The WDN vs. FAN doesn't seem so surprising to me; I believe it is commonly
accepted that Ferz is stronger than Wazir, despite its colorboundness,
probably because of its greater forwardness.

However, as the length of a move increases, the probability that it is
still on the board drops off more quickly for diagonal moves than
orthogonal ones.  The average chance that a one-space move is on the board
doesn't differ much between orthogonal and diagonal (.875 vs. .766, a
factor of 1.14), while the difference for a seven-space move is much larger
(1/8 vs. 1/64, a factor of 8).  Thus, the relative mobility advantage of
Rook over Bishop (1.6 on empty board, 1.37 with 30% crowding) is much
higher than Wazir over Ferz.

I suspect the Rook-move may also gain a bonus for King-restriction
(controlling a continuous region the enemy royal piece can't cross),
though that's purely speculative.  It would be interesting to see how the
values of pieces change when substituting a royal piece with a different
move pattern.