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It might be good to mention the revised rules here. Jean-Louis Cazaux makes a very strong case, based on scrutinizing the original old Spanish text source. He arrives by this at rules that make much more sense than those presented here (whech were based, directly or indirectly, on Murray's work). The latter makes the Lion a virtually worthless piece, assigns impractically large leaps to most of the pieces, have two piece types move the same (as B) for most of the game, assigning a pretty point-less initial move to one of them...
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The moves according to Jean-Louis are:
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King: King, or initial Alfil / Dababba
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Griffon: Ferz followed by outward Rook slide
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Unicorn (Rhino): Knight jump optionally followed by forward (not outward!) diagonal slide away from the starting file
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Lion: jump 3 orthogonally, or (3,1) like Camel
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Rook: modern Rook
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Crocodile: modern Bishop
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Giraffe: jump (3,2) like Zebra
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Pawn: Sjatranj Pawn, promotes on 12th rank to piece that started there.
</li></ul>
I want to add some comments on this, however:
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I do not understand the origin of the idea that the Griffon could not move to the (Betza) F squares. The text seems to stress that a Griffon on black cannot move to the four adjacent <i>white</i> squares, and vice versa. But the squares of opposite color are W squares, not F squares! I consider this very strong evidence that the Griffon could actually move like Ferz, as otherwise this complex mentioning of colors would just be a waste of ink, and the author would simply have written "a Griffon cannot go to any adjacent square".
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As to the Rhino I have my doubt where this interpretation comes from that only one of the two diagonal slides could be used after the Knight jump. The quoted text seems to state that the Rhino cannot turn back after its Knight jump, but 'back' could have very well have meant "make a sharp turn to move towards its origin". The description suggests the move was inspired by the perceived behavior of a Rhino in real-life, and making sharp turns (as you would get on a backward Knight jump followed by a forward diagonal slide) would certainly not be amongst those. The only reason I can see for not allowing the Knight jump to continue in two directions is that it would make the piece too strong.