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H. G. Muller wrote on Wed, Oct 8, 2008 07:42 PM UTC:
Has there been any investigation on the piece value of hoppers at all?

You state that Grasshopper is better than Cannon (Pao), but I have strong
doubts about that. Grasshopper has at most 8 targets, as it reverts to
leaper (stepper, actually) after the hop. Cannon has 4 directions, but
remains slider. The reasoning you employ (8 directions) would imply
Commoner > Rook, which we know to be not true.