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Michael Nelson wrote on Thu, Jul 17, 2003 03:21 PM UTC:Excellent ★★★★★
It's wonderful to hear from the Master on this topic.  I really mentioned
the geometric move length becuse you mentioned it in the article--the key
point was the comparison of mobility ratios to value ratios and the Rook
discrepancy.

We need about 10 orders of magitude above excellent for Ralph's work on
the value of Chess pieces--I would nominate it as the greatest
contribution to Chess Variants by a single person.

I am convinced that the capture power and the move power are not equal,
but that the difference will only be discenable when extreme.  

An example--compare the Black Ghost (can move to any empty square, can't
capture) to a piece that cannot move except to capture, but can capture
anywhere on the board (except the King, for playability)--clearly the
Ghost is weaker, though its average mobility is higher.  

I feel that WcR will be perceptibly stronger than WmR but I could be
wrong. I suspect the effect is non-linear with a cutoff point where we
don't need to worry about this factor. I also think that the disrepancy
will be less than the discrepancy between the actual value of the WcR and
the average of the Wazir and Rook values. This discrepancy may be
non-linear as well.

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