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Joe Joyce wrote on Thu, Jul 26, 2007 04:02 AM UTC:
Gentlemen, thank you for the interest you've shown in this question. 

I have attempted to calculate piece values by several means, and I'm not
sure that any are accurate, nor that I applied the methods right, not
being any sort of mathematician. The first method I tried was one by John
K Lewis, at the Yahoo CV site, that gave me values of 6 for an Oliphant, 7
for a Lightning warmachine, 10 for a High priestess, 11 for a Minister, and
14 for a Jumping general. This is on an 8x8 FIDE board, with all 32 black
and white pawns and pieces still on the board some 10-15 or so moves into
a game. 

I next got values of 8-9 for the High priestess and Minister using
Reinhard's method. Or as close as I could come to it. Numbers are on the
CV wiki. Also did some serious thinking about the 2-step pieces I've used
and the way they've moved. Did some comparison numbers in 'Attack
Fraction', again on the wiki, that are very suggestive, but only
qualitatively. 

Got info from David Paulowich that gives numbers for some of my pieces,
the bent Hero and Shaman, in his game Opulent Lemurian Shatranj, that
pegged the shaman to the rook's value of 5.5 on a 10x10, and the hero's
value at 7.5. David is generally quite good at giving values - the times
I've disagreed with him, I've found him to be right. These numbers
don't match up with any of the other numbers.

I am not sure the value of leaping, not to mention double-step pieces or
leaping twice with a possible direction change, is properly handled by
current theory. This is not a knock on past and current theoreticians, who
seem to agree fairly well among themselves on the values of the standard
FIDE pieces and the common non-standard pieces. But these pieces fall into
1 class, that of unlimited sliders, and one remnant shortrange leaper.
Short and medium-range leapers are a category, and multi-jumpers are
another, related category barely touched by consideration of the
nightrider. This doesn't even touch on Mats Winther's collection of
pieces. 

I believe we need a wider theory.