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Joe Joyce wrote on Wed, Apr 30, 2008 11:16 PM UTC:
Yes, Ji, this is interesting - pity I didn't know all this before that
exchange... gentlemen, an interesting midpoint. I was going to note
that some of the Muller numbers are quite similar to others' numbers.
For example, the values of the minister and priestess fell between 6
and 7 by both HG and Reinhard's methods. Yet other numbers are quite
far apart, like the commoner values. This, of course, presents 2
problems, one to explain the differences, and the other to explain the
similarities. Derek, could you give us a verbal explanation of what you
did and found?

Reinhard, my apologies for some sloppy phraseology. You've posted your
theory for all to see. You have provided numbers both times we've
spoken on this. In fact, you have been kind enough to correct my
mistakes in using your theory as well as providing the 2 sets of numbers.
[I will have to find some time to upgrade the wiki on this. Excellent.]
Thank you; I could ask for very little more. [Heh, maybe a tutorial on
that 3rd factor; Graeme had to correct my mistakes too.] I wish you the
very best with your new endeavor.

Ji is right, the number of squares attacked may be a first
approximation, but the pattern of movement is a key modifier. I put
together a chart a while ago after discussing the concept of
approachability with David Paulowich. The numbers in the chart are
accurate; the notes following contain observations, ideas, statements
that may be less so. Fortunately, the numbers in themselves are rather
suggestive, one way to look at power and vulnerability. They present a
two-dimensional view of pieces, a sort of looking down from above view
in chart form.
http://chessvariants.wikidot.com/attack-fraction

The chart clearly could be expanded, should anyone be interested. [The
archbishop, chancellor, amazon should be added soon, for example; any
volunteers? :-) ] But can it be used for anything? Colorboundness, and
turns to get across board, both side to side and between opposite
corners, are factors that must have some effect. [Board size and
edge effect are 2 more, this time mutually interactive factors. How
much will they be explored? Working at constant board size sort of
moots that question.] What do your theories, gentlemen who are carrying
on or following this conversation, have to say about these things?

Please note this conversation is spread over 3 topics:
this Piece Values thread,
Aberg's Variant game comments
Grand Shatranj game comments

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