Derek Nalls wrote on Thu, Jul 26, 2007 04:44 AM UTC:
'I believe we need a wider theory.'
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Yes, definitely.
What I think I have discovered is that the methods for properly measuring
the relative values of pieces throughout a game cannot reduce the
complexity of the function of the pieces toward playing the game
resourcefully without introducing unacceptably-large errors. Be mindful
that some of the games we create are as complex as any known mathematical
entities.
A truly universal theory would have to take every unique piece type (e.g.,
limited and unlimited range, steppers and leapers, exotic types, etc),
method of capture, conversion (usually, promotion) potential, turn order,
board geometry, game-winning condition, positional and material factor
(with adjustments throughout the course of the game) into account WITHOUT
ANY CONCEPTUAL OR NUMERICAL ERRORS to have adequate accuracy to be
useful.
This cannot be accomplished in 50+ pages. If extremely-well designed,
minimally complete yet maximally applicable, I wildly estimate it would
require at least 250-500 pages. Who is willing to work this hard
exploring all major classes of chess variants (by the broad definition) in
detail where most would surely be foreign to the interest of the person
doing the work?