Mathematical Position Analysis
Submitted by on Thu, 10/01/2009 at 11:17am.
1. Set p, for pawn, such that the numerical weight of p is p=1.0
2. Set d, for development. In general, 3d=p (Siegbert Tarrasch)
A sub-expansion of d: Nd4 is equivalent to 2d because of its excellent placement. So Nd4=(2/3)p. Also, Ba4 is given a special value of 1.5d, as it is well placed with the possibility of being easily tranferred to b3 or c2, and it also aims at f7 often.
3. Set m, for mobility:
a. Find total number of moves for both white and black.
b. Subtract the side with the least number of moves from the side with the greater number of moves, then multiply by 1/10 of a pawn for its numerical value (if w is white's legal moves and b is black's, then if w is greater than b,
(w-b)(0.1p) is the worth of mobility expressed in pawns.
4. Set the value of individual pawns, where the value of: (GM Edward Gufeld's analysis)
e, d pawns =1.0
c,f pawns=0.9
b,g pawns=0.8
a,h pawns=0.7
and add totals of all pawns.
5. Convert development values into pawn values, find sub-total. Add sub-total from mobility. Then add values from specific pawns. Repeat process for black, and subtract black's total value from white's total value. If the result is +, then white has an advantage. If the result is -, then black has an advantage. But the great thing about this is we can assign real particlur numerical weights for each position!
NOTE: This is not entirely comprehensive. For example, I still need a rigorous mathematical way to define spatial advantages. Of course standard material weight is accounted for as well.