Mathematical Position Analysis

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 always applicable, and incomplete; I need to still know a rigorous mathematical way to quantify spatial advantages.

The simple answer is that there are no simple answers in chess.  Hence when I leave two top (2900+) analysis engines running for a long time on the same position, their assessment can differ by 0.8.

Of course, my analysis is not complete. Chess engines are only as good as the axioms on which they are built. Still, this does not mean that a rigorous mathematical quantification of a position is impossible.

To me it seems clear that there can be no reliable evaluation of the value of a position without analysis of the possibilities afterwards. And given a chosen depth of analysis there will always be positions that will be incorrectly evaluated if the analysis is stopped at that depth, because of the horizon effect. To hope to get a completely accurate evaluation without analysis is unreasonable, but it is certainly possible to get evaluations that have a strong correlation with the true value of a position, and only rarely very badly wrong.

Chess positions are not formally undecidable, nor are moves "true" or "false". If a system is not formally undecidable, then in principle it is at least possible to construct a perfect model. Chess games have sufficient mechanisms for terminating so infinite analysis is not required. This means analysis will terminate. So it is merely a practical problem.