Mathematical Position Analysis

Submitted by strangequark 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 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.

» posted in strangequark's Blog
 

Comments:

by strangequark - 39 days ago
Quantum Superposition of States United States
Member Since: Oct 2008
Member Points: 2509

The calculations rely on general tactical principles though. As I said, it is not entirely comprehensive.

by namn_kiev - 39 days ago
Kyiv Ukraine
Member Since: Oct 2008
Member Points: 138

I am sorry, but formal criteria for evaluation of position seems of minor utility, and ways ( moves) that add something to the value calculated obviously might be wrong from tactical point of view! It is just good as points of Milton Wokr (York? Sorry, I know the name only in Russian!) in bridge! I am absolutely sure that the way to evaluate the position is, in general, so complex that it it might be used only by computers. 

Alex

by strangequark - 1 month ago
Quantum Superposition of States United States
Member Since: Oct 2008
Member Points: 2509

It is similar, especially the mobility factor. Only this is a way to use that is fairly easy for us humans to calculate.

by zankfrappa - 1 month ago
Virginia United States
Member Since: Nov 2008
Member Points: 2671

I see, is this similar to the method computers use to analyze games?

by strangequark - 1 month ago
Quantum Superposition of States United States
Member Since: Oct 2008
Member Points: 2509

Use this as an example to calculate:

1. both sides have seven pawns, so we can ignore this

2. white has 4 pieces developed vs. black with 2 developed= +1.0 for white (the knight on d4 is separate) -0.666...for black's d gives us:

+0.333...

3. white has -0.1 in terms of pawn value because of cxd4, but +0.666...pawns because of Nd4

4. black's mobility: 32 legal moves (I think!) white's mobility: 37 legal moves (I think, I just glanced!) so 1/10 (37-32) gives a +0.5 advantage for white here

so in total:

0.333...+0.666+0.5 = +1.5 pawn advantage for white

by zankfrappa - 1 month ago
Virginia United States
Member Since: Nov 2008
Member Points: 2671

Somewhat, although I am trying to grasp how to apply it in a game.

by strangequark - 1 month ago
Quantum Superposition of States United States
Member Since: Oct 2008
Member Points: 2509

Basically, if we can quantify mobility, pawns, development, and space, we can mathematically analyze it. Using the above is a crude and early way for us to do so, but GMs have thought of this, and it at least works to some extent. Did I answer your q?

by zankfrappa - 1 month ago
Virginia United States
Member Since: Nov 2008
Member Points: 2671

     Please explain the general purpose of this in a simpler to understand form, I
am not following it.

 

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