Numerical criterion of positional evaluation

Sort:
Yigor

There are engine evaluations as well as statistical evaluations of openings:

https://www.chess.com/forum/view/chess-openings/statistical-sharpness-and-evaluation

In this topic, I wanna introduce the new measure called positional evaluationpeshka.png

  

Definition 1. A square on the chessboard is said to be partially controlled by white (resp. black) when this square is under direct attack by a certain white (resp. black) piece.

  

Example 1. There are 22 squares (b1-g1, a2-h2, a3-h3) partially controlled by white in the initial position. Formally speaking, a1 and h1 are not defended by other pieces and are not considered to be partially controlled (despite the fact that white rooks occupy these squares). In the same manner, black also controls 22 squares in the initial position.

  

Let W (resp. B) be the number of squares partially controlled by white (resp. black) in a certain position with the equal material for white and black (otherwise the material difference should be added to pev).

  

Definition 2. The positional evaluation (pev) is defined by the formulas

pev = W/B - 1 if W >= B

pev = 1 - B/W if B >= W

  

Example 2. In the King's Pawn opening:

  

  

we have W=29, B=22, so pev=+0.32.

  

Positional evaluations of the first move:

  • pev=+0.32 : 1. e3, e4
  • pev=+0.27 : 1. d4
  • pev=+0.23 : 1. d3
  • pev=+0.18 : 1. Nc3, Nf3
  • pev=+0.14 : 1. c3, c4
  • pev=+0.09 : 1. Na3, b3, b4, f3, f4, g3, g4, Nh3
  • pev=+0.05 : 1. a3, a4, h3, h4

Refined positional evaluations, taking into account the effectiveness and kingside/queenside separation, are defined here:

https://www.chess.com/forum/view/chess-openings/refined-positional-evaluation#last_comment

Yigor
DanlsTheMan wrote:

Can you explain how/why d3 is equal to d4?

Start position=22

d3 diff= +5 [pawn control (c4, e4)] + [bishop control (f4, g5, h6)]

27/22=0.227 (0.23)

d4 diff=+ 6 [pawn control (c5, e5)] + [bishop control (f4, g5, h6)] + [queen control (d4)]

28/22=0.272 (0.28)

 

Hey Dan, thanks for your interest and this correction! wink.png I calculated quickly and forgot to count d4, controlled by the queen, in the case of 1. d4.

Yigor
DanlsTheMan wrote:

This example adds an element of space. d4 also controls 2 squares on the opponent's side of the board. No more value for e4 tham e3?

 

Good question. blitz.png My definition is preliminary and could/should be modified. It's indeed more important to control squares on the opposite side of the board. There is also the question of effectiveness and multiplicity of the control. peshka.png

Yigor
DanlsTheMan wrote:

What about Nf3/Nc3?

Should we value the increased protection of a1/h1? King side safety perhaps more than queen side?

 

Yeah, maybe it make sense to add more values for controlling squares around both kings !?!

Yigor
DanlsTheMan wrote:

Have you tried to apply beyond move 1 for white?

 

Not yet, I defined it quickly and without any interest from other participants switched to other things. Now I/we can make some caculations beyond the 1st move. wink.png

Yigor

Refined positional evaluations, taking into account the effectiveness and kingside/queenside separation, are defined here:

https://www.chess.com/forum/view/chess-openings/refined-positional-evaluation#last_comment

Yigor
DanlsTheMan wrote:
Yigor wrote:
DanlsTheMan 

Not yet, I defined it quickly and without any interest from other participants switched to other things. Now I/we can make some caculations beyond the 1st move. 

I did say "we". Your project, but I like your idea. What other positional elements might you include?

 

All right, "we" sounds better anyway. wink.png Please look at my new thread (the link is posted above) about refined positional evaluations. I have taken some of your remarks into account thumbup.png, in particular, making kingside/queenside separation. An example of Sicilian defense shows that the refined Pev gives more useful info than the initial pevpeshka.png

 

I guess that we should indeed make some calculations now beyond the initial position and compare positional evaluations with statistical and engine evaluations. computer.pngexplorer.png

Yigor

Refined positional evaluations of the first move:

  • pev=+0.32, Pev=(+0.14,+0.18) : 1. e3, e4
  • pev=+0.27, Pev=(+0.18,+0.09) : 1. d4
  • pev=+0.23, Pev=(+0.18,+0.05) : 1. d3
  • pev=+0.18, Pev=(+0.14,+0.05) : 1. Nf3
  • pev=+0.18, Pev=(+0.05,+0.14) : 1.Nc3 
  • pev=+0.14, Pev=(0, +0.14) : 1. c3, c4
  • pev=+0.09, Pev=(+0.09, 0): f3, f4, g3, g4, Nh3
  • pev=+0.09, Pev=(0, +0.09) : 1. Na3, b3, b4
  • pev=+0.05, Pev=(+0.05, 0) : 1. h3, h4
  • pev=+0.05, Pev=(0, +0.05) : 1. a3, a4
Yigor

@DanlsTheMan Well, I started this thread as a numerical evaluation. If U wanna evaluate openings in words, it's a different issue. peshka.png

Yigor

@DanlsTheMan All right, so let's concentrate on the positional evaluation alone (without comparisons with statistical/engine evaluations). 

Yigor

I've corrected the calculations for the 1st move (post #10) returning back to the notion of partial control.