We can define a chess metric which can help one evaluate weaknesses on arbitrary board configurations. Here I define a metric which depends on the force applied to each board square, by all attacking pieces. The force a piece exerts on an attacked square, is defined as: F=(-1)^{K(p)}/V(p), where K(p) in {0,1} (white, black) and V(p) is the intrinsic value of a piece, as in V(p)={9(Q), 5(R), 3(B), 3(N), 1(P)}.
If we then color grade each square corresponding to the intensity of the force by making a simple correspondence between magnitude of force and color saturation, we can get a nice visual of which squares are affected by the attack. This reveals a lot about potential weaknesses in the general case and is an immediate indicator of blunders and pieces which (may) fall.
Note that the force applied is taken as the inverse of the value of the piece, as this conforms to the more intuitive way of attacking a square using the least value pieces first. It would be wrong to consider a square vulnerable if it was attacked only by larger pieces, as the utilitarian force of attack is inversely proportional to the value of the piece. This way, when we add all the forces, adding negative and positive elements, showing a color gradient will reveal the dominant piece on each side.
When one designs a chess engine, one needs to add small benefits on various difficult configurations, so it's not always chess through the value of the pieces, through strict positional evaluation. The chess force metric shows how some of these positional benefits can be screened in advance, to give hints about further and deeper analyses.
Download a Maple 9 worksheet here that implements such a mapping (Input your configuration in L:=[]; and run the entire sheet).
Config | Position & Attack Force via color gradient |
1:^{[1]} Theoretical position showing color gradients according to force applied, with square d5 experiencing the maximum force from combined forces. | |
2: Alternate theoretical position showing again color gradients accodring to force applied, with square d5 again experiencing maximum force. | |
3: Starting position initial configuration, showing positive and negative forces applied for both sides. | |
4: Random position. Weak spots and blunders are immediately obvious. For example, d5 and a8 are suspect and d7, f7 and g6 are weak spots. Note the very strong pawn at b6. | |
5: White to move: It's fairly obvious that f2, g2 and h2 are weak spots for white (hinting at x: Kf1 Qh2, followed by ...Qh1, etc). | |
6: After: 1. e4 c6 2. d4 d5 3. exd5 cxd5 4. Nc3 Nf6 5. Bb5+ Bd7 6. Bxd7+ Nbxd7 7. Bg5 e6 8. Bxf6 Qxf6 9. Qd3 Bd6 10. Nge2 a6 11. a4 Qh6 12. Ng3 Nf6 13. O-O O-O *. Arasan shows a slight +0.27 advantage for White on this position, which is justified by the force metric. The weak spots are c4, e4, f4 for white, but they are counterbalanced by the weak spots c5, e5 and f5 for black, so the position is fairly balanced. |