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.
