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How many squares are controled by each piece

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luckisK

 

POSITION= it can be positioned in so many squares

CONTROL=it can control so many squares from the squares it can be positioned

                 POSITION    CONTROL

rook           64              896

bishop       32              284

knight        64              336

Now what is the strength of each of these three pieces according to this. Should I divide the CONTROL number by 64, or by the POSITION number?

dmc6502
If you count the number of squares a piece can attack for every square on the board and average them out, you will be pretty close to the values for each piece.

I've done this several times, it's a fun exercise.
luckisK

Rook's strength is 896/64=14, knight's strength is 336/64=5.25, but they concluded that it is higher than 5.25 because it can jump over other pieces. Bishop's strength is 284/64=4.4375 or 284/32=8.875? I guess they concluded the 8.875 as 8.875/14=0.6339... is closer to the known 3/5, but why did they concluded that. Also, how did they conclude knight's and pawn's strength, do you know any literature?

 

FroggerMatt

My math has bishop's avg square coverage at exactly 8.75

Bishop = on 14 of the squares it will control 7, 10 control 9, 6 control 11, 2 squares control 13=280/32 =8.75

I got the same strength of 14 for rook and 5.25 for Knight. I got 1456/64 = 22.75 for queen.

If queen is given a value of 9, then proportionally the value (if only related to square coverage strength) is,

Rook 14/22.77 = 0.654 x 9 = 5.53
Bishop 8.75/22.75 = 0.385 x 9 = 3.46
Knight 5.25/22.75 = 0.231 x 9 = 2.08

Interestingly, Although these square coverage ratios are all skewed for each piece from the 5, 3, 3 point value system for the a knight, bishop, and rook, which equal11 points, the sum above is 11.07!

Less Interestingly, the square strenght average above for Knight + Bishop avg = 2.77. If the Queen is given a value of 10 (which I think it used to be, at least in one chess book I read as a kid), then the bishop and knight would be 3.85 and 2.31 respectivly, averaging 3.07.... very close.

None of this square coverage power is really that relevant for Knight and bishop, as I agree they considered the knight higher because it can jump, and isn't limited to one color, and knights can protect each other. Personally, I'd rather deal with any 1 bishop in a tough end game than a knight, but i'd rather have a bishop pair than a knight pair.