The bishop is generally regarded as slightly more valuable than the knight. In part because the bishop pair can be very effective (in some computer evaluations, as much as half a point is given for a bishop pair). I also tend to value the bishop more highly because it tends to be more effective in the endgame.
I remember a rating system that rated knights at 3.25 and bishops at 3.5
I would say it's more like
Pawn = 1
Knight = 3
Bishop =3.5
rook = 5
Queen = 9
King = Inf.
The rating system that I go by is
Pawn: 1
Knight: 3.25
Bishop: 3.25
Rook: 5
Queen: 9.75
If I have two bishops and my opponent doesn't have two bishops, I add a bonus 1 point to my pair, so they equal 7.5 altogether.
Anything you would ever want to know about why those values were assigned to the pieces:
http://en.wikipedia.org/wiki/Chess_piece_relative_value
And Dan Heisman's reprint of the Larry Kaufman article:
http://home.comcast.net/~danheisman/Articles/evaluation_of_material_imbalance.htm
It's all relative. If you are up a queen, but mate is imminent, then how much is the queen worth? Not much, right? If you are down a pawn, but you have a rook on the seventh rank and your opponent's pieces have to stay passive, then you have the real advantage, don't you?
first baseless, arbitrary number pulled out of my rear; 97
second baseless, arbitrary number pulled out of my rear; .235
third baseless, arbitrary number pulled out of my rear; 87,823
fourth baseless, arbitrary number pulled out of my rear; aleph null
fifth baseless, arbitrary number pulled out of my rear; 5 + the number of pawns on light squares/3
first baseless, arbitrary number pulled out of my rear; 97
second baseless, arbitrary number pulled out of my rear; .235
third baseless, arbitrary number pulled out of my rear; 87,823
fourth baseless, arbitrary number pulled out of my rear; aleph null
fifth baseless, arbitrary number pulled out of my rear; 5 + the number of pawns on light squares/3
?
Isn't it funny that sometimes I get Aleph-null, and sometimes I just can't?
here is my system
Pawn =1
scince i know that 4 pawns can checkmate a lone king (with a king) that means that
Q=7(rook plus bishop plus the combination factor of 1)
R=4
B=2
N=1.5
K=A. Material value= infinate B. Fighting value =3
For those of you who think these numbers are worthless, you are very wrong. Of course it's all relative to what's on the board, but I know I'd rather have a rook than a knight in MOST engames. What chess axiom is not without it's exceptions? Sometimes it's better to promote to a knight instead of a queen, but calling the "queening" square the "Queening Most of the Time, Unless the Position Dictates Otherwise" square is not that much of a help. The point system is a great way for beginners to understand what many a chess player feels in his gut, just another tool to help cut through the madness.
I think that using all nonstandard system is quite stupid. Apart from the obvious fact that things depends on position , counting minor pieces like 3.2 and 3.14839483829348320 for a bishop or 3.100323484529 for a knight efficently make all counting during the game impossible. Stick to classics , and eventualy add 0.5 pawn for a bishop pair , if your opponent has none .
A pawn on the 7th rank is worth much more than the pawn on the second rank, due to it's queening potential. At some point you need to quit counting "points" and consider the aspects of position on the board to make the best move.
Most people use this system
Pawn=1
Bishop/Knight= 3
Rook= 5
Queen= 9
King= Inf.
I however use and propose this:
Pawn= 1
Bishop: 3
Knight: 4
Rook: 6
Queen: 10
King: Infinite.