This article is by WIM Alexey Root
Previously we learned the values of the bishop, rook, and queen. Just as for those three pieces, the values of the knight, the pawn, and the king depend on how many squares they can move to in your current chess game. The more squares, the better!
A knight is usually worth 3 points (3 pawns). A pawn is typically worth one point (one pawn). A king cannot be traded, so we don't have to worry about what he is worth! But we can still assess the king's mobility compared to other chessmen. Mobility means the number of squares to which a chessman can move. The value of each chessmen is based on its mobility on an empty board. In terms of mobility, the value of the king is about 3.5 points (between 3 and 4 pawns).
The knight can get to more squares from the center than from the corner or edge of an empty board. In the diagram below, count how many squares the knight on h1 can move to. Then count how many squares the knight on d5 can move to.
Did you get the answer of two squares (for the Nh1, which can move to f2 and g3) and eight squares (for the Nd5, which can move to c7, e7, f6, f4, e3, c3, b4, and b6)? You have just proved the expression "A knight on the rim is grim."
The knight isn't picky about being surrounded by pawns and pieces because he can hop over them. In the bishop, rook, and queen article, we saw that a bishop is a bad bishop when its diagonals are blocked by pawns. In contrast, knights don't mind pawns around because they can jump over them. The knight looks like a horse. And horses can jump.
Pawns move forward. They move either one (or two squares on their first move), and then one square after that initial move. When they reach the end of the board, they promote. Unlike other chessmen, pawns capture differently than they move. A pawn captures on the square one rank ahead and one file adjacent to it. In other words, pawns capture "diagonally forward."
In the following diagram, analyze the pawn moves only. If it were white's turn, the a-pawn could move to either a3 or a4. Since it is black's turn, the c-pawn may capture on d4 (and give check to the white king) or move to c4. No matter whose turn it is, the h-pawns cannot move at all, because they block each other. Of course, each pawn could also choose to sit still and let some other chessman (the king or the knight) move instead.
A special rule for pawns is en passant. In terms of mobility, pawns are somewhere between one and two squares on an empty board. A pawn's mobility value is set at one point (one pawn). All other chessmen's values are based on pawn (point) value.
In this article, we learned the following values:
A knight is worth 3 points (3 pawns).
A pawn is worth 1 point (1 pawn).
A king isn't assigned a value, since we can't trade him for any other chessman. But his mobility compared to other chessmen is about 3.5 points.
Mobility for most chessmen is greatest in the center of the board. Values are based on an empty chessboard. A piece or pawn is less valuable if it can't move. Knights don't mind being surrounded by pieces and pawns, since they can jump to get to a new square. If you have a pawn that can't move at all, or a piece that can only move to one square, trade your less-mobile chessman for one of your opponent's more-mobile chessmen.