Blue Devil Knight addresses a very interesting question in his post.
How do you correctly quantify piece mobility?
Usually the value of a piece is expressed in units of 1 pawn.
Q = 9
R = 5
B = 3
N = 3
p = 1
These are STATIC values.
It can happen during a whole game that your rook stands on a1 without moving.
Sometimes it even doesn't make a difference if your rook was placed next to the board in stead of on the board.
In such cases the DYNAMIC value of the rook is 0 (zero).
In other situations the rook can be so active that it is worth a queen.
So the static value of a rook is representing the AVERAGE dynamic value of the rook.
Because we have no good algorithm to express the dynamic value of a rook, the use of the static value has become very popular.
Have a look at the diagram below.
White to move.
The space of the black bishop is severely limited by its own pawn.
The space of the black king is limited by the rim of the board.
White can make use of this by playing Rc1, threatening to conquer the bishop.
If both players occupy about the same space, usually every threat can be met by a defence.
But if one of the players occupies very little space, the attacking side can change from threat to threat, and the opponent comes in trouble because he has a lack of space to move his pieces to defend against all threats.
This is a statistical matter. The CHANCE that you can do something harmful which your opponent cannot prevent increases with you having more space and he less.
All positional play is based on the principle to limit the space of your opponent and to increase your own space. Thus increasing your chances.
The ultimate goal is to take all space away from the enemy king and to conquer him.
Another important aspect to space is the element of time (begins to look like an essay of Einstein).
Have a look below.
White to move.
Geometrically spoken white has almost the whole board to walk to.
But since black is to move after white, he can limit the space of the white king to the first rank.
The temporary and dynamic fence that the black king carries with him makes it difficult to find a correct algorithm to express mobility. If black is to move first, the situation is totally different.
I'm sure a correct algorithm of mobility would be a major step in solving the riddle of chess.
But untill that time we have to work with parts of the algorithm and with averages of dynamic values.
Color complexes, opposition, improve the position of your worst placed piece etc. are all parts of this same ultimate algorithm of mobility. Often these parts are simplified for convenience and easy use.
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