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When playing chess, two of the most important considerations to have are position and material. With that fact in mind, it is important to consider BOTH of these fundmental ideas of chess, just not one or the other. Iniatative must be considered! With that in mind, let us first look of the general rule of point count.
Pawn = Pawn
Knight = 3 Pawns
Bishop = 3 Pawns
Rook = 5 pawns
Queen = 9 pawns
(The King of course is priceless)
Although point count certainly has its advantages, the position is by no means written in stone by who has more material! Let us consider example 1 as the first nail in the grave of point count!
The thing about material gain is it is lasting, where as an advantage in position can quickly dissolve and needs to be used before it vanishes.
The most inexperienced beginner can count his material, but even top class players misjudge positions.
How do you know that in the first position black actually has the advantage? Did you have a computer play it a few hundred times against itself, to see who wins most?
The other positions seem tactical to me. Material does not mean anything in a tactical situation; I can be a Queen up, but if it is not my turn and the opponent forks me, it is bye-bye Queen... Like any strategic evaluation term, material only means something in quiet positions.
From Chess programs it is well known that there are (apart from material) evaluation terms that can run up to well over a Pawn. King safety is defnitely one of those. Passed Pawns are another. An isolated passer on the 7th rank is worth nearly 3 Pawns, on the 6th nearly 2. Protected passers are worth more, connected passers still more. It is well known that 2 connected 6th-rank passers beat a Rook.
Material is also not purely additive. Seven Knights beat three Queens quite easily, which cannot be explained by addition of any plausible value for the individual pieces.
There are two types of elements of chess. One is the static elements, those which require something extraordinary (a brilliant combination or a serious oversight) to alter. These are Material and Pawn Structure (understood to mean primarily the central pawn structure once determined, although the shape of the flank pawns also count). Once you're a piece ahead, it's going to take something to win it back. And pawn structures are defined finally only when fixed, so although a structure may include fluidity, if it includes volatility it may not yet be a "structure."
What this means is that in most situations your "point count" of material will be pretty close to the relative strength of your side. This can however be affected by the dynamic elements, thosee which can change quickly. Obviously if the opponent sacrifices his Queen for a forced checkmate, your "winning" point count is meaningless.
So the forms which compensation for material deficits can take resolve into the dynamic elements: King Safety, Mobility, and Time. A sufficient advantage in any of these areas can balance a deficit of material (or pawn structure), but usually these are fleeting things which must be realized immediately. It's like energy on the board - if not utilized, it quickly dissipates.
The short answer is that your point count evaluation is a perfect measure of the situation on the board, except when it is not.
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