This interesting description on the value of the pieces of a chess set was written by the great Cuban chess champion Jose Raul Capablanca (1888 - 1942) in his book on the chess basics called, appropriately, "Chess Fundamentals."
It is advisable to give the student an idea of the proper relative value of the pieces. There is no complete and accurate table for all of them, and the only thing to do is to compare the pieces separately.
For all general theoretical purposes the Bishop and the Knight have to be considered as of the same value, though it is my opinion that the Bishop will prove the more valuable piece in most cases; and it is well known that two Bishops are almost always better than two Knights.
The Bishop will be stronger against Pawns than the Knight, and in combination with Pawns will also be stronger against the Rook than the Knight will be.
A Bishop and a Rook are also stronger than a Knight and a Rook, but a Queen and a Knight may be stronger than a Queen and a Bishop.
A Bishop will often be worth more than three Pawns, but a Knight very seldom so, and may even not be worth so much.
A Rook will be worth a Knight and two Pawns, or a Bishop and two Pawns, but, as said before, the Bishop will be a better piece against the Rook.
Two Rooks are slightly stronger than a Queen. They are slightly weaker than two Knights and a Bishop, and a little more so than two Bishops and a Knight. The power of the Knight decreases as the pieces are changed off. The power of the Rook, on the contrary, increases.
The King, a purely defensive piece throughout the middle-game, becomes an offensive piece once all the pieces are off the board, and sometimes even when there are one or two minor pieces left. The handling of the King becomes of paramount importance once the end-game stage is reached.
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