On the Exchange Value of the Pieces.
In the course of the contests above described the aggressor may often, if he so chooses, capture hostile men at the price of sacrificing some of his own men. To capture a piece of the enemy and in compensation to give up a piece therefor is called an "exchange." You exchange Bishop for Knight, if your Bishop captures the Knight and is recaptured. You exchange Pawn for Pawn, Queen for Queen, Rook for Rook in the same way. But if you capture Rook for Knight or Bishop, you are considered to have made a good bargain, you have "won the exchange." Some Chess-friends prefer the Knight to Bishop, others the Bishop to Knight and they make exchanges accordingly. Who is in the right? Or is there neither right nor wrong in these proceedings; are they, maybe, under the rule of an incomprehensible hazard?
In the games of most Chess lovers such a hazard seems to dominate; even though this law of chance, or whatever it might be, cannot be considered truly incomprehensible, since Psychology may assist us in deciphering it, it is sufficiently difficult of explanation as to balk the human stupidity that we proudly call "intellect." But it is not this difficulty that we are trying to assail at the present. We rivet our attention on the games of the experienced, the thinking, the strong players, preferably the strongest of them, the masters, and among them certain regularities show very plainly. The experience derived from games played between such as deserve the title of masters, during centuries has proven these regularities. Hence, we know that __ceteris paribus__ Knight and Bishop are even, either is __ceteris paribus__ worth three Pawns, Rook __ceteris paribus__ as strong as Knight or Bishop and two Pawns, Queen very nearly as strong as two Rooks or three minor pieces.
The supposition implied in the term "_ceteris paribus_" is, however, of importance. "All other circumstances being equal," that is the meaning of _ceteris paribus_. In strict Logic, the other circumstances are never equal. The supposition is that we consider them of equal weight or import. And the "we" in no wise refers to the inexperienced player. The nearly perfect player -- say the master -- is he who judges. We erring mortals, try to guess his judgment. While in this we are doing our level best, we modestly keep him in mind and seek to approach his efficiency and his methods. To leave the __ceteris paribus__ out of reckoning would plunge us into the claws of Nonsense that would reduce our proud intellect to blundering romanticism akin to madness. To give an instance, here is a position where a Pawn is stronger than a Knight and a Queen and a Rook.
White with the move plays PxX, calls for a Knight, says Check, simultaneously attacks Queen, then captures Queen and thereafter the immobile and helpless Rook. Mark the exceeding value of the right to move. Black to move would have an enormous superiority.
_Ceteris paribus_ notwithstanding, the exchange values of which a few are set down above, are therefore always somewhat problematical. For all that, they are to the Chess-player a most needed compass. If he conscientiously follows them, his ship nearly always, even though only after many moves, runs safely into port.
We are not without a method to probe the above values and to discover others. All we have to do is to build simple positions, in which the values under discussion, say Rook against Bishop and Pawn, with due regard to the __ceteris paribus__ are set to fight each other and carefully to analyse the course of that fight. Of the application of this method a few examples are here given.