ON CHESS
XVIII - On The Power of Pieces and Pawns
WE have hitherto supposed the reader to be acquainted with, at least, the alphabet of chess; and have not hesitated to employ many of the technical terms used in the game. In the concluding articles of this course we hope to furnish some curious and useful information on subjects which are scarcely noticed in books devoted to the elements of chess-play.
We quite agree with the suggestion of a recent writer that the best method of learning the names of the pieces with their moves, and the manner of placing them at thu beginning of the game, is to take an hour's lesson from a friend. Supposing this to have been done, and the student to be engaged in actual play, he will soon perceive that the various pieces have different degrees of power; that a rook is of more value than a bishop or a knight, and that a pawn is of far less value than a minor piece. He will find the queen to be a match for several pieces, and may be willing to part with a rook, a bishop, and a knight, in order to capture his antagonist's queen. The different values of the pieces and pawns are soon appreciated by the player, and he endeavours to regulate his exchanges accordingly; nevertheless, few persons have attended to the circumstances which decide these values, and although they are numerically expressed in most elementary works yet the computations which have led to them are alwavs omitted.
If a general had two bodies of troops similar in most respects, but one of which, from any cause whatever, could occupy only a particular part of any hostile district; while the other was capable of occupying different posts at distant points by a series of rapid movements; the first body would, generally speaking, be far less valuable than the second. Now something analogous to this occurs at chess: those pieces which are capable of taking the greatest range over the board, and of making the most rapid movements, are the most valuable. For the hills and valleys of a contested country, we have nothing but black and white squares on the chess-board: therefore the test of strength which we are now considering is this, how many squares of the chess-board can each piece or pawn command at one time?
In the first place, let us suppose the board to be cleared of its pieces and pawns, and one of each to be placed on it in succession. Choose a central square, such as the king's 4th, and ascertain how many squares a pawn or a piece can command from that position. A pawn placed on that square commands two other, being those to which it would move if it made a capture. The knight could move to any of 8 squares; the bishop to any one of 13 squares; the rook to 14; the queen to 27; and the king to 8. We refrain from demonstrating these numbers, because the reader can easily satisfy himself on this point, by placing the pieces, ono after another, on the king's 4th square, all the other squares being unoccupied. So far, then, as this mode of comparison is concerned, the power of the pieces to move on to other squares is
Pawn ... = 2
Knight ... = 8
Bishop ... = 13
Rook ... = 14
Queen ... = 27
King ... = 8
But we have now to inquire whether this proportion exists for all the squares equally. A very little experience will show that it does not: every piece is diminished in value as it approaches the edges of the board; but this diminution is not the same for all. Let us select the king's rook's square, And notice the change in the powers of the pieces. Testing them one by one, we shall find that the number of squares to which each can move is
Pawn ... = 1
Knight ... = 2
Bishop ... = 7
Rook ... = 14
Queen ... = 21
King ... = 3
Here it will be seen, that while the rook has not changed in value, the others have done so considerably, but. in different ratios. If we select any other square intermediate between the centre and the corner, we shall find the numbers to be higher than the one, and lower than the other of our two lists. The knight, for instance, commands 2, 3, 4, 6, or 8 squares, according to where he may be situated; the bishop commands 7, 9, 11, 13 squares; and so on. The correct way, therefore, of comparing the powers of the pieces in moving over the open board is to suppose a piece to be placed on every one of the sixty-four squares in succession to add up the respective powers in all these positions, and to divide the result by 64. This is a process analogous to that employed in every department of science for the obtaining of an average or mean, whereby small errors, variations, and discrepancies, become absorbed, or expunged by mutual correction in the general result; and it is perfectly applicable iu the present case. This being done, it is found that the average power of each piece to move over the open board is nearly as follows:
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Pawn ... = 1 1/4
Knight ... = 5 1/4
Bishop ... = 8 3/4
Rook ... = 14
Queen ... = 22 3/4
King ... = 8 1/2
Here the bishop is said to be 8 3/4, which means that in consequence of his sometimes commanding as many as 13 squares, and at other times as few as 7, the average of the whole is 8 3/4; and so of the others the rook being of constant value in any position on the open board.
We have now something like a test of the respective powers of the pieces, by which we begin to see the ad vantage of making exchanges of one for another. But still this is nothing more than a groundwork on which to found subsequent calculations, for we have proceeded on a supposition which never occurs in practice, viz., an open or cleared board. The intermixture of pieces among each other over the field of contest, gives rise to variations so complicated and so remarkable that it has required great analytical research from distinguished men, to trace them to their sources. We strongly doubt whether this has yet been done correctly; but still an approximation to correctness has been made, and we will briefly notice the manner in which the inquiry has been conducted.
We have hitherto considered the board to bo cleared, and have ascertained the relative values of the pieces on that supposition. Let us now suppose the pieces and pawns to be arranged for the commencement of a game, and view their positions before the game begins. Here we are struck with the remarkable fact that the pieces are almost powerless; it is true they act as defenders of the pawns which front them; but as to the power of moving, none of them possess it except the knight. The king, the queen, the bishop and the rook cannot move a step until some of the pawns are moved, and the knight owes his power of moving to his singular privilege of leaping over other pieces or pawns. So far, then, as the power of moving is concerned, a pawn is actually more powerful than even a queen at the commencement of the game.
Now in actual play, the relative powers of moving are always intermediate between the two extremes which we have mentioned, from the time of the first move being made, the constrained limits of the pieces begin to be broken, and their natural powers to be developed; but on the other hand, these powers never attain the rank given to them by our first supposition, for the two kings even if nothing else are always on the board. The power of moving from square to square varies as the game proceeds, but not with equal rapidity: for instance; the knight is powerful from the very beginning of the game, because whatever be near him he can leap over the intervening piece; while the rook is seldom of much use till several of the pieces and pawns are off the board. The rook increases his value by the thinning of the combatants more rapidly than any other piece, and therefore the ratio of his value is continually increasing.
It thus appears that the degree of openness of the board changes the proportionate value of the pieces, and it is difficult to fix a point where the power may be deemed an average between the highest and lowest. It is assumed, however, that we may suppose each party to have lost three pieces and four pawns, leaving four pieces and four pawns to defend the king. This is a fraction more than half the original forces, and may therefore be taken as an average or medium between the powers possessed by the respective pieces when the board is quite open, and when all the pieces are arranged for the commencement of a game.
If during the progress of a game, when about half tho pieces and pawns have been removed by mutual exchanges, one of the players estimate the various powers of his remaining pieces, he may sometimes observe that a whole rank, or file of squares is blocked up by the intervention of one single piece or pawn, and moreover, that the intervening piece or pawn may be of his own party. In such a case his own troops actually stand in each other's way; and the less skilful the player, the more likely is this self-imposed blockade to occur. It may, and sometimes does happen in practice, that every square to which the knight's peculiar leap allows him to move, is occupied by one of his own forces; and the queen, after making a capture, is frequently found to be so hemmed in by inferior pieces and pawns, some of her own party, and others belonging to the antagonist, but well supported that she becomes almost useless. If a piece be blocked up by one of the same party, the moving power in that direction is temporarily suspended, until the obstructing piece is removed; and if the obstructing piece be of the opposite party, but of inferior value, and supported, to capture that piece would be a loss, so that a passage in that direction may be deemed practically blocked out. From all this it will be seen, that the comparative values of the pieces, at and about the middle of tho game, are greatly modified by the liability of obstruction, arising from the intervention of a piece belonging to the same party, or of a supported inferior piece of the opposite party.
Other variations in value will be not ced in our next article on this subject.
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Chess Archeology 
