In the first chapter, when considering special cases in elementary combinations, we have already noticed the important part played in each skirmish by the balance between the attacking and defending units.  Speaking quite generally, common-sense will tell us that, in all operations on the chess-board, the main consideration for the defence will be to maintain that balance, and that there is only justification for an attack when it is possible to concentrate more forces on the strategic point than can be mustered by the defence.  However, one very important point must not be neglected, though I did not touch upon it when discussing elementary combinations for fear of complicating matters for beginners:  the balance between the contending forces is by no means established by their numerical equality.  A paramount factor is the mobility of such forces, and as soon as it is no longer one of the elementary cases of capture and recapture described previously, this factor must be taken into account in order to decide, on a general survey, whether there is a sufficient defence to an impending attack, or whether one’s own intended attack is likely to prevail.  That mobility is the first and foremost consideration should be self-evident, since the relative value of the pieces can only make itself felt by their greater or lesser mobility.

Except in certain positions, which are brought about by some particular array of the pieces, the intrinsic value of a Rook is greater than that of a Bishop, because it can command all the squares on the board, whilst a Bishop is tied to its own colour; Knight and Bishop are considered equivalent, because the Knight’s advantage in being able to act on all the squares of either colour is balanced by the fact that the Bishop can sweep long diagonals.  Two Bishops are, generally speaking, of greater value than two Knights, because together they also act on all the squares, and their command of long diagonals is a clear advantage.  The whole of this valuation, however, comes to nought when the pieces are hindered in their mobility by the peculiarity of any particular position.

We will consider one instance from end-game play, and one from the openings.

In Diagram 13, White derives no advantage from being

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8 |    |    |    |    |    |    |    |    |
|---------------------------------------|
7 |    |    |    |    |    |    | #K |    |
|---------------------------------------|
6 |    | #P |    |    |    | #P |    |    |
|---------------------------------------|
5 | #P |    | #P |    | #P | ^P | #P |    |
|---------------------------------------|
4 | ^P |    | ^P | #Kt| ^P |    |    |    |
|---------------------------------------|
3 |    | ^P |    | ^R |    |    | ^P | ^K |
|---------------------------------------|
2 |    |    |    |    |    |    |    |    |
|---------------------------------------|
1 |    |    |    |    |    |    |    |    |
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A    B    C    D    E    F    G    H

Diag. 13