Of Calculation

We can describe a normal, average game of chess in the following way: Both sides will employ their available forces more or less advantageously to execute attacking and defensive maneuvers which should gradually lead to exchanges. If one side or the other emerges from the conflict with some material gain, it will generally be possible to force a mate in the endgame, whilst if both sides have succeeded, by careful play, to preserve equality of material, a draw will generally ensue.

It will be found that a single pawn may suffice, with some few exceptions, to achieve a victory, and we shall adopt the following leading principle for all combinations: Loss of material must be avoided, even if only a pawn.

Let us master a simple device that makes most combinations easy both for attack and defense. It amounts merely to a matter of elementary arithmetic, and if the beginner neglects it, he will soon be at a material disadvantage.

This diagram may serve as an example.

It is Black's move, and we will suppose he wishes to play ... e5. A beginner will probably calculate thus: I push on my pawn, he takes with his pawn, my knight takes, so does his, then my bishop takes, and so on. This is quite wrong, and means waste of time and energy.

When the beginner considers a third or fourth move in such a combination, he will already have forgotten which pieces he intended to play in the first moves. However, the calculation is perfectly simple upon the following lines: I play ... e5, then my pawn is attacked by a pawn and two knights, a bishop and two rooks, six times in all. It is supported by a bishop, two knights, two rooks and a queen, six times in all. Therefore I can play ... e5, provided the six men captured at e5 are not of greater value than the six white men which are recaptured. In the present instance both sides lose a pawn, two knights, two rooks, and a bishop, and there is no material loss. This established, he can embark on the advance of the king's pawn without any fear.

Therefore, in any combination which includes a number of exchanges on one square, all you have to do is to count the number of attacking and defending men, and to compare their relative values; the latter must never be forgotten.

If Black were to play ... Nxe4 because the pawn at e4 is attacked three times, and only supported twice, it would be an obvious miscalculation, for the value of the defending pieces is smaller.

Chess would be an easy game if all combinations could be tested and probed exhaustively by the mathematical process just shown. But we shall find that the complications met with are extremely varied. To give the beginner an idea of this, I will mention a few of the more frequent examples. It will be seen that the calculation may be, and very frequently is, upset by one of the pieces involved being exchanged or sacrificed. An example of this is found below:

A second important case, in which our simple calculation is of no avail, occurs in a position where one of the defending pieces is forced away by a threat, the evasion of which is more important than the capture of the man it defends.

A further example of the same type is given below.

We will now go a step further and turn from "acute" combinations to such combinations as are, as it were, impending. Here, too, I urgently recommend beginners (advanced players do it as a matter of course) to proceed by way of simple arithmetical calculations, but, instead of enumerating the attacking and defending pieces, counting the number of possibilities of attack and defense.

Let us consider a few typical examples.

The following examples show typical positions, in which simple calculation is complicated by side issues.

Finally, one more example, in which one of the defending pieces being pinned makes simple calculation impracticable.

These illustrations will be sufficient to give the beginner an understanding of economy of calculation in all kinds of combinations. His power of combining will grow speedily on this basis, and thrive in the fire of practical experience.

We have noticed the important part played in each skirmish by the balance between the attacking and defending men. Speaking quite generally, common-sense will tell us that the main consideration for the defense 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 defense.

-- Edward Lasker, 1915