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 unit it defends.  In Diagram 7, for instance, Black may not play KtxP, because White, by playing P-Q6, would force the Bishop to Kt4 or B1, to prevent the pawn from Queening and the Knight would be lost.  A further example of the same type is given in Diagram 8.  Here a peculiar mating threat, which occurs not

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

Diag. 8.

infrequently in practical play, keeps the Black Queen tied to her KB2 and unavailable for the protection of the B at bi.

White wins as follows: 

1.  KtxB, KtxKt; 2.  RxKt, QxR; 3.  Kt-B7ch, K-Kt1; 4.  Kt-R6 double ch, K-R1; 5 Q-Kt8ch, RxQ; 6.  Kt-B7 mate.

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, to count the number of possibilities of attack and defence.

Let us consider a few typical examples.  In Diagram 9, if Black plays P-Q5, he must first have probed the position in the following way.  The pawn at Q5 is attacked once and supported once to start with, and can be attacked by three more White units in three more moves (1.  R-Q1, 2.  R(B2)-Q2, 3.  B-B2) Black can also mobilise three more units for the defence in the same number of moves (1.  Kt-B4 or K3, 2.  B-Kt2, 3.  R-Q1).  There is, consequently, no immediate danger, nor is there anything to fear for some time to come, as White has no other piece which could attack the pawn for the fifth time.

---------------------------------------
8 |    |    |    |    | #R | #B | #K |    |
|---------------------------------------|
7 | #P | #P |    | #R |    |    |#Kt | #P |
|---------------------------------------|
6 |    |    |    |    |    |    | #P |    |
|---------------------------------------|
5 |    |    |    | #P |    |    |    |    |