it will be unimportant, if the
target is so large and so close that even the inferior marksman
can hit it at each shot. The probability of hitting a target--so
far as overs and shorts are concerned (or deviations to the left
and right)--varies with the fraction _a/y_, where _a_ is the half
height (or width) of the target, and _y_ is the mean error. The
greater the size of the target, and the less the mean error, the
greater the probability of hitting. The size of the two targets
being fixed, therefore, the smaller the mean error the greater
the probability of hitting. The probability of hitting, however
(as can be seen by the formula), does not increase greatly with
the decrease of error, except in cases where _a/y_ is small, where
the mean error is large relatively to the width or height of the
target. For instance, if _a/y_ is .1 in one case, and .2 in another
case, the probability is practically double in the second case;
whereas, if _a/y_ is 1 in one case, and 2 in another, the probability
increases only 55 per cent; while if it is 2 in one case and 4 in
the other, the probability of hitting increases only 12 per cent.

This means that if two antagonists engage, the more skilful should,
and doubtless will, engage under difficult conditions, where _y_
is considerable relatively to _a_; for instance, at long range.
Suppose that he engages at such a range that he can make 10 per
cent of hits--that is, make 90 per cent of misses; and that his
misses relatively to the enemy's is as 90 to 95--so that the enemy
makes 95 per cent of misses. This does not seem to be (in fact it
is not) an extreme case: and yet _A_ will hit _B_ twice as often
as _B_ will hit _A_. In other words, the effective skill of _A_
will be twice that of _B_.

This illustrates the effect of training--because all that training
in handling any instrument can do is to attain as closely as possible
to the maximum output of the instrument; and as the maximum output
is attained only when the instrument is handled exactly as it should
be handled, and as every departure is therefore an error in handling,
we see that the effect of training is merely to diminish errors.

That this illustration, drawn from gunnery, is applicable in general
terms to strategy seems clear, for the reason that in every strategical
situation, no matter how simple or how complex, there is, and can be
only one _best_ thing to do; so that the statement of any strategic
situation, if f