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 followed by a question as to what is the best thing to do, becomes a problem, to which the answer is--_the best thing to do_.

Of course, in most strategic problems, there are so many factors almost unknown, and so many factors only imperfectly known, that we can rarely ascertain mathematically what is the best thing to do.

Nevertheless, there must be a best thing to do, even if we never ascertain exactly what it is.