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ollowed 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. Now in arriving at the decision as to the best thing to do, one estimates the weight of each factor and its bearing on the whole. If one estimates each factor correctly, that is, if he makes no errors in any estimate, and if he makes no error in summing up, he will make an absolutely correct decision; and any departure from correctness in decision can result from no other cause than from errors in his various estimates and in their final summation. In other words, skill in strategy is to be attained by the same process as is skill in other arts: by eliminating errors. So, when we take the decisions of the game-board and the war problem, we must not allow ourselves to forget that there has been a tacit assumption that the numbers and the skill of the personnel have been equal on the two sides; and we must supplement our decision as to the best material to be employed by another decision as to how we shall see to it that the assumption of equality of personnel shall be realized in fact--or rather that it shall be realized in fact that our personnel shall get the maximum of effectiveness out of the material. In designing the machine, therefore, we are confronted with the curious fact that, in general, we must design the various material parts before designing the personnel parts that are to operate them. The most obvious characteristic of the personnel parts is that the number of personnel parts shall be sufficient to operate the material parts. To ascertain the number of personnel parts, the only means is actual trial; though naturally, if we have previously ascertained the number of men needed to operate any kind of mechanism, say a certain kind and size of gun, we can estimate quite accurately the number needed to operate a similar gun, even if it differ somewhat from the other gun. After the gun is tried, however, we may have to change our original estimate, not only because the estimate may have been in error, but because the requirement of operating the gun may have changed. For instance, the re
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