On Strategy and War

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The Value of the Game
There is a branch of mathematics called "Game Theory", which is closely related to strategy. There are differences: game theory assumes that we know everything relevant, and provides an optimum solution, while strategy must operate in ignorance and has no optima. There is one concept from game theory that we need here: the value of the game.

To use game theory, we have all the possible outcomes listed by desirability, and we know what the outcomes will be given what we and our opponent do. We can do some number crunching, and find out what the average outcome will be. Depending on chance factors, we may do better than this, and we may do worse. We know that this is the best we can expect to do.

It may be that we find this outcome acceptable, in which case we know what to do. We may find it unacceptable, in which case we have to try to change the situation. There are various ways to try to wriggle out of the logical results, but we must remember that we are trying to beat the odds and cannot expect to do so all the time. We might take more risks, accepting the possibility losing big in order to gain the possibility of winning big. We might try to change the nature of the "game" in our favor, but our enemy will be doing that also.

Duelling Reasons
Strategy is a hostile contest, and there will be winners and losers. If we want to be successful, we must realize that there is no pre-ordained reason why our side will win. The winner and loser are determined by a complex nest of reasons, and therefore we want to find reasons why we win and the enemy loses. These reasons have to apply properly, and if there were one standard way of winning a war, the enemy would apply it also, and so both of us would win, a logical impossibility in war.

War is theoretically a symmetrical situation, but in practice there are infinite assymmetries. The job of the strategist is to make the asymmetries come out right.

Attrition vs. Maneuver: Which is Correct?
In World War II, the Germans were seen as capable of amazing feats, making startling maneuvers with great potential. The Allies had a great preponderance of soldiers and weapons, and less brilliant generals. A war of maneuver, with thrust and counter-thrust, would play into German hands, while a war of attrition would emphasize the Allied strangths and de-emphasize the German ones. As long as brilliant maneuver dominated the war, the Germans seemed unstoppable. Once their maneuvers had either run into barriers (the English channel, for one), run into emptiness (the Soviet Union), or faced sufficiently strong forces that brilliance was impractical, the Germans lost. In this case, attrition was the proper strategy for the Allies, and won the war for us. This is in sharp contrast to, say, Napoleon's campaigns around Ulm in 1805, in which he maneuvered the main Austrian army into a position so hopeless that they surrendered without a major battle. In this campaign, maneuver was decisive on a large scale. The answer to the question at the head of the paragraph is, and always will be, "It depends".

Attrition vs. Maneuver: Which is Preferable?
We can ask another question, which is what sort of strategy we should prefer to use when given a choice. Since neither is inherently superior in winning wars, we need to consider other things besides victory. The dominant thing is probably the effects of victory or defeat. In maneuver warfare, soldiers are going to find themselves helpless because they are misplaced or unsupplied or uninformed. In attrition warfare, soldiers are going to find themselves helpless because they are wounded or dead. Maneuver warfare isn't necessarily the best way to win a war, but if possible it is the best way to set up the peace.