In War and Peace, Book III, Part Two, Chapter 19, Leo Tolstoy explains a theory of exchanges that applies in chess, checkers, and warfare:

How and with what object were the battles of Shevardino and Borodino given and accepted? Why was the battle of Borodino fought? There was not the least sense in it for either the Russians or the French. Its immediate result for the Russians was, and was bound to be, that we were brought nearer to the destruction of Moscow (which we feared more than anything in the world), and for the French, that they were brought nearer to the destruction of their whole army (which they feared more than anything in the world). The result then must have been quite obvious, and yet Napoleon offered and Kutuzov accepted this battle.

If the commanders had been guided by reasonable considerations, it would seem that it must have been clear to Napoleon that, by advancing two thousand versts and giving battle with the probability of losing a quarter of his army, he was heading for certain destruction, and it must have been equally clear to Kutuzov that by accepting battle and risking the loss of a quarter of his army he would certainly lose Moscow. For Kutuzov this was mathematically clear, as clear as it is that if I have one man less in a game of checkers and go on making even exchanges, I am bound to lose, and therefore I should not make the exchanges. When my opponent has sixteen men and I have fourteen I am only one eighth weaker than he, but when I have exchanged thirteen more men he will be three times as strong as I.

(from the Ann Dunnigan translation, 1968; cf. TruthInBattle (11 Feb 2001), OozeOnVerst (22 Sep 2004), BodyMnemonic (4 Dec 2004), PerfectCommunication (14 Feb 2005), LadderOfLife (10 Apr 2005), BeaconOfHope (17 Apr 2005), ModernMedicine (29 Apr 2005), NationalCharacters (16 May 2005), ...)

TopicLiterature - TopicScience - TopicRecreation - 2005-05-25

(correlates: Career Choice, PatienceAndTime, AntiBumperstickerization, ...)