If the commanders had been guided by reason, it would seem that it must have been obvious to Napoleon that by advancing thirteen hundred miles and giving battle with a probability of losing a quarter of his army, he was advancing to certain destruction, and it must have been equally clear to Kutúzov that by accepting battle and risking the loss of a quarter of his army he would certainly lose Moscow. For Kutúzov this was mathematically clear, as it is that if when playing draughts I have one man less and go on exchanging, I shall certainly lose, and therefore should not exchange. 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 am.