There is a section in War and Peace, that says:
"If the commanders had been guided by reasonable causes, it would seem it should have been quite clear to Napoleon that, having gone thirteen hundred miles and accepting battle with the likely chance of losing a quarter of his army, he was marching to certain destruction;it should have been as clear to Kutuzov that, in accepting battle and also risking the loss of a quarter of his army, he would certainly lose Moscow. For Kutuzov this was mathematically clear, as it is clear that, in a game of checkers, if I have one man less and keep trading man for man, I will certainly lose, and therefore I should not keep trading. When my opponent has sixteen pieces and I have fourteen, I am only one-eighth weaker than he; but when I have traded thirteen pieces, he will be three times stronger than I.
Before the battle of Borodino, our [Russian] forces were approximately five to six with the French, but after the battle they were one to two; that is, before the battle it was a hundred thousand to a hundred and twenty thousand, but after the battle it was fifty thousand to a hundred thousand. And yet the intelligent and experienced Kutuzov accepted battle."
This makes no sense to me, and the numbers seem random so I'm using my own example below:
IF I have, say, 100 people in my army and the YOU have 200, and I lose, say, half of them and you lose half, the relationship will be the same, as 100/200 is the same as 50/100. It seems to me Tolstoy is saying that if we both lost the SAME NUMBER and not SAME RATIO of people, then the relationship would change and favor the army with more people, and I think that's true. Since if I lose the same number, 50, as you do, then I will have 50 left and you will have 150 left, so instead of 1/2 relationship, now it's 1/3.
What am I missing? I googled this but did not find anybody else having problems with this apparently....
Tolstoy does indeed mean trading the same number, not proportion, but he's quite clear about this:
(emphasis mine) Trading "man for man" means exactly trading the same number of pieces: for each piece ("man") that I take from you, I also lose one piece.