Exchanging nearly all man in draughts (checkers)

I haven't played draughts (checkers) for a long time, but I recall that exchanging 3-5 men into kings in a single game is quite rare and performing more than 5 exchanges in one game is very rare.

Yet, I found this piece of text in Leo Tolstoy's "War and Peace":

For Kutuzov 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.

What kind of exchange or game move is he writing about?

He could possibly be talking about standard man-to-king promotion, because it is not practically possible (or very, very rare) to exchange thirteen pieces into kings, nor would doing so make my opponent three times stronger than I am.

He has 14 pieces and his opponent 16. So his strength compared to his opponent is 14/16 = 7/8.

The exchange is the trade. Trade 13 pieces for 13 other pieces. So he has 14-13 = 1 and his opponent 16-13 = 3. So his opponent has three times as much pieces as he. The exchange has nothing to do with the promotion to king.

When you are behind, it is often not advantageous to trade. Unless you get a better position.

• It seems that I misunderstood "exchange" with "promotion". Shame on me! Commented Feb 20, 2017 at 7:31

That's commonly referred as a "trade". In strategy / combat games, a trade can be applied to when you and your opponent equally lose with a move. You trade your pawn's life, for his, with the move leading to both player losing a pawn each.

If you eat a opponent's piece putting yours in a position where it'll be eaten right after, that's a trade.

Trades are advantageous to someone who is winning, as they maintain their advantage and lead the game to an early end. A losing player should avoid trades as that just puts him one piece closer to losing.

Trades are not always bad for the losing side - you can use it with a long term strategy that'll capitalize on that trade (the trade cleans a side of the board for you to turn a few Men into Kings for example). But as a short term move, trades should be avoided if you are losing.

Trades are common in games like checkers, chess, fighting games when both players punch each other at the same time, MtG when players lose creatures of approximately the same power, and so on.