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.