"How often should you beat your kids?", by Don Zagier.
> This note is a follow-up to the note "How to beat your kids at their own game" by K. Levasseur, in which the author proposes the following game to be played against one's own children: ... Levasseur analyzes the game and shows that on average you will have a score of n + (sqrt(pi * n) - 1) / 2 + O(n^{-1/2}), while the kid, of course, will have an average score of exactly n.
> We maintain, however, that only the most degenerate parent would play against a 2-year-old for money, and that our concern should therefore be not by how much you expect to win, but with probability you will win at all.
"How often should you beat your kids?", by Don Zagier.
> This note is a follow-up to the note "How to beat your kids at their own game" by K. Levasseur, in which the author proposes the following game to be played against one's own children: ... Levasseur analyzes the game and shows that on average you will have a score of n + (sqrt(pi * n) - 1) / 2 + O(n^{-1/2}), while the kid, of course, will have an average score of exactly n.
> We maintain, however, that only the most degenerate parent would play against a 2-year-old for money, and that our concern should therefore be not by how much you expect to win, but with probability you will win at all.