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Zagier, D. (1990). How Often Should You Beat Your Kids? Mathematics Magazine, 63(2), 89–92. https://doi.org/10.1080/0025570X.1990.11977493

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We, however, maintain that only the most degenerate parent would play against a two-year-old for money, and that our concern must therefore be, not by how much you can expect to win, but with what probability you will win at all. Our principal result is that this probability tends asymptotically to 85.4% (more precisely: to 1/2 + 1/sqrt(8)) as n tends to infinity. This shows with what unerring instinct Levasseur's mother selected the game — the high 85% loss rate will instill in the young progeny a due respect for the immense superiority of their parents, while the 15% win rate will maintain their interest and prevent them from succumbing to feelings of hopelessness and frustration.
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Taylor & Francis

How Often Should You Beat Your Kids?

Published in Mathematics Magazine (Vol. 63, No. 2, 1990)

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Zagier, D. (1990). How Often Should You Beat Your Kids? Mathematics Magazine, 63(2), 89–92. https://doi.org/10.1080/0025570X.1990.11977493

<...>
We, however, maintain that only the most degenerate parent would play against a two-year-old for money, and that our concern must therefore be, not by how much you can expect to win, but with what probability you will win at all. Our principal result is that this probability tends asymptotically to 85.4% (more precisely: to 1/2 + 1/sqrt(8)) as n tends to infinity. This shows with what unerring instinct Levasseur's mother selected the game — the high 85% loss rate will instill in the young progeny a due respect for the immense superiority of their parents, while the 15% win rate will maintain their interest and prevent them from succumbing to feelings of hopelessness and frustration.
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