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Zusammenfassung:
This note is a follow-up to the note ``How to beat your kids at their own game'', by \\it K. Levasseur [ibid. 61, No.5, 301-305 (1988; Zbl 0667.90103)], in which the author proposes the following game to be played against one's two-year-old children: Starting with a deck consisting of n red cards and n black cards (in typical applications, n=26), the cards are turned up one at a time, each player at each stage predicting the color of the card which is about to appear. The kid is supposed to guess ``Red'' or ``Black'' randomly with equal probability (this solves the problem of constructing a perfect random number generator), while you play what is obviously the optimal strategy - guessing randomly (or, if you prefer, always saying ``Black'') whenever equal numbers of cards of both colors remain in the deck and otherwise predicting the color which is currently in the majority. Levasseur analyzes the game and shows that on the average you will have a score of n+(\\sqrtπ n-1)/2+O(n\\sp- 1/2), while the kid, of course, will have an average score of exactly n. \\par 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/\\sqrt8) 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.
