PEDIATRICS Vol. 98 No. 6 December 1996, pp. A49
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TOSSING TEN HEADS IN A ROW

Student

[Think of a coin-tossing tournament.] One player tosses and the other calls; the winner advances. The winner of this tournament will be that single player who has won n consecutive coin-tosses without a loss, depending on how many rounds it takes to complete a tournament.

There is something strange and trivial about this tournament, but what is it? The winner does have a rather remarkable property. How often have you ever met anyone who just won, say, ten consecutive coin-tosses without a loss? Probably never. The odds against there being such a person might seem enormous, and in the normal course of events, they surely are. If some gambler offered you ten-to-one odds that he could produce someone who before your very eyes would proceed to win ten consecutive coin-tosses using a fair coin, you might be inclined to think this a good bet. If so, you had better hope the gambler doesn't have 1,024 accomplices (they don't have to cheat—they play fair and square). For that is all it takes 2 competitors) to form a ten-round tournament. The gambler wouldn't have a clue, as the tournament started, which person would end up being the exhibit A that would guarantee his winning the wager, but the tournament algorithm is sure to produce such a person in short order—it is a sucker bet with a surefire win for the gambler.