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How to select a loser. (English) Zbl 0795.90103
The author considers the following problem: A party of $$N$$ people selects one of its members. Everybody is flipping a coin with outputs 0 and 1, each with probability 1/2. Then, recursively, the 0-party continues until the loser is found. It is shown that this procedure stops on the average after about $$\log_ 2 N$$ steps. The average size (number of nodes) of such an incomplete tree is about $$2\log_ 2 N$$, the average number of coin-flippings being exactly $$2N$$. Some modifications of the selection problem are also discussed.

##### MSC:
 91A60 Probabilistic games; gambling 11B68 Bernoulli and Euler numbers and polynomials
##### Keywords:
coin-flippings; selection problem
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##### References:
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