Open Access
February, 1984 Tree Algorithms for Unbiased Coin Tossing with a Biased Coin
Quentin F. Stout, Bette Warren
Ann. Probab. 12(1): 212-222 (February, 1984). DOI: 10.1214/aop/1176993384


We give new algorithms for simulating a flip of an unbiased coin by flipping a coin of unknown bias. We are interested in efficient algorithms, where the expected number of flips is our measure of efficiency. Other authors have represented algorithms as lattices, but by representing them instead as trees we are able to produce an algorithm more efficient than any previously appearing. We also prove a conjecture of Hoeffding and Simons that there is no optimal algorithm. Further, we consider generalizations where the input is a sequence of iid discrete random variables and the output is a uniform random variable with $N$ possible outcomes. In this setting we provide an algorithm significantly superior to those previously published.


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Quentin F. Stout. Bette Warren. "Tree Algorithms for Unbiased Coin Tossing with a Biased Coin." Ann. Probab. 12 (1) 212 - 222, February, 1984.


Published: February, 1984
First available in Project Euclid: 19 April 2007

zbMATH: 0536.60018
MathSciNet: MR723740
Digital Object Identifier: 10.1214/aop/1176993384

Primary: 60C05
Secondary: 60G40

Keywords: biased coin , Binary tree , discrete distribution , Random numbers , unbiased coin

Rights: Copyright © 1984 Institute of Mathematical Statistics

Vol.12 • No. 1 • February, 1984
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