Open Access
May 1999 Parrondo's paradox
D. Abbott, G. P. Harmer
Statist. Sci. 14(2): 206-213 (May 1999). DOI: 10.1214/ss/1009212247


We introduce Parrondo's paradox that involves games of chance. We consider two fair gambling games, A and B, both of which can be made to have a losing expectation by changing a biasing parameter $\epsilon$. When the two games are played in any alternating order, a winning expectation is produced, even though A and B are now losing games when played individually. This strikingly counter­intuitive result is a consequence of discrete­time Markov chains and we develop a heuristic explanation of the phenomenon in terms of a Brownian ratchet model. As well as having possible applications in electronic signal processing, we suggest important applications in a wide range of physical processes, biological models, genetic models and sociological models. Its impact on stock market models is also an interesting open question.


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D. Abbott. G. P. Harmer. "Parrondo's paradox." Statist. Sci. 14 (2) 206 - 213, May 1999.


Published: May 1999
First available in Project Euclid: 24 December 2001

zbMATH: 1059.60503
MathSciNet: MR1722065
Digital Object Identifier: 10.1214/ss/1009212247

Keywords: Brownian ratchet , Gambling paradox , noise

Rights: Copyright © 1999 Institute of Mathematical Statistics

Vol.14 • No. 2 • May 1999
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