Statistical Science

Parrondo's paradox

D. Abbott and G. P. Harmer

Full-text: Open access

Abstract

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.

Article information

Source
Statist. Sci., Volume 14, Number 2 (1999), 206-213.

Dates
First available in Project Euclid: 24 December 2001

Permanent link to this document
https://projecteuclid.org/euclid.ss/1009212247

Digital Object Identifier
doi:10.1214/ss/1009212247

Mathematical Reviews number (MathSciNet)
MR1722065

Zentralblatt MATH identifier
1059.60503

Keywords
Gambling paradox Brownian ratchet noise

Citation

Harmer, G. P.; Abbott, D. Parrondo's paradox. Statist. Sci. 14 (1999), no. 2, 206--213. doi:10.1214/ss/1009212247. https://projecteuclid.org/euclid.ss/1009212247


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References

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