## Statistical Science

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

### Parrondo's paradox

#### 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