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How strong can the Parrondo effect be?

Part of: Limit theorems Markov processes

Published online by Cambridge University Press:  11 December 2019

S. N. Ethier  and
Jiyeon Lee Open the ORCID record for Jiyeon Lee [Opens in a new window]
S. N. Ethier*
Affiliation:
University of Utah
Jiyeon Lee*
Affiliation:
Yeungnam University
*
*Postal address: Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, UT 84112, USA.
**Postal address: Department of Statistics, Yeungnam University, 280 Daehak-Ro, Gyeongsan, Gyeongbuk 38541, South Korea. Email address: [email protected]
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Abstract

Parrondo’s coin-tossing games were introduced as a toy model of the flashing Brownian ratchet in statistical physics but have emerged as a paradigm for a much broader phenomenon that occurs if there is a reversal in direction in some system parameter when two similar dynamics are combined. Our focus here, however, is on the original Parrondo games, usually labeled A and B. We show that if the parameters of the games are allowed to be arbitrary, subject to a fairness constraint, and if the two (fair) games A and B are played in an arbitrary periodic sequence, then the rate of profit can not only be positive (the so-called Parrondo effect), but can also be arbitrarily close to 1 (i.e. 100%).

Keywords

Parrondo gamesrate of profitstrong law of large numbersbinomial-like distribution

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60F15: Strong theorems
Type
Research Papers
Information
Journal of Applied Probability , Volume 56 , Issue 4 , December 2019 , pp. 1198 - 1216
Copyright
© Applied Probability Trust 2019 

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