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Parrondo’s Paradox: New Results and New Ideas

Author Affiliations

  • 1Department of Physics, Panskura Banamali College, Panskura, Dist. East Midnapore, Pin: 721 152, WB,India
  • 2Department of Physics, Chandernagore Govt. College, Chandernagore, Dist. Hooghly, Pin: 712 136, W.B,India

Res. J. Recent Sci., Volume 5, Issue (ISC-2015), Pages 8-12, -----Select----,2 (2016)


Parrondo’s paradox is about a paradoxical game and gambling. Imagine two kinds of probability dependent games A and B, mediated by coin tossing. Each of them, when played separately and repeatedly, results in losing which means the average wealth keeps on decreasing. The paradox appears when the games are played together in random or periodic sequences; the combination of two losing games results into a winning game! While the counterintuitive result is interesting in itself, the model can very well be thought of a discretized version of Brownian flashing ratchets which are employed to understand noise induced order. There are a plenty of examples from physics to biology and in social sciences where the stochastic thermal fluctuations or other kinds actually help achieving positive movements. It is in this context, the Brownian ratchets and the kind of prototype games may be explored in detail. In our study, we examine various random combinations of losing probabilistic games in order to understand how and how far the losing combinations result in winning. Further, we devise an alternative model to study the similar paradox and examine the idea of paradox in it. The work is mostly done by computer simulations. Analytical calculations to support this work, is under progress.


  1. ParrondoJ. M.R. (1996), How to cheat a badmathematician, EEC HC&M Network on Complexity andChaos (, ERBCHRX-CT940546)
  2. ParrondoJ. M.R. and Dinis L. (2004), Brownian motionand gambling: from ratchets to paradoxical games, Contemporary Physics, 45(2), 147-157,arXiv:1410.0485v1 [physics.soc-ph].
  3. Dinis L. and Parrondo J.M.R. (2003),, Optimal strategiesin collective Parrondo games, Europhys. Lett., 63, 319-325.
  4. ShuJian-Jun, Wang Qi-Wen (2014),, Beyond Parrondo’sParadox., Sci. Rep., 4, 4244; DOI:10.1038/srep04244.
  5. Parrondo J.M.R., Harmer George P. and Abbott D.(2000), New Paradoxical Games Based on BrownianRatchets., Phys. Rev. Lett., 85, 5226.
  6. Harmer G.P. and D. Abbott (1999),, Game Theory –Losing strategies can win by Parrondo’s paradox., Nature(London) 402, 846.
  7. Astumian R.D., Hanggi P. and Brownian Motors (2002).Phys. Today, Nov., 33-39.