Two losing gambling games can be set up so that when they are played one after the other, they become winning. There are many ways to construct such scenarios, the simplest of which uses three biased coins (Harmer and Abbott 1999).
Parrondo's Paradox
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References
Doering, C. R. "Randomly Rattled Ratchets." Il Nuovo Cimento 17D, 685-697, 1995.Harmer, G. P. and Abbott, D. "Losing Strategies Can Win by Parrondo's Paradox." Nature 402, 864, 1999.Harmer, G. P.; Abbott, D.; Taylor, P. G.; and Parrondo, J. M. R. "Parrondo's Paradoxical Games and the Discrete Brownian Ratchet." In Proc. 2nd Internat. Conf. Unsolved Problems of Noise and Fluctuations, 11-15 July, Adelaide (Ed. D. Abbott and L. B. Kiss). Melville, NY: Amer. Inst. Physics Press, pp. 189-200, 2000.Harmer, G. P.; Abbott, D.; Taylor, P. G.; Pearce, C. E. M.; and Parrondo, J. M. R. "Information Entropy and Parrondo's Discrete-Time Ratchet." In Proc. Stochastic and Chaotic Dynamics in the Lakes, 16-20 August, Ambleside, UK (Ed. P. V. E. McClintock). Melville, NY: Amer. Inst. Physics Press, pp. 544-549, 2000.McClintock, P. V. E. "Unsolved Problems of Noise." Nature 401, 23-25, 1999.Pearce, C. E. M. "Entropy, Markov Information Sources and Parrondo Games." In Proc. 2nd Internat. Conf. Unsolved Problems of Noise and Fluctuations, 11-15 July, Adelaide (Ed. D. Abbott and L. B. Kiss). Melville, NY: Amer. Inst. Physics Press, pp. 207-212, 2000.Pearce, C. E. M. "On Parrondo's Paradoxical Games." In Proc. 2nd Internat. Conf. Unsolved Problems of Noise and Fluctuations, 11-15 July, Adelaide (Ed. D. Abbott and L. B. Kiss). Melville, NY: Amer. Inst. Physics Press, pp. 201-206, 2000.Referenced on Wolfram|Alpha
Parrondo's ParadoxCite this as:
Weisstein, Eric W. "Parrondo's Paradox." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ParrondosParadox.html