# Can Two Wrongs Make a Right? Coin-Tossing Games and Parrondo’s Paradox

```@article{Percus2002CanTW,
title={Can Two Wrongs Make a Right? Coin-Tossing Games and Parrondo’s Paradox},
author={Ora E. Percus and Jerome K. Percus},
journal={The Mathematical Intelligencer},
year={2002},
volume={24},
pages={68-72}
}```
• Published 2002
• Mathematics
• The Mathematical Intelligencer
Background On frequent occasions, a logical oddity comes along, which attracts a sizeable audience. One of the most recent is known as Parrondo's paradox [5, 6]. Briefly, it is the observation that random selection (or merely alternation) of the playing of two asymptotically losing games* can result in a winning game. Conceptually similar situations involving only the processing of statistical data are not novel. What has been referred to as Simpson's paradox [8] is typified by this scenario…
16 Citations
Parrondo’s Principle
Parrondo's Paradox states that two games, each with a negative expectation, can be combined via deterministic or nondeterministic mixing of the games to produce a positive expectation. For Parrondo's
Randomly chosen chaotic maps can give rise to nearly ordered behavior
• Mathematics
• 2005
Abstract Parrondo’s paradox [J.M.R. Parrondo, G.P. Harmer, D. Abbott, New paradoxical games based on Brownian ratchets, Phys. Rev. Lett. 85 (2000), 5226–5229] (see also [O.E. Percus, J.K. Percus, Can
How strong can the Parrondo effect be?
• Mathematics, Computer Science
Journal of Applied Probability
• 2019
It is shown that if the parameters of the games are allowed to be arbitrary, subject to a fairness constraint, and if the two games A and B are played in an arbitrary periodic sequence, then the rate of profit can not only be positive, but can also be arbitrarily close to 1 (i.e. 100%).
• Mathematics
• 2009
That there exist two losing games that can be combined, either by random mixture or by nonrandom alternation, to form a winning game is known as Parrondo's paradox. We establish a strong law of large
• Mathematics
• 2003
Since coming to the attention of the general news media several years ago, the paradoxical combination of two losing games into a winning game by J. M. R. Parrondo has been the subject of numerous
Chaos Control and Anticontrol of Complex Systems via Parrondo’s Game
In this chapter, we prove analytically and numerically aided by computer simulations, that the Parrondo game can be implemented numerically to control and anticontrol chaos of a large class of
Discrete–time ratchets, the Fokker–Planck equation and Parrondo's paradox
• Mathematics, Physics
Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
• 2004
Parrond's games manifest the apparent paradox where losing strategies can be combined to win and have generated significant multidisciplinary interest in the literature. Here we review two recent
Parrondian Games in Discrete Dynamic Systems
• Computer Science
Fractal Analysis
• 2019
The method described in this chapter is based on the Parrondo’s paradox, where two losing games can be alternated, yielding a winning game, and can be used as a stabilization method to control chaotic dynamics.
Can two chaotic systems give rise to order
• Mathematics, Physics
• 2005
Abstract The recently discovered Parrondo's paradox claims that two losing games can result, under random or periodic alternation of their dynamics, in a winning game: “losing + losing = winning”. In
Paradoxical games and a minimal model for a Brownian motor
I give an extended analysis of the very simple game that I previously published that shows the paradoxical behavior whereby two losing games randomly combine to form a winning game. The game, modeled

## References

SHOWING 1-10 OF 10 REFERENCES
• Mathematics
• 1999
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 « .
Game theory: Losing strategies can win by Parrondo's paradox
• Computer Science
Nature
• 1999
This work models the behaviour of two losing gambling games such that, when they are played one after the other, they becoming winning, a striking new result in game theory called Parrondo's paradox.
• Mathematics
Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
• 2000
We introduce Parrondo's paradox that involves games of chance. We consider two fair games, A and B, both of which can be made to lose by changing a biasing parameter. An apparently paradoxical
Decisions and elections
It is not uncommon to be frustrated by the outcome of an election or a decision in voting, law, economics, engineering, and other fields. Does this 'bad' result reflect poor data or poorly informed
New paradoxical games based on brownian ratchets
• Economics, Physics
Physical review letters
• 2000
New games where all the rules depend only on the history of the game and not on the capital are presented, which significantly increases the parameter space for which the effect operates.
Decisions and elections : explaining the unexpected
1. Do we get what we expect 2. Arrow's theorem 3. Explanations and examples 4. What else can go wrong? 5. More perversities 6. A search for resolutions 7. From Sen to prisoners and prostitution 8.
Randomly rattled ratchets
SummaryRatchets are anisotropic periodic potentials. Particles subject to ratchet forces and simultaneously to thermal and nonthermal fluctuations can rectify the nonequilibrium noise, thereby