# 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} }

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

- Mathematics
- 2009

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 ScienceJournal 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%).

Limit theorems for Parrondo's paradox

- 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…

Parrondo's paradox

- 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

- Mathematics
- 2016

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, PhysicsProceedings 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 ScienceFractal 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

- Physics
- 2005

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…

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