Parrondo's Paradox is Not Paradoxical

3 Pages Posted: 25 Aug 2004 Last revised: 4 Feb 2008

Thomas K. Philips

NYU Tandon School of Engineering - Department of Finance and Risk Engineering

Andrew B. Feldman

OppenheimerFunds, Inc.

Date Written: August 2004

Abstract

Parrondo's paradox concerns two games that are played in an alternating sequence. An analysis of each game in isolation shows them both to be losing games (i.e., to have a negative expectation). However, when the two games are played in an alternating sequence, the resulting compound game is, paradoxically, a winning game with a positive expectation.

This paradox has aroused a great deal of interest in recent years, and a number of sophisticated resolutions of it have been published. It is the purpose of this article to show that the paradox is not paradoxical at all, and is easily resolved using elementary probability.

Keywords: Parrondo, paradox, resolution, probability

JEL Classification: A19, A20, Z00

Suggested Citation

Philips, Thomas K. and Feldman, Andrew B., Parrondo's Paradox is Not Paradoxical (August 2004). Available at SSRN: https://ssrn.com/abstract=581521 or http://dx.doi.org/10.2139/ssrn.581521

Thomas K. Philips (Contact Author)

NYU Tandon School of Engineering - Department of Finance and Risk Engineering ( email )

Brooklyn, NY 11201
United States

Andrew B. Feldman

OppenheimerFunds, Inc. ( email )

2 World Financial Center
New York, NY 10085
United States

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