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Parrondo's Paradox is Not Paradoxical


Thomas K. Philips


Malbec Partners; OTA Asset Management

Andrew B. Feldman


OppenheimerFunds, Inc.
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.

Number of Pages in PDF File: 3

Keywords: Parrondo, paradox, resolution, probability

JEL Classification: A19, A20, Z00

working papers series


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Date posted: August 25, 2004 ; Last revised: February 4, 2008

Suggested Citation

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

Contact Information

Thomas K. Philips (Contact Author)
Malbec Partners ( email )
200 Park Avenue, 46th Floor
New York, NY 10166
United States
(212) 271-4013 (Phone)
OTA Asset Management ( email )
1 Manhattanville Road
Purchase, NY 10577
United States
(914) 460-4059 (Phone)
(914) 694-5831 (Fax)
Andrew B. Feldman
OppenheimerFunds, Inc. ( email )
2 World Financial Center
New York, NY 10085
United States
Feedback to SSRN (Beta)


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