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On Parrondo's paradox: how to construct unfair games by composing fair games

Published online by Cambridge University Press:  17 February 2009

E. S. Key ,
M. M. Kłosek  and
D. Abbott
E. S. Key
Affiliation:
Department of Mathematical Sciences, University of Wisconsin Milwaukee, Milwaukee WI 53201, USA; e-mail: ericskey@uwm.edu.
M. M. Kłosek
Affiliation:
Department of Mathematical Sciences, University of Wisconsin Milwaukee, Milwaukee WI 53201, USA. Currently at the Center of Scientific Review, National Institutes of Health This article was written in a personal capacity and does not necessarily represent the opinions or reflect the views of the National Institutes of Health, the Department of Health and Human Services, or the Federal Government.
D. Abbott
Affiliation:
Centre for Biomedical Engineering (CBME), Department of Electrical & Electronic Engineering, University of Adelaide, Adelaide SA 5005Australia; e-mail: dabbott@eleceng.adelaide.edu.au.
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Abstract

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We construct games of chance from simpler games of chance. We show that it may happen that the simpler games of chance are fair or unfavourable to a player and yet the new combined game is favourable—this is a counter-intuitive phenomenon known as Parrondo's paradox. We observe that all of the games in question are random walks in periodic environments (RWPE) when viewed on the proper time scale. Consequently, we use RWPE techniques to derive conditions under which Parrondo's paradox occurs.

Keywords

random walk in a periodic environmentrandom transportrandom gamesParrondo's paradox.
Type
Research Article
Information
The ANZIAM Journal , Volume 47 , Issue 4 , April 2006 , pp. 495 - 511
Copyright
Copyright © Australian Mathematical Society 2006

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