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

ANZIAM J. 47 (2006), 495-511

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

E. S. Key
Department of Mathematical Sciences
University of Wisconsin Milwaukee
Milwaukee WI 53201
USA
ericskey@uwm.edu

M. M. Klosek
Department of Mathematical Sciences
University of Wisconsin Milwaukee
Milwaukee WI 53201
USA.
Currently at the Center of Scientific Review
National Institutes of Health.

and

D. Abbott
Centre for Biomedical Engineering (CBME)
Department of Electrical & Electronic Engineering
University of Adelaide
Adelaide SA 5005
Australia
dabbott@eleceng.adelaide.edu.au

Abstract

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.

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