Preprint No. A-02-09

Ehrhard Behrends

Parrondo's paradox: a priori and adaptive strategies

Abstract: Several hundred pages in the WWW and a number of articles in (mostly) popular journals deal with Parrondo's paradox: it states that there are losing gambling games which, when being combined stochastically or in a suitable deterministic way, give rise to winning games.
Here we investigate the probabilistic background, methods from graph theory, (elementary) functional analysis and stochastic control theory come into play.
We show how the properties of the equilibrium distributions of the Markov chains under consideration give rise to the paradoxical behaviour, and we provide methods how to find the best a priori and adaptive strategies.

Keywords: Parrondo, paradox, Markov chain, stochastic control theory

Mathematics Subject Classification (MSC2000): 60J10, 60J20

Language: ENG

Available: Pr-A-02-09.ps

Contact: Ehrhard Behrends, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (behrends@math.fu-berlin.de)

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