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Analytical Expressions for Parrondo Games

2002/10/23 by Lars Rasmusson, Rasmusson, Lars, Magnus Boman +1
Decision Sciences · Economics, Econometrics and Finance · Physics and Astronomy · #Classical Physics (physics.class-ph) #Complex Systems and Time Series Analysis #FOS: Physical sciences #General Physics (physics.gen-ph) #Stock Market Forecasting Methods #physics.class-ph #physics.gen-ph

paper · pdf · doi:10.48550/arxiv.physics/0210094

6 pages Changed title, abstract, refs + corrected typos and one algebraic mistake (optimal value approximation)

openalex publication_date 2002/10/23 · arxiv created 2002/12/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present some new analytical expressions for the so-called Parrondo effect, where simple coin-flipping games with negative expected value are combined into a winning game. Parrondo games are state-dependent. By identifying the game state variable, we can compute the stationary game state probabilities. Mixing losing games increases the probability of entering into a game state with positive value, as can be seen clearly from our analytical expressions for the Parrondo game value.

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