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Parrondo's effects with aperiodic protocols.

Marcelo A Pires1, Erveton P Pinto2, Rone N da Silva3

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This summary is machine-generated.

The Thue-Morse sequence effectively creates a Parrondo

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Area of Science:

  • Complex systems
  • Chaos theory
  • Information theory

Background:

  • Parrondo's paradox demonstrates how combining losing games can yield a winning strategy.
  • Aperiodic sequences offer complex patterns for potential paradox exploitation.

Purpose of the Study:

  • To investigate the effectiveness of archetypal aperiodic sequences (Fibonacci, Thue-Morse, Rudin-Shapiro) in generating Parrondo's paradox.
  • To analyze the impact of sequence properties on capital gain and paradox manifestation.

Main Methods:

  • Employing Fibonacci, Thue-Morse, and Rudin-Shapiro sequences in switching protocols.
  • Analyzing capital gain, cross-correlation with losing games, lacunarity, and persistence.

Main Results:

  • Thue-Morse sequence yielded the most effective Parrondo's paradox, outperforming other aperiodic and benchmark strategies.
  • Strong anti-correlation with isolated losing games is crucial for robust paradox manifestation.
  • Optimal performance requires balancing sequence persistence and heterogeneity (lacunarity).

Conclusions:

  • Aperiodic sequences, particularly Thue-Morse, can successfully induce Parrondo's paradox.
  • Sequence properties like persistence and lacunarity critically influence strategy performance.
  • Fine-tuning sequence characteristics is key to optimizing Parrondo-based strategies.