Parrondo's effects with aperiodic protocols

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.