Parrondo's games as a discrete ratchet

Abstract

We write the master equation describing the Parrondo's games as a consistent discretization of the Fokker--Planck equation for an overdamped Brownian particle describing a ratchet. Our expressions, besides giving further insight on the relation between ratchets and Parrondo's games, allow us to precisely relate the games probabilities and the ratchet potential such that periodic potentials correspond to fair games and winning games produce a tilted potential.

4 pages, 3 figures

References in corpus (4)

• Brownian motors: noisy transport far from equilibrium
• New paradoxical games based on Brownian ratchets
• Quantum Parrondo's Games
• Stationary and Oscillatory Spatial Patterns Induced by Global Periodic Switching

Cited by in corpus (10)

• Brownian motion and gambling: from ratchets to paradoxical games
• Discrete--time ratchets, the Fokker--Planck equation and Parrondo's paradox
• Extended Parrondo's Game and Brownian Ratchets: Strong and Weak Parrondo Effect
• Quantum Parrondo's game with random strategies
• Reversals of chance in paradoxical games
• Winning in Sequential Parrondo Games by Players with Short-Term Memory
• The flashing Brownian ratchet and Parrondo's paradox
• Multi player Parrondo games with rigid coupling
• The tilted flashing Brownian ratchet
• A new generalization of Parrondo's games to three players and its application in genetic switches