The Game You Win By Losing (Parrondo's Paradox)

While working on the interplay between thermodynamics and information theory, physicist Juan Parrondo realized that a system of losing games could actually produce a winning result. And it isn’t just by playing them in a highly-strategic way; it’s even possible for two guaranteed losers to generate a winner when played randomly.

At the heart of that counterintuitive conclusion is a test of our understanding of probability and relationships between events. From the simplest money-based games and coin flip scenarios to theoretical perpetual motion machines like the Brownian ratchet and flashing Brownian ratchet, Parrondo’s Paradox explores elements of game theory that are inspiring research in fields like biogenetics, finance, and evolutionary biology.

*** SOURCES ***

Finite Math -- Markov Chains
https://www.youtube.com/watch?v=tYaW-1kzTZI
https://www.youtube.com/watch?v=afIhgiHVnj0

Derek Abbot, Peter Taylor, and Juan Parrando, “Parrondo's Paradoxical Games and the Discrete Brownian Ratchet”
https://www.academia.edu/269127/Parrondos_Paradoxical_Games_and_the_Discrete_Brownian_Ratchet

Stan Wagon’s Parrondo Paradox Demonstration
http://demonstrations.wolfram.com/TheParrondoParadox/

Abhijit Kar Gupta and Sourabh Banerjee, “Parrondo’s Paradox: New Results and New Ideas”
https://arxiv.org/ftp/arxiv/papers/1602/1602.04783.pdf

New York Times, “Paradox In Game Theory: Losing Strategy That Wins”
https://www.nytimes.com/2000/01/25/science/paradox-in-game-theory-losing-strategy-that-wins.html

S. N. Ethier and Jiyeon Lee, “The flashing Brownian ratchet and Parrondo’s paradox”
https://royalsocietypublishing.org/doi/full/10.1098/rsos.171685

Andrew Gelman and Deborah Nolan, “You can load a die but you can’t bias a coin”
https://www.stat.berkeley.edu/~nolan/Papers/dice.pdf

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