Brownian motion and gambling: from ratchets to paradoxical games

TL;DR

This paper reviews the paradox where alternating losing gambling games can become winning, inspired by physical Brownian ratchets, and explores recent collective game studies with intuitive explanations.

Contribution

It provides a comprehensive review connecting Brownian ratchets to collective gambling games, offering insights into the paradoxical phenomena involved.

Findings

Alternating losing games can produce winning outcomes.

Brownian ratchets can rectify fluctuations to generate directed motion.

Recent studies extend the paradox to collective game scenarios.

Abstract

Two losing gambling games, when alternated in a periodic or random fashion, can produce a winning game. This paradox has been inspired by certain physical systems capable of rectifying fluctuations: the so-called Brownian ratchets. In this paper we review this paradox, from Brownian ratchets to the most recent studies on collective games, providing some intuitive explanations of the unexpected phenomena that we will find along the way.