Why Parrondo's Paradox Is Irrelevant for Utility Theory, Stock Buying, and the Emergence of LifeCoauthor(s): Raghuram Iyengar.
Since the initial publication of Parrondo's paradox [1, 2], a number of articles on the subject have appeared both in the academic literature and in the media. The paradox describes a reversal of fortune for a gambler who loses money by playing either of two games of chance, but who makes money by randomly playing the two games. The academic literature suggests that Parrondo's paradox advances von Neumann and Morgenstern's work on utility theory, that it offers money for free, that it has implications for investing strategies, and that it may hold the key for understanding certain biological processes, possibly even the emergence of life [3, 4]. Harmer and Abbott  suggest that the paradox might operate in economics or social dynamics to extract benefits from ostensibly detrimental situations. For example, if a society or an ecosystem suffers from declines in either the birth rate or the death rate, declines in both together might combine with favorable consequences. Parrondo's paradox appears to be a remarkable finding with far-reaching consequences in wide ranging situations.
Or is it? That's the question we ask and hope to answer. To do so, we need to look more closely at the rationale behind Parrondo's paradox, stripping it of all extraneous baggage and descriptive analogies as ratchets and pawls. We need to understand the structures of the associated games of chance and uncover what exactly drives the reversal of fortune in Parrondo's games. We will then be in a better position to assess if one or another phenomenon can be explained by it and what opportunities it offers to investors and gamblers, biologists and economists.
Iyengar, Raghuram, and Rajeev Kohli. "Why Parrondo's Paradox Is Irrelevant for Utility Theory, Stock Buying, and the Emergence of Life." Complexity 9, no. 1 (2003): 23-27.