The Economics of Uncertainty: Prospect Theory in Practice at the Poker Table

Abstract

This study explores the relationship between wealth, represented by stack depth, and risk, represented by voluntary and aggressive betting behaviors, among players in poker games. By examining poker—a game that mirrors real-world decision-making with its incomplete information and uncertainty—this study sheds light on how an individual’s resources, like chip stack size, shape their risk tolerance and propensity toward risk-seeking or risk-averse behavior in high-stakes environments. In this study, I use over 4.9 million observations of hand data from online No-Limit Texas Hold’em games across 65,000 unique players to run several fixed effects regressions that assess this relationship. The results reveal several key insights: (1) there is a significant positive and nonlinear relationship between stack depth and the amount that a player voluntarily wagers; (2) players psychologically set reference points for themselves at 100 BBs where they exhibit “kinked” nonlinear behavioral shifts; (3) players exhibit loss aversion, with players who are down money being significantly more risk-seeking as their stack grows than players who have already earned a profit; (4) players with larger stacks experience diminishing sensitivity, as they demonstrate weaker behavioral responses to additional gains, while those with smaller stacks respond more acutely to small changes in wealth; and (5) additional wealth is associated with a lower proportional betting, implying risk-aversion over accumulated resources. These findings are consistent with Prospect Theory and provide implications for behavioral modeling in finance, gaming, and consumer decision-making.