From House Money to Core Funds: Modeling Risk Attitudes in Consecutive Poker Hands

This paper develops a two-period behavioral model of poker bettingthat integrates mental accounting and prospect-theoretic reference depen-dence to explain how early wins or losses shape later risk-taking. In thefirst period a player bets a portion of her initial wealth, obtaining either again (win) or a loss. We then treat any first-period gain as “house money”(a separate mental account) and the remainder of original wealth as corefunds. If the player lost, the reduced bankroll becomes the new core andno house money is available. In period two the player chooses a secondbet on the basis of these mental accounts. Our formal analysis showsthat if the player won initially, the presence of house money reduces effec-tive loss sensitivity and leads to a larger second-period bet (capturing thehouse-money effect). If the player lost initially, the shrinkage of core fundsand loss aversion leads to a smaller bet (consistent with risk-averse be-havior in the gain domain and potential loss-chasing behavior to recouplosses). We incorporate reference-dependent value [K˝oszegi and Rabin,2006] and prospect-theoretic preferences [Kahneman and Tversky, 1979]to characterize the break-even effect (risk-seeking after losses) alongsidethe house-money effect. Our model is motivated by experimental find-ings: experienced poker players tend to gamble more aggressively whenbehind (“break-even effect”) and more conservatively when ahead. Wealso consider tilting – emotionally-driven reckless play after losses – asan amplifying mechanism. The implications for understanding gamblingbehavior are discussed, as are limitations of the two-stage abstraction.