A resource theory of gambling

• URL: http://arxiv.org/abs/2510.08418v1
• Date: Thu, 09 Oct 2025 16:37:27 GMT
• Title: A resource theory of gambling
• Authors: Maite Arcos, Renato Renner, Jonathan Oppenheim,
• Abstract summary: We recast the Kelly criterion for betting as a resource theory of adversarial information.<n>We compute the optimal strategy which maximises the probability of successfully reaching the target.<n>We generalize this framework to a distributed side-information game.
• Score: 0.509780930114934
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Betting games provide a natural setting to capture how information yields strategic advantage. The Kelly criterion for betting, long a cornerstone of portfolio theory and information theory, admits an interpretation in the limit of infinitely many repeated bets. We extend Kelly's seminal result into the single-shot and finite-betting regimes, recasting it as a resource theory of adversarial information. This allows one to quantify what it means for the gambler to have more information than the odds-maker. Given a target rate of return, after a finite number of bets, we compute the optimal strategy which maximises the probability of successfully reaching the target, revealing a risk-reward trade-off characterised by a hierarchy of R\'enyi divergences between the true distribution and the odds. The optimal strategies in the one-shot regime coincide with strategies maximizing expected utility, and minimising hypothesis testing errors, thereby bridging economic and information-theoretic viewpoints. We then generalize this framework to a distributed side-information game, in which multiple players observe correlated signals about an unknown state. Recasting gambling as an adversarial resource theory provides a unifying lens that connects economic and information-theoretic perspectives, and allows for generalisation to the quantum domain, where quantum side-information and entanglement play analogous roles.

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