# A resource theory of gambling

arXiv: https://arxiv.org/abs/2510.08418 · HTML: https://mlsanity.com/paper/2510.08418/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Oct 2025.

## Built on by (most cited first, 1 of 1)

- [All you need is log](https://mlsanity.com/paper/2606.27349/) (2026)

## Abstract (arXiv)

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.