# Gambling and R\'enyi Divergence

## TL;DR

This paper introduces a new family of utility functions for horse gambling, connecting optimal betting strategies to Re9nyi divergence, and extends the analysis to scenarios with side information, leading to a novel conditional divergence.

## Contribution

It proposes a one-parameter utility family encompassing Kelly and expected-return criteria, linking them to Re9nyi divergence, and introduces a new conditional divergence for informed betting strategies.

## Key findings

- Derived strategies that maximize the new utility functions.
- Established the connection between optimal strategies and Re9nyi divergence.
- Introduced a novel conditional Re9nyi divergence for side information scenarios.

## Abstract

For gambling on horses, a one-parameter family of utility functions is proposed, which contains Kelly's logarithmic criterion and the expected-return criterion as special cases. The strategies that maximize the utility function are derived, and the connection to the R\'enyi divergence is shown. Optimal strategies are also derived when the gambler has some side information; this setting leads to a novel conditional R\'enyi divergence.