Jarzynski-type equalities in gambling: role of information in capital growth

TL;DR

This paper derives Jarzynski-like equalities for gambling scenarios, quantifying how information and memory influence capital growth, and reproduces known bounds on growth rates.

Contribution

It introduces new equalities analogous to Jarzynski's in gambling, linking information effects to capital growth statistics.

Findings

Equalities relate information to capital growth in gambling.

Reproduces known upper bounds on average capital growth.

Provides new measures for information's impact on gambling outcomes.

Abstract

We study the capital growth in gambling with (and without) side information and memory effects. We derive several equalities for gambling, which are of similar form to the Jarzynski equality and its extension to systems with feedback controls. Those relations provide us with new measures to quantify the effects of information on the statistics of capital growth in gambling. We discuss the implications of the equalities and show that they reproduce the known upper bounds of average capital growth rates.