Online Gambling of Pure Chance: Wager Distribution, Risk Attitude, and Anomalous Diffusion

TL;DR

This paper analyzes online probability-based gambling logs, revealing wager distributions follow a log-normal pattern and identifying anomalous diffusion behaviors in gamblers' net incomes, which vary across different games.

Contribution

It introduces a comprehensive analysis of wager distributions and diffusive behaviors in online gambling, highlighting the presence of anomalous diffusion in net incomes.

Findings

Wager distributions follow a log-normal distribution.

Different gambling games exhibit distinct diffusive behaviors.

Evidence of anomalous diffusion in gamblers' net incomes.

Abstract

Online gambling sites offer many different gambling games. In this work we analyse the gambling logs of numerous solely probability-based gambling games and extract the wager and odds distributions. We find that the log-normal distribution describes the wager distribution at the aggregate level. Viewing the gamblers' net incomes as random walks, we study the mean-squared displacement of net income and related quantities and find different diffusive behaviors for different games. We discuss possible origins for the observed anomalous diffusion.