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

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.

20 pages, 12 figures

References in corpus (4)

• Power-law distributions in empirical data
• Parameter estimation for power-law distributions by maximum likelihood methods
• Crossover between Levy and Gaussian regimes in first passage processes
• Multiple-interaction kinetic modelling of a virtual-item gambling economy