---
author:
- Xiangwen Wang
- Michel Pleimling
title: 'Online Gambling of Pure Chance: Wager Distribution, Risk Attitude, and Anomalous Diffusion'
---

Introduction {#introduction .unnumbered}
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Today, gambling is a huge industry with a huge social impact. According to a report by the American Gaming Association [@AGA2018], commercial casinos in the United States alone made total revenue of over 40 billion US dollars in 2017. On the other hand, different studies reported that $0.12\%-5.8\%$ of the adults and $0.2\%-12.3\%$ of the adolescents across different countries in the world are experiencing problematic gambling [@Calado2016; @Calado2017]. Studying the gamblers’ behavior patterns not only contributes to the prevention of problematic gambling and adolescent gambling, but also helps to better understand human decision-making processes. Researchers have put a lot of attention on studying gambling-related activities. Economists have proposed many theories about how humans make decisions under different risk conditions. Several of them can also be applied to model gambling behaviors. For example, the prospect theory introduced by Kahneman and Tversky [@Kahneman1979] and its variant cumulative prospect theory [@Tversky1992] have been adopted in modeling casino gambling [@Barberis2012]. In parallel to the theoretical approach, numerous studies focus on the empirical analysis of gambling behaviors, aiming at 