games that follow very simple rules, which makes analyzing the gambling behavior much easier as there are much fewer degrees of freedom required to be considered. On the other hand, many online casinos have made gambling logs publicly available on their websites, mainly for verification purposes, which provides researchers with abundant data to work on. Due to the high popularity of online gambling, in a dataset provided by an online casino there are often thousands or even hundreds of thousands of gamblers listed. Such a large scale of data can hardly be obtained in a lab environment. Prior research has begun to make use of online gambling logs. For example, Meng’s thesis [@Meng2018] presented a pattern analysis of typical gamblers in Bitcoin gambling. It is worth arguing that although our work only focuses on the behaviors of online gamblers, there is no reason to think that our conclusions cannot be extended to traditional gamblers.

Naturally, we can treat the changing cumulative net income of a player during their gambling activities as a random walk process [@Wang2018]. We are particularly interested in the diffusive characteristics of the gambler’s net income. This is another reason why we want to analyze the wager 