f_m)\eta \Big)b\equiv -\xi b,$$ which is always negative since either $\eta$ or $f_\text{m}$ are non-zero. In gambling terminology, $\xi$ is called the house edge, from which the websites make profits. The house edge represents the proportion the website will benefit on average when players wager. In the four types of games we discuss, the house edge $\xi$ ranges from $1\%$ to $8\%$. If there is no house edge $\xi=0$, that means it is a fair game. In a fair game or when we ignore the house edge, the expected payoff would be 0. In the Results section, we begin with an analysis of wager distribution and log-ratios between successive wagers, which helps us to understand the gamblers’ wagering strategy. We then focus on an analysis of risk attitude by studying the distribution of the odds players choose to wager with. We conclude by extending our discussion to the analysis of net incomes of gamblers viewed as random walks. This allows us to gain insights into the gamblers’ behaviors by computing quantities like the ensemble/time-averaged mean-squared displacement, the first-passage time distribution, ergodicity breaking parameter, and Gaussianity. Detailed information about the games and datasets discussed in this paper can be found in 