the Methods section.

On the other hand, as we have pointed out in the previous study [@Wang2018], when players are restricted to use in-game skins as wagers for gambling, the wager distribution can be best fitted by a shifted power law with exponential cutoff. Now, with a similar situation in game (H), where wagers can only be in-game skins, we find that the early part of the curve can be again fitted by a power law with exponential cutoff, as shown in Fig. \[fig:wager\_distribution\](H). However, this time it does not maintain the exponential decay of its tail; instead, it changes back to a power-law decay. The overall distribution contains six parameters, given by the expression

$$\label{eq:powerlaw_exp_powerlaw}
\displaystyle P(x) = \left\lbrace \begin{split}
\displaystyle
&\frac{1}{c_1+c_2 c_3}\ 
\frac{(x-\delta)^{-\alpha}}{1+e^{\lambda(x-\beta)}},\ 
&\text{for}\ x \le x_\text{trans}, \\
\displaystyle
&\frac{c_3}{c_1+c_2 c_3}\ x^{-\eta}, \ 
&\text{for}\ x > x_\text{trans},
\end{split}\right.$$

where $\displaystyle c_1=\sum\limits_{x=x_\text{min}}^{x_\text{trans}}
\frac{(x-\delta)^{-\alpha}}{1+e^{\lambda(x-\beta)}}$, $\displaystyle c_2=\zeta\left(\eta, x_\text{trans}\right)$, and $\displaystyle c_3=x_\text{trans}^\eta
\frac{\left(x_\text{trans}-\delta\right)^{-\alpha}}
{1+e^{\lambda\left(x_\text{trans}-\beta\right)}}$.

We believe that when players are restricted to use in-game skins as wagers, the decision to include one particular skin in their wager is further influenced by the price and availability of that skin. These factors make the wager distribution deviate from the log-normal distribution, which is observed 