of gambler wealth distribution in different scenarios.

![ \[fig:wealth\] The tail of the wealth distribution of Bitcoin gamblers follows a pairwise power-law distribution. ](figure4.pdf){width=".5\columnwidth"}

Removing effects due to inequality in the number of bets {#removing-effects-due-to-inequality-in-the-number-of-bets .unnumbered}
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In the above sections, we have analyzed the distributions of several quantities at the population level. However, there is a huge inequality of the number of placed bets among gamblers. We therefore wonder whether those distributions we obtain result from the inequality of number of bets among individuals. To remove the effects of this inequality, we randomly sample in each dataset the same number of bets from heavy gamblers. We re-analyze the wager distribution and odds distribution with the sample data to see if we obtain the same distribution as before. In each dataset we randomly sample $500$ bets from each of those gamblers who placed at least $500$ bets above $b_\text{min}$ given in Table \[table:wager-distribution\]. Some datasets are excluded here as either they do not have enough data or we cannot identify individual gamblers. When re-analyzing the odds distribution, to ensure we have enough data, we respectively sample $100$ and $2000$ bets from each of those gamblers in games (C) and (F) 