in games (A-G). This is very clear when comparing the wager distributions of games (G) and (H) as both games are jackpot games of skin gambling, and the only difference is whether players are directly using skins as wagers or are using virtual skin tickets obtained from depositing skins. The power-law tail, which was not observed in the previous study [@Wang2018], might result from the increment of the maximum allowed skin price (from \$$400$ to \$$1 800$).

The above discussions, including the results for games (A-G) in Table \[table:wager-distribution\], show that the wager distributions in pure probability-based gambling games, no matter whether the game follows parimutuel betting or fixed-odds (preset/player-selected) betting, stay log-normal as long as the players are allowed to place arbitrary amounts of wagers. This commonality of log-normal distribution no longer holds when this arbitrariness of wager value is violated, e.g., in the scenario where the player can only wager items (in-game skins).

Log-normal distribution has been reported in a wide range of economic, biological, and sociological systems [@LIMPERT2001], including income, species abundance, family size, etc. Economists have proposed different kinds of generative mechanisms for log-normal distributions (and power-law distributions as well). One particular interest for us is 