by gamblers.

Meanwhile, the high positive auto-correlations, along with the higher probability densities at small integers/half-integers and their inverses, provide evidence that gamblers often follow a multiplicative process when wagering. The multiplication process can be explained by the wide adoption of multiplicative betting systems. “Betting system” here refers to the strategy of wagering where the next bet value depends on both the previous bet value and the previous outcome [@Dubins2014; @Epstein2012]. Although betting systems will not provide a long-term benefit, as the expected payoff will always be $0$ in a fair game, still they are widely adopted among gamblers. A well-known multiplicative betting system is the Martingale (sometimes called geometric progression) [@Epstein2012]. In Martingale betting, starting with an initial wager, the gambler will double their wager each time they lose one round, and return to the initial wager once they win. Martingale is a negative-progression betting system where the gambler will increase their wager when they lose and/or decrease their wager when they win.

Apart from multiplicative betting, there are many other types of betting systems, such as additive betting and linear betting [@Epstein2012]. The reasons why multiplicative betting systems are dominant in our datasets are: 1) Martingale is a 