The distribution of the logarithmic of the ratio (log-ratio) between consecutive bet values. For games ( A – C ), the log-ratio can be described by a Laplace distribution. For games ( D , F – H ), the log-ratio presents bell-shaped distribution. In general, the distributions are symmetric with respect to the y-axis, except in games ( D , F ). The x -coordinate \( _( _/ _ )\) is proportional to the parameter ν . 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 22,23 . 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) 23 . 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 23 . The reasons why multiplicative betting systems are dominant in our datasets are: 1) Martingale is a well-known betting system among gamblers; 2) Many online gambling websites provide a service for changing the bet value in a multiplicative way. For example, for the Crash games csgofast-Crash (C) and ethCrash (D), both websites provide a simple program for automatically wagering in a multiplicative way. For the Roulette games and Coinroll (F), the websites provide an interface with which the gambler can quickly double or half their wager. However, for Satoshi Dice (E) and csgospeed-Jackpot (G), no such function is provided, yet we still observe similar results, indicating that gamblers will follow a multiplicative betting themselves. Figure 2 provides us with the distribution of ν , however, it will not tell us whether the gamblers adopt the negative/positive-progression betting systems Therefore we further analyze the effect on the bet values of winning/losing a round. How the gamblers adjust their wager after winning/losing rounds is shown in Table 3. 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