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If we want to check whether gamblers follow multiplicative processes when they wager, we can first check the correlation between consecutive bets \((_,_)\) Due to the large variances of the wager distributions, Pearson’s correlation coefficient may perform poorly. Instead, we adopt two rank-based correlation coefficients, Kendall’s Tau 20 \(_\) and Spearman’s Rho 21 \(_\) . At the same time, we also check the mean and variance of the log-ratios \(\mathrm(_/_)\) between consecutive bets. These statistics can be found in Table 2. The results reveal that the values of consecutive bets exhibit a strong positive correlation, with all the correlation coefficients larger than 0.5. It shows that players’ next bet values are largely dependent on their previous bet values. At the same time, the bet values are following gradual changes, rather than rapid changes. These conclusions can be confirmed by the small mean values and small variances of log-ratios between consecutive bets., russian poker तीन पत्ती रियल मनी. Table 2 Correlation analysis shows that there is a strong positive correlation between consecutive bets, along with the small mean values and variances of log-ratio between consecutive bets. Further analysis of the distribution of ν shows an exponential decay on both of its tails, see Fig. 2. This means that ν approximately follows a Laplace distribution. However, compared to a Laplace distribution, the empirical log-ratio distribution shows a much higher probability at ν = 0, whose value can be found in the last column of Table 2. We also observe that ν presents higher probability densities around small integers/half-integers and their inverses. Due to the existence of these differences, we will skip the parameter fitting for the distribution of ν . The high probability of staying on the same wager indicates that betting with fixed wager is one of the common strategies adopted by gamblers. Figure 2. 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. We can see that although there is a high probability for sticking to the same bet values, the most likely outcome after losing a round is that the gambler increases their wager. When winning one round, gamblers are more likely to decrease their wager. This means that negative-progression strategies are more common among gamblers than positive-progression strategies. Table 3 Statistics about how gamblers change their bet values after winning/losing rounds. Risk attitude. Owner and manager with MultiMedia. Developer of MultiMedia Network. Partner with MultiMedia in several European and national research and development projects. Project Coordinator for European Teleworking Development Romania (ETD) Member of Rotary Club Bucuresti Atheneum. Cofounder of the regional association and president of the Mehedinti Branch of Romanian Association for Electronic Industry and Software, russian poker तीन पत्ती रियल मनी. Initiator, cofounder and president of Romanian Association for Telework and Teleactivities. Member of Internet Society. Initiator, cofounder and president of Romanian Teleworking Society. Cofounder and vice-president of the Mehedinti Branch of the General Association of Engineers in Romania.
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