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Now, let us focus on the analysis of the diffusive process of the gamblers’ net incomes, starting with the analysis of the change of the mean net income with the number of rounds played (time), $\langle \Delta w(t)\rangle =\langle w(t)-_\rangle =\langle _^\,_ (i)\rangle $ , where w 0 is the player’s initial wealth, w ( t ) is the player’s wealth after attending t rounds, and $_ (i)$ is the payoff from the i th round the player attended. $\langle \cdot \rangle $ represents an ensemble average over a population of players placing bets. In the rest of this paper, $\langle \cdot \rangle $ will always be used for representing an ensemble average. In Fig. 6 we show the change of $\langle \Delta w(t)\rangle $ over time. In most of the datasets, players’ mean net income decreases over time, which suggests that in general players will lose more as they gamble more. At the same time, in some datasets such as Ethcrash (D) and Coinroll (F), large fluctuations can be observed. Figure 6. Change of the mean net income with time for the different datasets. Most of the datasets present a decreasing net income as time t increases. Each point is obtained from an average over at least 200 players. An useful tool for studying the diffusive process is the ensemble-averaged mean-squared displacement (MSD), defined as. For a normal diffusive process, $\langle \Delta ^(t)\rangle \sim t$ , otherwise an anomalous diffusive behavior prevails. More specifically, when the MSD growth is faster (respectively, slower) than linear, superdiffusion (respectively, subdiffusion) is observed. In Fig. 7, we present the growth of the ensemble-averaged MSD against time for each of the datasets. To reduce the coarseness, MSD curves are smoothed with log-binning technique. The error bars in Fig. 7 represent 95% confidence intervals computed with bootstrapping using 2000 independent re-sampling runs. It is interesting to see that for different datasets we observe different diffusive behaviors. 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