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    Figure 8. A betting system similar to Martingale will lead to a crossover from superdiffusion to normal diffusion according to the growth of mean-squared displacement. Comparison between curves of different parameters shows that higher γ and lower α both will lead to a higher chance of huge losses/winnings. Next we examine the ergodicity of the random walk process of net income by computing the time-averaged mean-squared displacement and the ergodicity breaking parameter. The time-averaged MSD is defined as. $$\overline^>(t)=\frac\,\mathop\limits_^\,^,$$(t)\rangle \) and the ensemble-averaged MSD \(\langle \Delta ^(t)\rangle \) shows clear deviations in most datasets, except in the Coinroll (F), csgospeed (G) and csgofast-Jackpot (H) games. To further examine breaking of ergodicity, we have calculated the ergodicity breaking parameter EB 24,25,26 defined as. $$>(t)=\langle ^>(t))>^\rangle / ^>(t)\rangle >^-1.$$(t)\rangle \) (thick dashed black lines) and \(\langle ^\rangle \) (thick full red lines) reveals that these quantities are different for most games, with the exception of the Coinroll ( F ), csgospeed ( G ) and csgofast-Jackpot ( H ) games. Players who played less than 1000 rounds are filtered out in each dataset., red cliff सबसे अच्छा ऑनलाइन जुआ. For an ergodic process, the parameter EB should be close to 0. However, as shown in Fig. 10, in most datasets, with the exception of csgospeed (G) and csgofast-Jackpot (H), EB is large. It follows that non-ergodicity is observed in most games and that gambling processes indeed often deviate from normal diffusion, which further highlights the complexity of human gambling behavior. Figure 10.
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