rapid changes. These conclusions can be confirmed by the small mean values and small variances of log-ratios between consecutive bets.

\[table:log\_ratio\]

![ \[fig:log\_ratio\] The distribution of the logarithmic of the ratio (log-ratio) between consecutive bet values. For games (A, B, C), the log-ratio can be described by a Laplace distribution. For games (D, F, G, H), the log-ratio presents bell-shaped distribution. In general, the distributions are symmetric with respect to the y-axis, except in games (D) and (F). The $x$-coordinate $\log_{10}(b_{i+1}/b_i)$ is proportional to the parameter $\nu$. ](figure2.pdf){width="\columnwidth"}

Further analysis of the distribution of $\nu$ shows an exponential decay on both of its tails, see Fig. \[fig:log\_ratio\]. This means that $\nu$ approximately follows a Laplace distribution. However, compared to a Laplace distribution, the empirical log-ratio distribution shows a much higher probability at $\nu=0$, whose value can be found in the last column of Table \[table:log\_ratio\]. We also observe that $\nu$ 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 $\nu$. The high probability of staying on the same wager indicates that betting with fixed wager is one of the common strategies adopted 