distribution and risk attitude of gamblers, since both distributions are closely related to the displacement distribution for the gambler’s random walks. Within this paper, we will mainly focus on the analysis at the population level. Physicists have long been studying diffusion processes in different systems, and recently anomalous diffusive properties have been reported in many human activities, including human spatial movement [@Rhee2011; @Brockmann2008b; @Kim2010], and information foraging [@Wang2017]. In a previous study of skin gambling [@Wang2018], we have shown that in a parimutuel betting game (where players gamble against each other), a gambler’s net income displays a crossover from superdiffusion to normal diffusion. We have reproduced this crossover in simulations by introducing finite and overall conserved gamblers’ wealth (see [@Toscani2019] for a different way of modeling this using kinetic equations of Boltzmann and Fokker-Planck type). However, this explanation cannot be used in other types of gambling games where there is no interaction among gamblers (e.g., fixed-odds betting games, which will be introduced below), as they violate the conservation of gamblers’ overall wealth. In this paper, we want to expand the scope of our study to more general gambling games, check the corresponding diffusive properties, and propose some explanations for the 