Behavior analysis of virtual item gambling

TL;DR

This paper analyzes online lottery gambling logs to understand player behavior, revealing a transition in income dynamics from super-diffusive to diffusive regimes, and models this with truncated power-law random walks.

Contribution

It introduces a detailed statistical analysis of gambling behavior and models the income changes using novel random walk models with truncated power-law distributions.

Findings

Identified a transition from super-diffusive to diffusive behavior in income dynamics.

Derived key features for modeling the crossover using truncated power-law step lengths.

Provided insights into the stochastic processes underlying gambling behavior.

Abstract

From the gambling logs of an online lottery game we extract the probability distribution of various quantities (e.g., bet value, total pool size, waiting time between successive gambles) as well as related correlation coefficients. We view the net change of income of each player as a random walk. The mean squared displacement of these net income random walks exhibits a transition between a super-diffusive and a normal diffusive regime. We discuss different random walk models with truncated power-law step lengths distributions that allow to reproduce some of the properties extracted from the gambling logs. Analyzing the mean squared displacement and the first-passage time distribution for these models allows to identify the key features needed for observing this crossover from super-diffusion to normal diffusion.