Mathematical Models of Games of Chance: Epistemological Taxonomy and Potential in Problem Gambling Research

What is the current place of mathematics in problem gambling research, and how can mathematics contribute toward minimizing the harmful effects of excessive gambling? In this paper, I answer the first question; then I draw upon the main principles and propose further research in the matter of the second question. First, mathematics is strongly connected to gambling through the mathematical models1 underlying any game of chance. Games of chance are developed structurally and physically around abstract mathematical models, which are their mere essence, and the applications within these mathematical models represent the premises of their functionality. For instance, within statistical models, the house edge is ensured through precise calculations regarding expected value; if such calculations were not possible, the game would never run. Since in the research, treatment, and prevention of problem gambling we cannot separate the gambler from the game he plays, it follows that an optimal psychological intervention cannot disregard mathematics. Call this the gamblingmath indispensability principle (Bărboianu, 2013b). Determinants of the decision to gamble include not only the gambler’s biological and psychological constitution, but also the structural characteristics of the gambling activity itself (Griffiths, 1993), among which games’ structures are strictly related to the mathematical models of the games. Games’ structures directly influence their outcomes in an idealized mathematically-modeled way for instance, outcome volatility (see Turner, 2011) and the behavior of outcomes is determinant for gamblers’ decisions. A second premise is the specificity of the gambling addiction through the goals of the player and the monetary reward. Although addiction is a pathological issue (and thus a medical one), the existence of the goal of winning distinguishes gambling addiction from other types of addiction and relates it to mathematics. Thus far, the interventions involving mathematics to problem-gamblers were limited to didactical interventions, either school based or in experimental research. Past