Problem Gambling and Gambling Mathematics

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Problem gambling, pathological gambling, gambling addiction
There are various definitions of problem gambling. Most of them are based exclusively on biomedical models, being challenged by other definitions basing more on social or environmental models. The controversy of biomedical vs. environmental models is also reflected in the research in the field of problem gambling. All definitions include references to harmful consequences (either individual or social) and a popular definition would be:  Problem gambling is an urge to continuously gamble despite harmful consequences or a desire to stop.
Severe problem gambling may be diagnosed as pathological gambling if the gambler meets certain medical (psychiatric) criteria. Pathological gambling is classified as an impulse control disorder, with sufferers exhibiting many similarities to those who have substance addictions.
Pathological gambling is considered by the American Psychiatric Association to be an impulse control disorder rather than an addiction (Petry, 2006). However, for the other standards (for instance, DSM 5.0) pathological gambling is being considered as an addictive disorder as opposed to an impulse-control disorder.
According to many authors, evidence indicates that pathological gambling is an addiction similar to chemical addiction (Griffiths, 1994; Blanco & al., 2001). It has been seen that some pathological gamblers have lower levels of norepinephrine than normal gamblers (Meyer &al. 2004). Other studies indicated that deficiencies in serotonin might also contribute to compulsive behavior, including a gambling addiction (Moreno & al., 1991; Campbell-Meiklejohn & al., 2011). According to a study based on neuro-imaging technique, monetary reward in a gambling-like experiment produces brain activation very similar to that observed in a cocaine addict receiving an infusion of cocaine (Breiter & al., 2001). All these facts incline the balance in favor of biomedical models.
Still, the same monetary reward suggests that complexity of the games of chance in relation with the individual is an element that distinguishes gambling as a special type of addiction. Other authors pointed out that social factors are a far more important determinant of gambling behavior than brain chemicals and they suggest that a social model may be more useful in understanding the issue (for example, Ocean & Smith, 1993; Raylu & Oei, 2004; Griffiths, 2005; Moscrop, 2011). These facts incline the balance in favor of social/environmental models.


From non-problem to problem gambling
Not everyone who develops a gambling problem exhibits pathological criteria, nor do they necessarily have an underlying or contributing pathology. People with gambling problems fall into three main categories. 1. “Normal” problem gamblers are people whose entry into problem gambling is linked to environment and learning. The gambler does not necessarily have pre-existing psychological problems. 2. “Emotionally vulnerable” gamblers are people whose entry into problem gambling results from their difficulty in managing stress or crisis in their lives. They use gambling as an emotional mask and a way of avoiding underlying issues and current stresses. 3. “Biologically based” gamblers are people who have impulse disorders, and are the most challenging in terms of treatment success (Centre for Addiction and Mental Health, 2008).
Blaszczynski  & Nower (2002) advanced a pathways model that integrates the complex array of biological, personality, developmental, cognitive, learning theory and ecological determinants of problem and pathological gambling, represented through the following schemes, each corresponding to one the three types of gamblers above: Scheme 1, Scheme 2, Scheme 3.


The place and role of mathematics in problem-gambling
Mathematics is strongly connected to gambling through the mathematical models underlying any game of chance. Among the branches of mathematics dealing with these models, Probability Theory and Statistics are the most important, for providing objective measures and predictions for the random gaming events, for both gamblers and persons studying gambling.
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 (Barboianu, 2013). Call this the gambling-math indispensability principle.
There are also other mathematical models of games and gambling as a quantifiable activity besides the statistical & probabilistic models, which represent the physical systems and processes that make the games actually function as well as for applications related to the functioning.
Another premise is the specificity of the gambling addiction through the goals of the player. Although addiction is a pathological issue (and thus a medical one), the existence of the goal of winning (besides other objective or subjective goals such as reaching a certain emotional state or filling spare time) distinguishes gambling addiction from other types of addiction and relates it to mathematics.
The roles of mathematics in problem gambling correspond to its potential contributions to all kind of social and psychological interventions having the goal of minimizing the harmful effects of problem gambling. We identified three types of potential contributions that gambling mathematics has in this field: informative-ethical, didactical-cognitive, and clinical-cognitive; the last two types reflect in practical contributions to problem-gambling research, prevention and treatment. These matters are subject of published, as well as ongoing research.


Barboianu, C. (2013). Mathematician's call for interdisciplinary research effort. International Gambling Studies, 13(3), pp. 430-433.
Blanco, C., Moreyra, P., Nunes, E. V., Saiz-Ruiz, J., & Ibanez, A. (2001). Pathological gambling: addiction or compulsion?. Seminars in clinical neuropsychiatry, 6 (3), pp. 167-176.
Blaszczynski, A. & Nower, L. (2002). A pathways model of problem and pathological gambling. Addiction, 97 (5), 487-499.
Breiter, H., Aharon, I., Kahneman, D., Dale, A., Shizgal, P. (2001). Functional Imaging of Neural Responses to Expectancy and Experience of Monetary Gains and Losses. Neuron 30(2), pp. 619–639.
 Campbell-Meiklejohn, D., Wakeley, J., Herbert, V., Cook, J., Scollo, P., Ray, M. K., ... & Rogers, R. D. (2011). Serotonin and dopamine play complementary roles in gambling to recover losses. Neuropsychopharmacology, 36(2), 402-410.
Centre for Addiction and Mental Health, 2008. Pathways into Problem Gambling. In:  Problem Gambling. A Guide for Helping Professionals. CAMH (Eds.), pp.14-15.
Griffiths, M. D. (1994), An exploratory study of gambling cross addictions. Journal of Gambling Studies, 10 (4), pp 371-384.
Griffiths, M. D. (2005). A 'components' model of addiction within a biopsychosocial framework. Journal of Substance Use. 10 (4), pp. 191-197.
Meyer, G., Schwertfeger, J., Exton, M. S., Janssen, O. E., Knapp, W., Stadler, M. A., ... & Krüger, T. H. (2004). Neuroendocrine response to casino gambling in problem gamblers. Psychoneuroendocrinology, 29(10), pp. 1272-1280.
Moreno, I., SaizRuiz, J., & LópezIbor, J. J. (1991). Serotonin and gambling dependence. Human Psychopharmacology: Clinical and Experimental, 6(S1), S9-S12.
Moscrop, A. (2011). Medicalisation, morality, and addiction : Why we should be wary of problem gamblers in primary care. British Journal of General Practice 61(593), pp. 836.
Ocean, G., & Smith, G. J. (1993). Social reward, conflict, and commitment: A theoretical model of gambling behavior. Journal of Gambling Studies, 9(4), pp. 321-339.
Petry, N. (2006). Should the Scope of Addictive Behaviors be Broadened to Include Pathological Gambling?. Addiction 101 (s1), pp. 152.
Raylu, N., & Oei, T. P. (2004). Role of culture in gambling and problem gambling. Clinical psychology review, 23(8), pp. 1087-1114.
This entry should be cited as:
Barboianu, C. (2014). Problem gambling and gambling mathematics. Retrieved from .




The content of this section is based on resources from our Articles and Books sections, as well as other published research.

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