Clinical-Cognitive Contributions of Mathematics to Problem Gambling

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Premises, classical approach and resources
In the virtue of the math-indispensability principle, any clinical cognitive intervention cannot disregard gambling mathematics.
Thus far, mathematics has not entered the therapists’ offices and clinics yet. Psychologists, although they accept that mathematics plays an important role in the gambling phenomenon, have avoided going deeper into the mathematics of gambling in search of new elements that could help in their endeavor; this avoidance can be attributed to the nature of their profession (Barboianu, 2013). Still, the potential of mathematics exists and is ready to be activated.
The relationship mathematics has developed with psychology in the course of problem-gambling interventions is an indirect one – mathematical intervention is addressed exclusively to gamblers via an instructional entity, and psychology only conducted the empirical studies and interpreted the results in terms of predicted behavior after the intervention. The direct contribution of mathematics to psychological intervention in problem gambling was facing the odds and correcting misconceptions, which actually are the tasks of a didactical-cognitive intervention based on the probabilistic & statistical models of games and gambling, either in the form of a course or readable educational material.
A professional contribution to the cognitive assets of gamblers with respect to gambling mathematics was the Harvard Medical School's Division on Addictions’ module called Facing the Odds: The Mathematics of Gambling and Other Risks (Shaffer & Vander Bilt, 1996), a middle-school curriculum on probability, statistics and number sense designed to increase young people's mathematics literacy while concurrently preventing or reducing their participation in risky and potentially addictive behaviors.
Other professional resource on odds, probabilities and mathematics facts of gambling is the content of this website.
As we mentioned, such resources are external to the clinical environment and to the relation between therapist and problem gambler.
Facing the odds is in fact a principle that has been tested. Probability, as the central concept of gambling mathematics, ought to receive greatest attention. However, facing is not enough and some empirical studies (see Hertwig et al., 2004; Steenbergh et al., 2004; Williams & Connolly, 2006) confirmed that premise. Besides studies, we have at hand the lottery example, in which lottery players continue to play against the lowest odds of winning in the gambling realm.
Further research
Directions of research have been designed to find and test new principles of psychological intervention that would employ the cognitive potential of mathematics. One of such principles is reduction to models. In the process of mathematical modeling, the games are idealized through removal of their physical components unessential for the modeling purposes, and reduced to pure mathematical structures. This physical surplus that is removed includes (but is not limited to) cases, external design, interface, commands, motion of the mechanical components, and visual effects.
Gaming risk factors such as illusion of control, near miss and near-miss effect, and sound and image effects do not belong to the mathematical models of the games (Barboianu, 2015). Having the risk factors outside the mathematical models, the potential of a cognitive intervention based on knowledge related to mathematical models could manifest in a clinical intervention developed so as to create for the patient a representation of the games s/he plays as pure mathematical structures free of risk factors. Such a clinical intervention would be in some aspects equivalent, for example, to an intervention treating the phobia of speaking in public, in which the patient is encouraged to imagine that the audience is naked. Such interventions based on the principle of reduction to models would be based largely on functional models, not just on the probabilistic and statistical ones, the latter still remaining important. The reduction-to-models principle would be a completion of the facing (and interpreting)-the-odds principle, and their expected positive effects on decreasing excessive gambling can be tested only through empirical studies following this research.
Further research, both theoretical and empirical, is necessary in various directions for establishing the following:
- whether such mathematical and mathematical-modeling knowledge can be comprised enough to be delivered as practical modules to both the therapist and the patient;
- whether a common language can be found to accommodate the delivered information with the various levels of mathematical education of the gamblers, as well as with the non-mathematical background of the therapist;
- whether such knowledge can be reduced to warning messages and how such warning messages differ from the warning messages specific to other addictions.


Barboianu, C. (2013). Mathematician's call for interdisciplinary research effort. International Gambling Studies, 13(3), pp. 430-433.

Barboianu C. (2015). Mathematical models of games of chance: Epistemological taxonomy and potential in problem-gambling research. UNLV Gaming Research & Review, 19(1).

Hertwig, R., Barron, G., Weber, E.U., Erev, I. (2004). Decisions from experience and the effect of rare events in risky choice. Psychological Science, 15 (8), pp. 534-539.

Shaffer, H., & Hall, M. Vander Bilt (1996). Facing the Odds: The Mathematics of Gambling and Other Risks. Billerica, MA: Harvard Medical School Division on Addictions and the Massachusetts Council on Compulsive Gambling.

Steenbergh, T.A., Whelan, J.P, Meyers, A.W., May, R.K., & Floyd, K. (2004). Impact of warning and brief intervention messages on knowledge of gambling risk, irrational beliefs and behavior. International Gambling Studies, 4 (1), pp. 3-16.

Williams, R.J., Connolly, D. (2006). Does learning about the mathematics of gambling change gambling behavior? Psychology of Addictive Behaviors, 20 (1), pp. 62-68.


This entry should be cited as:
Barboianu, C. (2014). Clinical-Cognitive Contributions of Mathematics to Problem Gambling. Retrieved from


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