 Premises, classical approach
and resources
 In the virtue of the
mathindispensability 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 problemgambling
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
didacticalcognitive 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
middleschool 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 nearmiss 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 reductiontomodels
principle would be a completion of the facing (and
interpreting)theodds 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
mathematicalmodeling 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 nonmathematical 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.

References
Barboianu, C.
(2013). Mathematician's call for interdisciplinary research effort.
International Gambling Studies, 13(3), pp. 430433.
Barboianu C. (2015).
Mathematical models of games of chance: Epistemological
taxonomy and potential in problemgambling 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. 534539.
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. 316.
Williams, R.J., Connolly, D. (2006). Does learning about the mathematics
of gambling change gambling behavior? Psychology of Addictive
Behaviors, 20 (1), pp. 6268.


This entry should be cited as:
 Barboianu, C.
(2014).
ClinicalCognitive Contributions of
Mathematics to Problem Gambling.
Retrieved from
http://probability.infarom.ro/clinical.html.
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Gambling index
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