Gambling-math Knowledge and Gambling Behavior

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Dr. Catalin Barboianu

December 8, 2025

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In problem-gambling research, a topic of interest was whether the cognitive-educational achievements of the players have any influence in changing their gambling behavior. In particular, given that games of chance are conceived on the basis of mathematical models that govern their functionality and outcomes, the question arose whether teaching players about the mathematics of gambling will result in any decrease of their gambling activity and have any effect in correcting the common misconceptions and fallacies associated with gambling.

Surprisingly, the results of the empirical studies investigating this topic were non-conclusive and some of them tended to answer no to this question. Among those strongly supporting this answer was a study in 2006 on university students, which were subject to an educational intervention teaching them about gambling-math basics. The authors found that the intervention improved gamblers’ knowledge and skill, but this was not associated with any decreases in actual gambling behavior. Further research challenged these results.

Problem gambling and preventive educational initiatives

Several studies have found the prevalence of gambling to be higher in young adults. In North American college and university students, the average lifetime rate of gambling is between 70% and 94%. As it concerns problem and pathological gambling, the rates are also high among young people, with a peak in the age interval 18 to 24.

Government agencies dealing with the gambling phenomenon have taken various initiatives in both the areas of prevention and counseling of problematic gambling. In the category of educational initiatives, awareness campaigns, 24-hour counseling hotlines, media promotion of responsible gambling, posters and videos on problem gambling in gaming environments are common tools and strategies used to fight against the development of problem gambling, however their actual effectiveness is questionable.

It’s worth noting that in some jurisdictions prevention programs have also been introduced into the school curriculum, for instance Australia, United States, and Canada.

A good fit for achieving critical thinking about gambling are college or university Introductory Statistics courses teaching fundamentals of probability theory and statistics. While the higher-education students have some of the highest rates of problem gambling, it was found that those who eventually earn post-secondary degrees tend to have significantly lower rates of problem gambling. Therefore, it is fair for one to hypothesize that college/university students are well suited for changing their gambling behavior as result of teaching them about the mathematical facts of gambling. But is this actually the case?

Does the acquisition of gambling-math knowledge changes gambling behavior?

First, it is important to say that research on this topic was mainly empirical. There were two directions of such research. Studies carried in one direction found a positive impact of educating problem gamblers on the nature of randomness, true gambling probabilities, and the errors of thinking underlying gambling fallacies. Studies in the second direction showed that college students trained in statistics are less susceptible to fall prey of certain fallacies and have better general reasoning skills for everyday problems, including gambling related.

The results of the research dedicated to the impact of improved statistical knowledge on the actual gambling behavior were not encouraging:
At the end of the 1990s, a study found that university students who received statistical training made superior decisions in a gambling task compared to untrained students. However, another study found that students asked to evaluate the probability of a certain sport team winning tended to overestimate the actual chances and gambled more compared to the students not asked to evaluate any chances.

At the beginning of the 2000s, a study found that students taught about the probabilities of certain events gambled on rare events more than they should compared to students who were given direct experience with these probabilities but did not know the actual odds. Another study found that university students who received an explicit warning about erroneous beliefs in gambling and the negative expectation of gambling games acquired superior knowledge on these matters, but were just as likely to gamble on roulette compared to students not receiving these messages.

On the other hand, other studies have reported improvements in students’ critical thinking about gambling as result of a specific educational intervention, associated with declared intentions to reduce their gambling activity in the future. Overall, there were no conclusive results which to tell whether the acquisition of gambling-math knowledge actually change gambling behavior, not even for the students population.

Setting up more ‘real world’ empirical research

Obviously, the mentioned studies have several limitations, namely the relatively short period of training, the didactic nature of some interventions, and the laboratory based evaluation of gambling behavior.

In 2006, two researchers from University of Lethbridge (Canada) conducted a study claimed to investigate the topic in discussion as basing on a much more substantive and ‘hands-on’ educational intervention impacting real-world gambling behavior.

Method and curriculum

The sample consisted of 470 students from the University of Lethbridge, where an ‘Introduction to Probability and Statistics’ course is taught, consisting of 39 fifty-minute lectures and 13 fifty-minute labs. The sample was split in three groups, namely the Intervention group (198 students taught specific sections of the mentioned course), the Math Control group (134 students taught other specific sections), and the Non-Math Control group (138 students attending an Introductory History class and an Introductory Sociology class).

The topics covered in both the Intervention and Math Control group were: descriptive statistics, graphical representation, probability, discrete and continuous random variables, expectation, binomial, normal, and student’s t-distribution, large and small sample inference and estimation, and the central limit theorem.

The Intervention group differed from the Math Control group in the following respects: five out of ten probability lectures were devoted to the probabilities associated with gambling; four out of thirteen labs provided hands-on experience with games like roulette, craps, and blackjack; a supplemental text dealing with gambling probabilities was assigned; there was one lecture on the gambling fallacies; and the questions on the mid-term and final exams were conceived with a greater emphasis on gambling probabilities.

A 30-minute ‘Gambling Questionnaire’ was administered at the beginning of each class, which collected demographic information and assessed the following factors:

1. Knowledge and ability to calculate gambling odds, assessed by a 10-item Gambling Math Skill Scale;
2. Gambling fallacies, assessed by the 10-item Gambling Fallacies Scale, measuring awareness and resistance to common gambling fallacies;
3. Attitude toward gambling, assessed by the 3-item Gambling Attitude Scale.
4. Gambling behavior in the past six months, expressed through type of gambling, time and money spent gambling;
5. Problem gambling, assessed by the 9-item Canadian Problem Gambling Index (CPGI).

The Gambling Questionnaire was administered again, six months after the course has ended.

Tested hypotheses

The following hypotheses were tested by the statistical analysis:

H1. Students who received the intervention will prove higher skills in calculating basic gambling odds compared to before attending the course and to the control groups.
H2. Students who received the intervention will demonstrate more awareness of and resistance to gambling fallacies compared to before attending the course and to the control groups.
H3. Students who received the intervention will have a more negative attitude toward gambling compared to before attending the course and to the control groups.
H4. Students who received the intervention will manifest a decrease in gambling activity outside the classroom compared to before attending the course and to the control groups.
H5. Students who received the intervention will manifest a decrease in problematic gambling behavior compared to before attending the course and to the control groups.
H6. Students who acquired the largest improvements in gambling math skill and awareness of gambling fallacies will manifest the highest decreases in gambling and problem gambling behavior.

Results of the study

The statistical analysis assessed the effectiveness of the intervention on each of the following variables: gambling math skill; awareness and resistance to gambling fallacies; attitude toward gambling; time spent gambling; money spent gambling; and average CPGI score.

As expected, the intervention proved effective in improving student’s ability to calculate gambling odds as well as awareness and resistance to gambling fallacies. These changes occurred in Statistics classes being trained on gambling-specific probabilities. On the contrary, Statistics classes receiving general information on probability theory did not have such improvement.

Unexpectedly, hypotheses H4 to H6 were not confirmed: Students receiving the intervention had no significant self-reported decrease in their likelihood of gambling, of being a problem gambler, and the amount of time or money spent gambling. There was no significant change in their attitude toward gambling either.

The majorities of students in this study were non-problem gamblers prior to the intervention and remained as such after it.
In the regression analyses, the lack of association between changes in gambling-math skill or course grade with changes in gambling behavior provides some further evidence that knowledge about the mathematical-statistical facts of gambling may not be that important.

Conclusions and new research prospects

The stream of research in the late 1990s and beginning of the 2000s on the topic of whether acquisition of gambling-math knowledge does change actual gambling behavior was not conclusive. It provided some empirical evidence that teaching gamblers about the mathematics behind gambling is unlikely to change their gambling behavior, including in correcting their gambling fallacies and erroneous beliefs, as the discussed study did.

With respect to these misconceptions and fallacies in gambling, such results submit to the thesis that the psycho-biological constitution of the individual prevails over their cognitive assets acquired through education. Under this thesis, the addictive potential of an activity like gambling remains and manifests despite any improved knowledge, including mathematical.

The results of the empirical studies of the sort of that discussed in this article have been questioned for their methodology by new research, especially in the respects that the optimal content of the curriculum in the intervention has not been established theoretically and the laboratory setup of the study cannot reproduce the real intentions and facts in the real world of gambling. Besides the methodological criticism, the results of such studies and the above thesis itself have been also challenged by new theoretical research in the last decade. This research has claimed that gambling-mathematics knowledge is more than formal math applied in gambling; it is actually about how math is applied in the real world of gambling and how the probability and statistics concepts relate to the real-life gambling events. Consequently, the curriculum of an educational intervention should also reflect this non-mathematical knowledge (of an epistemological type), which is addressed in an interdisciplinary framework.

References

Barboianu, C. (2015). Mathematical models of games of chance: Epistemological taxonomy and potential in problem-gambling research. UNLV Gaming Research & Review Journal, 19(1), 17-30.

Gerstein, D., Volberg, R.A., Murphy, S., Toce, M., et al. (1999). Gambling impact and behavior study. Report to the National Gambling Impact Study Commission. Chicago: National Opinion Research Center at the University of Chicago.

Kang, S.K. & Hsu, C.H.C. (2001). University students’ perceptions on legalized gambling and their casino gaming behaviors. The Consortium Journal, Vol. 5, 5-16.

Kosonen, P. & Winne, P.H. (1995). Effects of teaching statistical laws on reasoning about everyday problems. Journal of Educational Psychology, Vol. 87, 33-46.

Ladouceur, R., Sylvain, C., Letarte, H., Giroux, I., & Jacques, C. (1998). Cognitive treatment of pathological gamblers. Behavior Research & Therapy, Vol. 36, 1111-1119.

Riniolo, T.C. & Schmidt, L.A. (1999). Demonstrating the Gambler’s Fallacy in an Introductory Statistics class. Teaching of Psychology, 26 (3), 198-201.

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