Non-mathematical dimensions of randomness: Implications for problem gambling

My paper with the same title, published in July 2024 in Journal of Gambling Issues, is another piece of research showing how theoretical philosophy can be as applicative as possible in concrete problems, in a psychology field governed by empirical research, as is problem gambling.
Non-mathematical dimensions of randomness: Implications for problem gambling
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In this theoretical research I have argued in terms of foundation and history of probability theory, in an epistemological framework, that general randomness is not a mathematical concept because it does not have a mathematical definition to describe it in its full complexity. In sciences and mathematics, randomness has a theoretical-methodological dimension and role, which submits to its more general epistemic dimension. I qualified such dimensions of randomness as strong and its mathematical dimension as weak, the latter per its indirect relationship as a primitive notion with probability theory.

In industrial gambling, randomness has interdependent functional and ethical dimensions, as a necessary prerequisite for the functionality and fairness of games of chance. I have shown that its mathematical dimension is not involved decisively in these roles, although the PRNGs are constituted on the basis of mathematical algorithms and as such provide an algorithmic randomness. The concerns for the fairness of the PRNGs actually pertain to the concrete application of these algorithms rather than their mathematical constitution, and I have claimed that the effort and resources allocated by players for overcoming such concerns are not justified when weighed against the much more certain harms produced by a problematic gambling behavior, in particular gambling-specific cognitive distortions.

In problem gambling, randomness has been conventionally or artificially granted a strong mathematical dimension or mathematical nature, as the review studies revealed. While one may see such qualification as just a lexicographic simplification or simplistic reference, I argued that it has implications for both the research and the educational-cognitive programs in problem gambling having as topics cognitive distortions and gamblers’ education.

I took the Gambler’s Fallacy as a theoretical case study for discussing this distortion relative to the nature of randomness and found that its constituent misconceptions about ‘equally probable’ and ‘statistical independence,’ both directly related to the concept of randomness by its epistemic dimension, cannot be supposed to be corrected in a merely mathematical cognitive-educational framework if randomness is assumed to be a mathematical concept. Such an assumption would elude the nature of the relationships between the concepts involved in the fallacy, and implicitly the distinction between the kinds of these relationships, which constitutes essentially the structural knowledge about them. In pragmatic terms of correcting the Gambler’s Fallacy, directing the individuals affected by this distortion to a program or counseling based on mathematical curricular content would not change their perception of randomness from subjective to objective or from inadequate to adequate, simply because randomness is not part of the formal mathematics of gambling, but of the whole epistemic context of it. This of course does not apply to every math-related cognitive distortion in gambling. For instance, the conjunction fallacy consists of an incorrect understanding of or lack of knowledge about a specific property of probability, although circumstantial factors (such as the descriptive text of the situation) are known to influence the correct belief (Costello & Watts, 2017); correction of the conjunction fallacy would have no essential elements left outside the mathematical context of the issue.

Instead, for the near-miss effect, in another paper (Bărboianu, 2019) I have argued that by focusing equally on the mathematical description of the near-miss fallacy and its epistemology, we can identify more precisely the cognitive tools recommended as strategies to correct the distortion. As in our Gambler’s Fallacy analysis, the epistemic dimension of the mathematical description of the near-miss phenomenon is decisively associated with the inadequate perception of the near-miss, and its role manifests before any hypothetical mathematical fallacy (when splitting the “near-missed” outcome in a matching and non-matching part).

It follows from our current and cited research that the epistemic dimension of the math-related concepts involved in the gambling cognitive distortions should not be given merely marginal attention, and conceptual distinctions should be made before proceeding to any theoretical approach of these distortions. In particular, randomness has to be employed in its non-mathematical dimensions (including the epistemic one) as well as in its mathematical one in problem-gambling research. And since educational programs dedicated to prevention and awareness are the result of applying research, these should adopt the same distinctions and distributed focus.

As it follows from our analysis, there are three main arguments for employing the distinctions between the dimensions of randomness in problem gambling research and associated educational-cognitive programs, and focusing on the non-mathematical dimensions:

First, whether we talk about studies on educational interventions for gamblers or programs delivered in the awareness/prevention zone, they all have a didactic component which is associated with a certain academic discipline from which the specific curricular content is imported. The beneficiaries of the interventions or programs as non-experts are referred tacitly or directly to a certain discipline by the simple reference to the attribute or dimension of the subject matter of study. Telling them about a mathematical or statistical randomness will direct them to mathematics; however, I have argued that courses in this discipline will tell them nothing about randomness. Call this the disciplinary argument.

Second, the studies about educational interventions on gamblers for evaluating the changes in their gambling behavior (such as those cited in a previous section) consists of an interventional knowledge base (what is taught) and evaluation of the new condition after the intervention (by answers to questionnaires, reflecting intentions and acquired knowledge). The results of such studies not only assess the changes in behavior (as declared by subjects), but also make associations between the various elements of the two components (units of the learning content, the values of the variables describing the acquisition of the new knowledge, items in the questionnaire and answers). Any distinction or fine-graining in a concept or unit delivered (such as would be the distinctions between the mathematical and non-mathematical dimensions of randomness) leads to a change of the set of possible associations and may change some associations themselves; this means changing the conclusions of a study, including in what concerns the interpretation of the results. Call this the methodological argument.

Third, merging all dimensions of randomness into a mathematical dimension or referring only to the latter actually means lessening the complexity of the concept; however, complexity is what characterizes randomness, and adequate understanding of a complex concept is inconsistent with excessive simplification.

Moreover, inducing to the non-expert gambler the idea of a mathematical randomness is supposed to incline their cognitive balance toward order rather than disorder as an attribute of the concept, since mathematics applied in gambling exhibits a kind of order (equal probabilities for similar events and the Law of Large Numbers or Law of Averages). Under this cognitive condition, there is no reason to believe that a gambler will be more convinced that a black is not “due” after a streak of ten reds than they would had randomness been explained to them as a “non-mathematical disordered order” – more so, in fact, as the individual also may not distinguish between math and applied math in gambling. The latter may even be tricky in terms of interpretation in empirical terms, since probability itself is a tricky concept for those unfamiliar with it). Call this the epistemic argument.

The disciplinary and epistemic arguments apply to any kind of research, program, or counseling scheme having as its object the adequate understanding or perception of the concept of randomness in gambling, especially relative to the gambling-specific cognitive distortions. Focusing on the philosophical aspects of randomness for cognitive-educational goals should not be viewed as something unusual, as turning to philosophy for enhancing understanding in an educational context is not a novelty.

Per all the above arguments, I advance the thesis that the cognitive-developmental model of educational programs, focused on correcting the gambling cognitive distortions, envisioned by Keen & al. (2019), should be designed by assimilating the distinctions between non-mathematical and mathematical dimensions of randomness and give the former the deserved attention. Such distinctions should be also adopted by research dealing with the mathematically-related gambling cognitive distortions, where approaching the involved mathematical concepts beyond their mathematical nature is worth pursuing.

Further theoretical research is needed to provide the adequate design of future studies incorporating the advanced epistemic approach of randomness and other gambling-specific mathematical concepts, and of those investigating or assessing the effectiveness of this approach. Theoretical research is also needed to establish the adequate conceptual framework of an interdisciplinary cognitive model of educational programs that incorporates the epistemic approach here discussed.

 

This research has been conducted at the PhilScience Gambling Lab.

 

References:

Bărboianu, C. (2024). Non-mathematical dimensions of randomness: Implications for problem gambling. Journal of Gambling Issues, Vol. 36, 1.

Bărboianu, C. (2019). The epistemology of the near miss and its potential contribution in the prevention and treatment of problem-gambling. Journal of gambling studies35(3), 1063-1078

Costello, F., & Watts, P. (2017). Explaining high conjunction fallacy rates: The probability theory plus noise account. Journal of Behavioral Decision Making30(2), 304-321.

Keen, B., Anjoul, F., & Blaszczynski, A. (2019). How learning misconceptions can improve outcomes and youth engagement with gambling education programs. Journal of Behavioral Addictions8(3), 372-383.

Related articles:

Bărboianu, C. (2024). The philosophy, psychology, and math of the Gambler’s Fallacy. PhilScience Magazine. Retrieved from https://www.magazine.philscience.org/2024/03/16/the-philosophy-psychology-and-math-of-the-gamblers-fallacy/

 

 

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