Randomness in Gambling and Problem Gambling

Randomness is a concept to which mathematicians, scientists, and philosophers dedicated their full attention and theoretical reflection. The reason is that, although this concept is foundational for some mathematical theories and for science, its nature is still surrounded in mystery.Randomness in Gambling and Problem Gambling

Randomness is strongly connected to gambling. In this article we will see how the nature of randomness impacts the games of chance, gambling, the gambling industry, and the problem-gambling field, and why all people involved in the gambling phenomenon must have a good understanding of this complex concept.

What is randomness?

The lexicographic definition of randomness across all major dictionaries is that of a quality or state of something of being random; further, the word ‘random’ is defined in dictionaries as an adjective meaning ‘happening/made/determined/chosen by chance/accident/guess rather than design/method/plan/determination/pattern/purpose’ (in all sort of choices and wordings).

In the context of probability theory, randomness is defined through ‘random experiment’: A random experiment is a well-defined procedure that obeys two conditions: 1. It produces more than one outcome; 2. The possible outcomes are unpredictable. Probability theory adopted this common definition of a random experiment and defined a ‘random event’ as a set of one or more outcomes of a random experiment. It is the primary notion of random experiment along with set theory that allow us to say that two outcomes are equally possible, the concept that all probability theory is built upon.

For mathematics and science, randomness is simply a convenient conceptual convention, for making the probabilistic/stochastic method operational and effective in scientific reasoning. This pragmatic feature of randomness grants it the quality of some order (for our reasoning).

On the other hand, randomness is conceptualized as a disorder (of the occurrences of events for which causes are not known in their entirety), given that concepts like ‘no law’, ‘no purpose’, indeterminacy, irregularity, independence, non-homogeneity fall within the concept. However, it is a special type of disorder, not just a chaotic one. It is a sort of total disorder, where the ‘total’ attribute can be expressed through ‘equally possible’, ‘equally unknown’, or just ‘totally independent’.

Accepting randomness as both an order and a disorder should not twist our mind in any way; this is just in the mere nature of randomness.

No mathematics of randomness

In an article published in Journal of Gambling Issues in 2024, Catalin Barboianu showed from an epistemological and historical perspective that randomness is not a mathematical concept and that its methodological-theoretical dimension (and not the mathematical one) mainly accounts for its foundational role in sciences and mathematics.

The main argument – endorsed by many other philosophers – is that a mathematical definition for randomness does not exist.  Mathematicians struggled from the beginning of the 20^th century to provide a mathematical definition for randomness and eventually failed.

In 1908, Emile Borel showed that a random sequence formed by only two symbols (0 and 1) like 0001101000111… cannot be built without experimental intervention. Borel proposed an inductive logical proof: If we assume the first n terms of the sequence were built and it follows to write the n + 1 -th term, then two options are available: the first n results are taken into account or they are not. The first option cancels the random attribute of the construction. The second option brings us back to the same situation as we have at the beginning of the construction: How to choose one of the symbols 0 or 1 without taking into account any difference between these? Such a choice would be equivalent to a draw, but a draw assumes an experimental intervention, which cancels the mathematical character of the construction.

Such a difficulty has never been surmounted with the further works of the mathematicians. All that they achieved was a notion of ‘algorithmic randomness’, which yet does not capture all the features of randomness in the real life, but only a small part. The “real” randomness is more complex than algorithmic randomness and could not be captured in a mathematical definition, in the light of Borel’s old contemplation that “reason cannot reproduce the randomness.”

Functional and ethical roles of randomness in gambling

For a Randomness in Gambling and Problem Gamblinggame of chance to be functional and fair, unpredictability and equal chances for its outcomes are essential conditions. Functional, because it is a game of chance and chance should not be something predictable and fair, because no participant in the game should be favored with respect to chance.

‘Unpredictable’ alone is not sufficient to characterize randomness needed in gambling. For instance, a roulette wheel that is not in a horizontal plane will not make any outcome predictable in a given spin; however, certain numbers will be favored cumulatively in the long run, which means unequal chances for the outcomes and implicitly unequal chances for the players (those knowing that information will be favored).

Therefore, randomness is employed in the physics/hardware of the games with the role of ensuring fairness of the games, which grants it an ethical role. Such fairness has two forms:

1) Fairness between players: No player should have any advantage over the others with respect to the possibility of determining or predicting the outcomes of the game; and 2) Fairness of the operator: Outcomes that are theoretically possible in the same measure should remain equally possible in practice. These two conditions say that chance has to be effectively and fairly served, and the luck factor has to be decisive in the games of chance, as their name suggests.

Randomness and technical fairness

Fairness in gambling has multiple meanings and facets. I discuss here fairness from a technical perspective, where randomness is involved.

Pseudorandom Number Generators (PRNGs) are present today in the construction of all electronic versions of casino games. The algorithm of a PRNG outputs a distribution of the elements (numbers, in particular) in a given set or interval in the form of a sequence with special properties, after inputting a random number, called ‘the seed.’ The algorithm is in the form of special computable mathematical expressions. The main two properties of a sequence generated by PRNG are: any term of the sequence is independent of the previously generated terms (by no rule of determination), and the terms are uniformly distributed over the obtained sequence. In brief, the PRNG provides a sort of algorithmic randomness.

There are also other properties that the PRNG is required to have (large period, reproducibility, portability, and so on); however, independence and uniformity are the main requirements for a PRNG to be qualified as effectively random relative to its domain of application or good for the application.

As such, although a PRNG does not provide general (absolute) randomness in the sense we characterized it above, it still provides an “acceptable” randomness that ensures the technical fairness of a game.

Concerns for fairness

In the history of gambling, the PRNGs replaced classical mechanical devices because of the concern about the latter not being random. Next, the PRNGs were improved in their mathematical algorithms and implementation technology due to the concern about the possibility of the operators’ cheating with them. The implementation of the PRNGs was improved by new seeding processes involving players’ choices (the provably fair algorithms) due to the same concern. But new concerns for fairness have been raised again, and perhaps the process will no doubt continue with any new technology because it is human nature to doubt and be suspicious.

During this process serious research and technological resources have been allocated in the industry. As for the players, who are actually the main objectors, their concerns also assumed effort and consumption of resources – track-recording, debating, reading and participating in community discussions, getting informed about the PRNG and its issues, and so on. The question is to what extent is this worth the effort it consumes from the players’ perspective.

It was argued in the mentioned paper that an unfair, biased, or fraudulent game of chance still provides randomness, an altered randomness which is characterized not by ‘order and disorder’ somehow evenly (as we qualified randomness in general), but by disorder and less order (than the non-altered randomness). However, the alteration is the effect of the fairness concern itself and not of the constitution of that game. In simple gambling terms, gambling while being concerned for fairness is still gambling if no proof is available that the game is unfair.

Randomness and gambling misconceptions and fallacies

The question raised in the previous section gets a full answer if we consider the relationship between randomness and gambling cognitive distortions, in the form of misconceptions, fallacies, or irrational beliefs. These distortions have been recognized by problem-gambling researchers as important risk factors for developing a problematic gambling behavior and most of them are related to randomness.

Just to talk about the Gambler’s Fallacy, this distortion is the result of an inadequate perception and understanding of randomness, combined with a misconception on the notion of statistical independence and a mathematical error in applying the Law of Large Numbers. It worth noting that the last two mathematically related issues are still related to the concept of randomness.

In general, people have a poor or inadequate understanding and interpretation of randomness and this is not only a matter of education. It submits to the complexity of the concept, whose nature is unclear even for scientists and philosophers, and to the fact that it’s in the human nature to exhibit biases, heuristics, and irrational beliefs with respect to concepts that do not ensure an equilibrium state for the mind.

What is important to retain is that there is the non-mathematical dimensions of randomness that are responsible for such misconceptions and fallacies and not the mathematical one.

Under all these arguments, it comes clear now that the concern for fairness should be the problem of the industry and legal bodies and not of the players, as otherwise their efforts would be detoured from contributing to more important concerns – those for not developing problem gambling. In the light of this conclusion, players could instead get better informed about the randomness-related cognitive distortions in gambling as a first step.

Randomness and problem-gambling educational programs

Over the last decades, governmental or private programs of problem-gambling prevention and awareness have been developed in almost every country around the findings of the problem-gambling research, especially for the youths. In the clinical sector, new counseling schemes have been conceived with the contribution of several academic disciplines dealing with problem gambling.

These programs and schemes all have a strong didactic component, targeted to a responsible gambling attitude and to the correction of gambling-specific cognitive distortions. Within this component, the tendency has been to categorize randomness in the group of mathematical notions whose inadequate understanding or application is responsible for the math-related cognitive distortions. In 2019, at University of Sydney, a well documented wide-scope review on the studies that evaluated gambling-education programs revealed that randomness was placed in the category of gambling-related mathematical concepts, and learning about randomness was associated with math classes or gambling-math courses and with all the mathematical information or curricular content sometimes taught in such educational interventions.

However, as I argued, randomness is not a mathematical concept and it is not its mathematical dimension that accounts essentially for the gambling cognitive distortions.

Telling problematic gamblers about a mathematical or statistical randomness will direct them to mathematics; however, courses in this discipline will tell them nothing about randomness. In pragmatic terms, sending gamblers “back to school” to learn the formal

mathematics applied in gambling would be of no theoretical help in correcting their misconceptions and fallacies, just because no mathematical course will tell them about the nature of randomness; only philosophical courses do that.

From the beginning of the 2000s, educational programs in problem gambling have been conceived as basing on the principle of awareness about the possible harms of gambling. Over the last decade, a cognitive-developmental model of educational programs, focused on correcting the gambling cognitive distortions, got contoured and is today in full advent. It is the experts’ responsibility to get assured that the concept of randomness is included and presented adequately in such programs, for rendering them effective.

References:

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

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