Qualitative analysis of the reflection of the mathematical dimension
of gambling in gaming online content – Technical report no. 1
Cătălin Bărboianu, PhD
Mathematics is strongly connected to gambling through the mathematical models
underlying any game of chance. Mathematics is reflected not only in games’
design/characteristics and their outcomes, but also in gamblers’ perception and
knowledge of the mathematics-related facts of gambling – which influence their
The math-indispensability principle (Bărboianu, 2013) applies not only in problem-
gambling research, but also in the gambling industry. The structural, informative,
strategic, psychological, pathological, and ethical aspects of gambling have been
identified to be grounded in the mathematics of games and gambling (Griffiths, 1993;
Bărboianu 2014, 2015; Turner & Hobay, 2004; Harrigan, 2009, and others).
Gambling cognitive distortions, language, and miscommunication
Gambling-specific cognitive distortions (in the form of misconceptions,
misunderstandings, reasoning fallacies, biases, false or irrational beliefs, or illusions,
alone or mixed) are believed to be an important cause of the development of problem
gambling and are considered as major risk factors (Lambros & Delfabbro, 2007; Leonard
& Williams, 2016, and others). We have analyzed these cognitive distortions in relation
to the mathematical dimension of gambling and found that most of them are
mathematically related (Bărboianu, 2022, pp. 219-221).
An important element that shapes and influences the aspects of gambling mentioned
above, especially cognitive distortions, is language. The language of gambling can be
intentionally or innocently misleading, confusing or conflicting, largely due to the
mathematical nature of the essential concepts governing gambling, but also to the nature
of language itself. The language of gambling unavoidably uses mathematical and
mathematically-related terms and as such is a mixed language and therefore predisposed
to semantic conflicts. This language may aim toward descriptions of the games, of their
associated strategies, for communication between gamblers and between gamblers and
experts, and to express any observations or research results in regard to this phenomenon.
The fact that some specialized terms belong or are tightly related to probability theory
accounts for their conflicting potential in the gambling language, since the concepts of
probability theory are sensitive to interpretation, despite their mathematical nature
(Bărboianu, 2022, pp. 203-218).
The problematic gambling language manifests in the activity spheres of developers,
operators, gambling communities, information providers, experts (including problem-
gambling experts), and gamblers’ relationships with these people. This language affects
the descriptions of games and gambling that the players actually use to become informed
about the phenomenon; also affected are the communication between gamblers, and
between gamblers and people from the gambling industry or experts as well as gamblers’
own conceptual judgments related to gambling.
Goals and outcomes of the study
In this theoretical framework, research is able to derive concrete norms and criteria to
adequately reflect the mathematical dimension of gambling in the communication and
texts associated with the gambling industry. These norms and criteria of adequacy will be
further communicated to policy and decision makers in both governmental and private
sectors, with the recommendation for implementation.
Our study aims to evaluate qualitatively the reflection of the mathematical dimension of
gambling in the content of gambling websites. This analysis is necessary in order to have
an objective and concrete image of the actual state of this matter in the online industry
and of the challenges that such research and application would face in the real world of
A minimum number of 120 gambling websites will be reviewed annually for their content
in that respect. A statistical analysis will record the presence of the mathematical
dimension of gambling and its forms in the content of participating websites, and a
qualitative research will analyze and assess the quality of the content with respect to that
Methods and technical description of the instruments
The current study is a combination of quantitative and qualitative analysis, in which the
latter is predominant and is given the central role.
The participants in the study (gambling websites, through their webmasters) were
recruited through online advertising and direct invitations. Given the focus on the
qualitative aspect of the study, the sample is not representative for the entire population.
Besides, representativeness cannot be established with respect to the specificity of the
population (gambling websites) and of the targets of the study.
The criteria of eligibility for participation that we have applied are:
- not having legally prohibited content or advertising;
- meeting the gambling legal requirements;
- having informative content besides the games and games’ rules
- being fully operational and navigable.
The quantitative analysis will use basic descriptive-statistics methods, summarizing the
data recorded from the sample by standard statistical indicators, with the following main
v₁ - the presence of structural descriptions of the games in parametric terms (valued
v₂ - the presence of informative sections (‘How to’ articles, blogs, guides) (valued
v₃ - the presence of sections dedicated to odds/probability/math (valued yes/no);
v₄ - the usage of essential math terms specific to gambling (odds/probability, expectation,
average/mean, etc.) (valued yes/no);
v₅ - the presence of the definitions of the math terms used (valued yes/no);
v₆ - the correctness of the math definitions used (valued on a scale from 0 to 5)
v₇ - the presence of game strategy topics (valued yes/no);
v₈ - the presence of math-based game strategy topics where applicable (using notions of
probability theory, statistics, and game theory) (valued yes/no);
v₉ - the presence of systematic-learning or advanced content of gambling math (lessons,
academy-style sections, in-depth guides, etc.) (valued yes/no);
v₁₀ - the mentioning of author for math-related articles (valued yes/no);
v₁₁ - the match between the math-related articles and their authors’ declared expertise
(valued on a scale from 0 to 3);
v₁₂ - in-text presence of awareness on possible misconceptions, fallacies, and irrational
beliefs in regard to gambling (valued yes/no);
v₁₃ - the correlation of the above awareness with the mathematical aspects of gambling
(valued on a scale from 0 to 3).
The values are conditional on each other as follows:
v₃, v₇, v₉ conditional on v₂; v₅ conditional on v₄; v₆ conditional on v₅; v₈ conditional on v₇;
v₁₁ conditional on v₁₀; v₁₃ conditional on v₁₂.
The qualitative analysis will use as methods discourse analysis, content analysis, thematic
analysis, conceptual interpretation, semantic analysis, doubt about sense, and analysis of
arguments. It will have a strong component of linguistic-conceptual-logical analysis,
targeting the following main elements:
1 - the usage of terms with non-uniform semantics;
2 - the contextual usage of math terms;
3 - the conceptual linkages relative to the relevance for the topic;
4 - the soundness of arguments based on applied math;
5 - the association between game strategy and the concepts of probability theory and
6 - the presence and contextual impact of “mathematically prohibited” or misleading
terms (such as ‘winning strategy’, ‘how to win’, etc.).
Although the qualitative analysis is independent of the quantitative one, correlations will
be made between the conclusions of the former and the variables of the latter.
Representation of the mathematical dimension of gambling may or may not be adequate
in the content of gambling websites. The main goal of the qualitative analysis is to
establish the disciplinary areas, as well as their individual roles, which can contribute to
the theoretical framework that will derive the norms and criteria for such adequacy in the
content of the websites and of the gambling communication. These disciplinary areas
entitled for involvement include mathematics, psychology, linguistics, philosophy of
language, epistemology, and philosophy of mathematics.
Content and roles of the technical reports
Monthly technical reports describing the partial results of the qualitative analysis will be
published on academic channels, preceding the main publication at the end of the study.
Each technical report will cover the review and recording of data from ten websites,
which are nominated in the section titled Appendix, along with brief descriptions from
We found such technical reports necessary, first because the current study is atypical in
what concerns the statistical analysis and the qualitative analysis, as well as the objects
under investigation. Therefore, the main role of the technical reports is to detect and
define any methodological and technical difficulties encountered during this study and
any challenges they may pose, for them to be analyzed and surmounted in both the
continuation of the current study and any future similar research.
Besides presenting these difficulties and challenges, the technical reports will also
contain unpredicted observations regarding the analyzed content that might require the
revision or change of the methods and instruments used.
The results of the technical reports will be gathered, and general conclusions will be
drawn in the main publication.
Observations and conclusions from the review of the current sample
The first thing to note is that reading and navigation time exceeded our expectations. A
first issue needing optimization is that the content was actually double-checked – first for
the measurement of the variables of the statistical analysis, and second, with the reading
for the qualitative analysis. Some sections were cross-checked two times or more,
depending on how they are linked to the main content. This technical issue is due to the
fact that content is not linearly exposed (as in a written paper), but tree-like with not all
branches displayed at once, which is actually how any website is essentially organized.
Hence the issue applies to all the reviewed websites, no matter how effective their
navigation menus are.
The search for specific terms is made somewhat easier by using the text search tool of the
browser; however, this can work without reading the entire text only for measuring some
variables in the statistical analysis – variables v₄, v₁₀, v₁₂ and to a lesser extent, variables
v₇, v₈, v₉ – and checking element no. 6 in the qualitative analysis. The search tool is no
longer effective for the variables if the checked sections are also subject to the qualitative
analysis and as such need extensive reading.
As expected, the largest amount of time per section is consumed with the review of the
math-related targets of the qualitative analysis (no. 2, 3, 4, 5).
A website having expert gambling-math articles was detected, but it does not mention the
name of their author or authors.
The articles having the largest amount of applied math are those with poker topics. This
is explainable since poker is described by the largest number of combinatorial and
probabilistic models among all games of chance, and the objective strategies in poker are
probability- and statistics-based.
There are more similarities than differences among the websites reviewed. Although
content is organized differently, at its core it is very similar, at least for those websites
having affiliate casinos and no expert or advanced content. They label their sections with
almost the same names, which have been adopted in gambling slang, and apply a general
label for their main content, namely “guide.” The websites call themselves “guides,”
regardless of the level of expert contribution in their content (which can be seen right
from their brief descriptions in the Appendix) and regardless of any taxonomy for this
expertise. (They are just seen as ‘guides to gambling’ in general).
Although not included as a target of the qualitative analysis, it worth mentioning that
several websites provide ‘reviews’ of the casinos. Such reviews are not based on
comparisons, but rather, are individual reviews, looking together like advertising lists.
The main conclusion to be drawn after the first review pertains to the technique of
reviewing, which must be optimized with the aim of saving time to be dedicated to more
reviews over the unit time. The main processes to be optimized are reading and
searching. It should be investigated how software may help in this respect and what
software would be applicable and available for this task.
Appendix – Selective list of reviewed websites
bc.game (reviewed in October 2023)
Full-service online casino and sportsbook that supports deposits and withdrawals in many different
currencies, both fiat and crypto.
onlinecasinoinfo.eu (reviewed in January 2023)
A guide to gambling in online casinos for players in Europe. Expert picks and reviews for online European
professionalrakeback.com (reviewed in January 2023)
A guide to online gambling containing expertly-written poker, casino, sports and gambling news, articles,
btcgosu.com (reviewed in January 2023)
Bitcoin casino guide with up-to-date reviews of crypto gambling sites alongside analysis of the key aspects
of gambling with cryptocurrencies.
en.baste-sportive.com (reviewed in January 2023)
Online betting guide with a primary focus on sports betting. Football match previews and reviews alongside
sportsbook and bookmaker info.
bettingwebsites.org.uk (reviewed in January 2023)
General gambling guide covering sports, casino, gaming, poker and gambling psychology. Aimed at all
levels, from beginners guides up to strategy articles for experienced users.
bestcasinosites.net (reviewed in January 2023)
Site dedicated to the review and testing of regulated online casinos, providing information and advice for
potential casino players.
chipy.com (reviewed in January 2023)
A source of online gambling information aiming to help players learn about any casino game and online
gambling in general. In-depth guides written by industry experts.
slotsmate.com (reviewed in January 2023)
A source of user-generated casino and game reviews with focus on online slots. Gameplay video gallery
and editors opinions on games.
casinoreviews.net (reviewed in January 2023)
Information on everything related to gambling and iGaming: games, regulators, developers, live and land-
based casino reviews, news, and blog articles written by specialists.
Bărboianu, C. (2013). Mathematician's call for interdisciplinary research effort. International
Gambling Studies, 13(3), 430-433.
Bărboianu, C. (2014). Is the secrecy of the parametric configuration of slot machines rationally
justified? The exposure of the mathematical facts of games of chance as an ethical obligation.
Journal of Gambling Issues, Vol. 29, 1-23.
Bărboianu, C. (2015). Mathematical models of games of chance: Epistemological taxonomy and
potential in problem-gambling research. UNLV Gaming Research & Review Journal, 19(1), 2.
Bărboianu, C. (2022). Understanding Your Game: A Mathematician's Advice for Rational and
Safe Gambling. PhilScience Press.
Bărboianu, C. (2022). Qualitative analysis of the reflection of the mathematical dimension of
gambling in gaming online content – project. Philscience. Retrieved from
Griffiths, M. (1993). Fruit machine gambling: The importance of structural characteristics.
Journal of Gambling Studies, 9(2), 101-120.
Harrigan, K. A. (2009). Slot machines: Pursuing responsible gaming practices for virtual reels
and near misses. International Journal of Mental Health and Addiction, 7(1), 68-83.
Lambros, C. & Delfabbro, P. (2007). Numerical reasoning ability and irrational beliefs in
problem gambling. International Gambling Studies, 7(2), 157-171.
Leonard, C. A., & Williams, R. J. (2016). The relationship between gambling fallacies and
problem gambling. Psychology of Addictive Behaviors, 30(6), 694.
Turner, N. E., & Horbay, R. (2004). How do slot machines and other electronic gambling
machines really work? Journal of Gambling Issues, Vol. 11.