Gambling Mathematics online course

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As a result of suggestions and requests received from many gamblers and problem-gambling experts, and also noticing the necessity of an adequate gambling-mathematics education, PhilScience is organizing and maintaining an online course for Gambling Mathematics. All details of the course, including its thematic structure and rules, are posted on this page.

Our course in unique in the following respects:
- It addresses both the formal mathematical aspects of the games and gambling, and the knowledge required to deal with the mathematics-related elements of problem gambling.
- It is designed for an audience of students with minimal mathematical background (high school graduates).
- It is such structured so that students can attend a specific module dedicated to their preferred game.
- It aims to eliminate standard and non-standard gambling misconceptions and fallacies responsible for problem gambling, through adequate mathematical knowledge.
Due to the currently limited number of teaching personnel for this program, the number of participants will be limited at first to 20 students per course. Please send any questions regarding this course to info[at] (subject: "gambling mathematics course").

 Motivations for the course
- The books and other resources on gambling mathematics on the market cannot begin to cover the entire applicative spectrum of the subject and the training required for a correct application of the theory for all categories of readers, with respect to their varying levels of previous mathematical education. Thus, individual training is needed, starting with the “ABCs” and being suited also for players with little mathematical background.
- The mathematics of gambling is very broad, ranging from domains like probability theory, combinatorics, and topology to algebra and numerical analysis. The learning resources available on the internet do not offer an optimal selection of these domains and applications; such selection is absolutely indispensable to the practical goals, namely awareness and the use of mathematical results in gambling strategy. The available materials are isolated, unorganized, and presented in a commercial manner rather than a teaching manner, which is often confusing. The selection of only the notions and applications necessary to the player and their organization into an effective learning progression are needed, and these tasks can be accomplished only in a professional course.
- The existent educational and informative resources (including software programs) cannot provide the player with all possible mathematical results, covering any gaming situation and decision (these resources cover, at most, only general situations), and thus the individual development of calculus and application skills is truly necessary, along with the use of precalculated results provided only by verified and credible sources.
- In the absence of proper knowledge, the player is exposed to errors of conceptual interpretation of results taken from various sources, as well as to application errors. For instance, the probability concept is often interpreted exclusively statistically: for example, the outcomes of the "odds" calculators based on partial simulations are taken as probabilities, while in fact they are relative frequencies, approximations – more or less accurate – of the mathematical probability, the only concept that preserves the measurable character of the possibility of a gaming event to occur. Even when players operate with mathematical probabilities, many times they are not obtained using the appropriate probability field, or their evaluation prior to making a decision is done by comparing probabilities from different probability fields or irrelevant fields. A rigorous understanding of the mathematics of gambling is necessary in order to prevent such conceptual errors which have practical effects.
- The vast majority of players do not have an educational background which would allow them to study gambling mathematics through their own methods. Considering that the notions involved in gambling mathematics are based upon elementary concepts (sets, operations with sets, combinations, probability in a finite space, etc.), and the calculation processes are based on elementary calculus (operations with real numbers, basic algebraic calculus), a course having an applicative main goal can be developed and maintained so as to ensure the training of the player with no solid mathematical background, starting from the elementary notions and gradually developing his/her skills in obtaining the mathematical results and applying them.

 Goals of the course
- To familiarize players with those parts of the mathematical models behind the games that generate applications useful in game analysis and game strategy.
- To understand the necessary mathematical concepts, starting from the elementary notions and their adequate interpretation in the real game.
- To eliminate standard and non-standard gambling misconceptions and fallacies, responsible for problematic gambling, through adequate mathematical knowledge.
- To develop the skills of combinatorial and probability calculus specific to the gaming events.
- To develop the skills of calculation of all mathematical parameters and numerical indicators necessary for game analysis.
- To develop the skills of numerical estimation and approximation in a limited time.
- To correctly frame each application using the appropriate theoretical model.
- To develop the capacity of analysis of a gaming situation through probability criteria.
- To develop the capacity of removing irrelevant elements within such an analysis, so as to limit the heavy calculations.
- To implement the mathematical criteria within personal game strategies.
- To assure students are trained in solving concrete applications in a limited time (theoretical framing, calculations, applying precalculated results, use of external resources, and interpreting the data).

    General description of the course
The course will focus on the practical and applicative aspects of gambling mathematics, with the goal of the optimal use of mathematical information in a real game by any player. The course will operate on the understanding of theoretical notions necessary for the communication of mathematical information and in practical applications; however, it will be dedicated mostly to training in calculation and the proper use of available resources. The presentation and the flow of the course are adapted to a minimal level of players' initial mathematical education, having as its main goal the acquisition of the skills of application of theory through algorithmic procedures, rather than a deep understanding of the mathematical concepts involved.
The course will last about 4 months and will be structured on thematic modules containing 32-37 lessons (depending on the chosen game-specific module), delivered on average biweekly. It will have a static part consisting of the delivered lessons, as well as an interactive part, in sessions alternating with the lessons, consisting of: 1) answers to questions and issues of understanding arising from the previous lesson (maximum 5 questions per lesson, no calculation requests); 2) tests of acquired knowledge, with exercises/practical applications, which are returned corrected, containing recommendations for avoiding errors and improvement of the learning process; 3) case studies for open discussion. The lessons consist of a theoretical part, followed by practical applications, examples, solved and unsolved exercises (homework), the solutions of the exercises from the previous homework.

One module is dedicated to each specific game (Blackjack/Hold’em Poker/Roulette), which the student may choose according to his or her own preference. This choice does not influence the knowledge acquired through the common modules, which applies to all games.

course is not intended to be a gambling strategy course, but rather, a course that covers the mathematical aspects of the games which are necessary to an objective analysis and which generate criteria that can be further implemented in any personal strategy.
To download the thematic general structure of the course, its rules, terms, and conditions, click here

At the end of the course, the student will receive a diploma, which can be attached to any résumé applying to a job in the gambling industry and not only (such as coaching, for instance).

Instructional personnel
The course is conceived and supervised by Dr. Catalin Barboianu, who also maintains the interactive sessions with the help of an assistant.

The unit fee of the course is $25 per lesson ($250 for the first module, $800-925 for the entire course, depending on the chosen game-specific module). The fees may be paid in full at the time of registration, or in part; a partial payment must cover one complete module. Players may organize in groups at the fee for one student; however, only one member of the group can participate in the interactive sessions.

You can register for the course by completing the registration form below and sending it to address orders[at] (subject “gambling math course registration”). The only requirements for registration are the following: minimum 18 years of age and completion of high school studies, declared on registrant's own responsibility. Registration is limited to 20 students per class. If the course is already full when you register, you will be informed of this and you will remain in the queue to enroll in the course when a place becomes available.


Download registration form

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