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]philscience.org (subject:
"gambling mathematics course").
Motivations for the
- 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
- 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
- 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.
of the course
To familiarize players with those parts of the mathematical models
behind the games that generate applications useful in game analysis and
- 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.
correctly frame each application using the appropriate theoretical
- 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
- To implement the mathematical criteria within personal
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
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.
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
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).
course is conceived and supervised by Dr. Catalin
Barboianu, who also maintains the interactive sessions with the help
of an assistant.
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.
can register for the course by completing the registration form below
and sending it to address
orders[at]philscience.org (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