As a result of
suggestions and requests received from many poker players, either
beginners or professionals, and also noticing the necessity of an
adequate mathematical approach to the game, the Applied Mathematics
Department of Infarom Publishing is organizing and maintaining an
online course for Hold'em Poker Mathematics.
All details of the
course, including its complete structure and rules, are posted on this
page. Due to the
limited number of teaching personnel for this project, the number of
participants will be limited at first to 20 students per course.
Please send any
questions regarding this course to
"poker mathematics course").
Motivations for the
- The books on poker 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 no mathematical background.
- The mathematics of poker 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 goal, namely the use of
mathematical results in game 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 poker is necessary in order to prevent such conceptual errors which
have practical effects.
- The vast majority of players do not have a mathematical background
which would allow them to study poker mathematics through their own
methods. Considering that the notions involved in poker 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 mathematical background, starting from the elementary
notions and gradually developing his/her skills in obtaining the
mathematical results and applying them within his/her game strategy.
of the course
- To familiarize players with those parts of the mathematical models
behind the game 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
- To develop the skills of combinatorial calculus specific to poker
- To develop the skills of probability calculus specific to the
gaming events from poker.
- To develop the skills of calculation of all mathematical parameters
and numerical indicators necessary for hand and game analysis.
- To develop the skills of numerical calculation of the probability
formulas holding variables, including the use of calculation programs
- To develop the skills of numerical estimation and approximation in
a limited time.
- To select, use, and manage optimally only the appropriate external
resources (tables with precalculated odds and statistics, software
programs) and to avoid resources having no rigorous mathematical
- To correctly frame each application using the appropriate
- To develop the capacity of hand analysis through probability
- To develop the capacity of removing irrelevant elements within a
hand analysis, so as to limit the heavy calculations.
- To implement the mathematical criteria within personal game
- To obtain optimal organization, management, memorization, and
applying of the precalculated numerical results.
- 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
General description of the course
The course will focus on the practical and applicative
aspects of poker mathematics, with the goal of the optimal use of
mathematical information in a real game by any player, regardless of
his/her previous mathematical education. 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 14 weeks and will be structured on
thematic modules containing 2 lessons weekly. It will have a static
part, consisting of 28 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. 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. This course is not intended to be a poker
strategy course, but rather, a course that covers the mathematical
aspects of the game which are necessary to an objective analysis and
which generate criteria that can be further implemented in any personal
To download the
detailed structure of the course, its rules, terms, and conditions,
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 poker business (such as coaching, for
The course is conceived and supervised by Catalin Barboianu, and the
interactive sessions are maintained by the team of mathematicians from
The unit fee of the
course is $25 per lesson ($200 for the first module, $700 for the entire
course). 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. The course can be
stopped at any time and resumed at a later date.
You can register for the course by completing the registration form
below. 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.