 The mathematical facts of the
games as information
 Since games are developed around
their mathematical models, these models
actually define the games in the realm of gambling. There are two
types of mathematical facts that define a game of chance: its
parametric configuration and its probabilistic & statistical
results. The first type defines the game because it is indispensable
to its creation and the second because it involves the only
mathematical concepts related to its “chance” feature (namely, to
generate outcomes under uncertainty).
 Parametric configuration is
a basic numerical assignment for the game’s components participating
in game’s functioning and rules and is established by game’s
producer. It is also part of the mathematical models as a basic
hypothesis. For example:
  There are 52 cards in a regular
card deck, of which 13 values (from 2 to A) and 4 symbols (clubs,
hearts, spades, diamond), each value being paired with each of the 4
symbols on the cards. This is part of the parametric configuration
of a card game; 52, 13, 4 are parameters defining the game. Other
parameters add to this configuration when considering a specific
card game, with specific rules (for instance, the number of cards to
be discarded in draw poker, the number of community cards in Texas
Hold’em poker, etc.).
  There are 2 dices, each having 6
numbers on its faces in craps. Certain sums or numbers stand for the
winning rules. All these numbers form the parametric configuration
of the craps game.
  In slots, we have a parametric
configuration of the reels, consisting in the number of reels,
number of distinct symbols, number of stops on each reel and the
symbol distribution on each reel; we also have a parametric
configuration of the display, consisting in the topologic
arrangement of the lines and paylines, the length of the paylines,
etc. See more details on slots parametric configuration here.
 The probabilistic & statistical
results are mathematical facts derived through applications within
the mathematical models and are grounded on the parametric
configuration of the game. These include odds/probabilities attached
to the various gaming events and statistical indicators such as
expected value, house edge, volatility index, etc. Our sections on
gambling mathematics in this website
provide a good amount of essential probability results.
 In the virtue of their defining
feature explained at the beginning of this paragraph, both the
parametric configuration and the probabilistic & statistical results
can be considered as both knowledge and information (There is
a distinction between the two terms (Turban
& al., 2004).)


 The exposure of the
mathematical facts of a game as an ethical obligation

Exposing the parametric configuration of a game to the player
prior to playing is an ethical obligation in two aspects – one
commercial and the other humanitarian (Barboianu,
2013).
 The
commercial aspect treats the game as any commercial service, for
which full technical specifications are required from the
producer to the customer; a bet is still a purchased service
once the player inserts a nonreturnable coin in the machine.
 The
humanitarian aspect is related first to the free will of thought
and second, to the limitation of the risk factors through
further improved knowledge. Being informed on all parameters of
a game one plays is a condition for unconstrained personal
thinking leading to personal actions. It is as if someone asks
you to bet you can jump from a high place and land on your feet;
of course, if you know in advance the height from which you will
jump, or measure it before you bet, you might decline the bet or
propose another one for a certain measurement, and this means
free decision.

Regarding the limitation of risk factors through further
improved knowledge, this knowledge may be acquired either as
precalculated numerical results such as winning odds and other
statistical indicators, or by learning theoretical and applied
probability theory basics. The latter variant relates directly
to the cognitive contributions of mathematics in problem
gambling.


 Where to draw the line
between ethically required and optional information?
 The ethical obligation being
established, the question arises as to whether this obligation
should remain simply the parametric configuration of the game or
be extended to include basic or advanced mathematical results
coming from applications worked out on the mathematical model of
that game. The extension could consist of basic precalculated
numerical results, such as probabilities of the basic winning
events and expected value, or stretch further to more complex
gaming events and other statistical indicators, and the
interpretation of these results. The latter variant already
assumes a new level of mathematical knowledge, attainable only
through didactical intervention. For the
parametricconfigurationonly variant, which is merely
informative and either provided by the game producer or
retrieved by third parties, it would remain for the player to
inquire further for the mathematical results as an optional
action. The question, then, clearly becomes where to draw the
line between ethically required and optional information on the
mathematical facts of games of chance.
 On
the entire range of mathematical information possible to be
exposed, as the amount of information increases, there are three
specific levels as seen in the next figure: parametric
configuration, basic numerical results (odds of winning and EV),
and knowledge of the mathematics of gambling presented in a
specific teaching module.

 Figure. Dividing the range of the mathematical information
for a game of chance between ethically required and optional
information.
 If assigning the two aspects –
commercial and humanitarian – of the ethical obligation over the
range of the mathematical information, the commercial one covers
only interval I, while the humanitarian aspect could stretch
theoretically to the endpoint of interval II, if enhanced
mathematical knowledge can have an impact on gambling behavior.
 At
first glance, the best option seems to lean toward
position 2, which also has the highest number of corresponding
examples from other domains; however, further interdisciplinary
research is necessary for a rigorous standard, including how
"best" should be defined in this particular ethical context.


The slots case

Slot machines
gained and maintained this popularity despite some specific elements
that could limit their appeal:

a)
nontransparency: Players do not know the configurations of the
machines they play at, as this information is not exposed. Blackjack
players know the composition of the decks in play, roulette players
know the numbers on the wheel, lottery players know the numbers from
which the winning line is drawn, and so on. Slots remains the only
game in which players are not aware of the essential parameters of
the game, such as number of stops of the reels, number of symbols
and their distribution on the reels. For more on slots parametric
configurations, click here.

b) prevention from
odds estimation: Obviously, the lack of data regarding the
configuration of a machine prevents people from computing the odds
of winning and other mathematical indicators.

The socalled PAR
sheets (Probability Accounting Reports), exposing the weighting of
the reels, some of the probabilities associated with the winning
combinations, and other statistical indicators, are kept secret by
game producers.
 Recent research (Barboianu,
2014) showed that there is no rational justification for this
secrecy by giving two reasons, one psychological and the other
mathematical. For the latter, mathematics provides us with some
statistical methods of retrieving the missing data, which are
essential for the numerical probability computations in slots. Click
here for an overview on these statistical methods and the project
Probability Sheet for
any Slot Game. For more on slots mathematics, click
here.


Resources for the information
 The
information required to be exposed as parametric configurations
would be in the form of a technical/mathematical sheet specific to
each game, consisting of those parameters of the mathematical design
of that game that define the sets of possible outcomes and are
essential toward probability and statistical computations. For
example, in slots the parametricconfiguration sheet must show the
number of distinct symbols, number of stops of each reel, and the
symbol distribution (weighting) of each reel. In a card game, the
number of decks used, the number of cards in each deck, and the
composition of each deck (numbers of card values and symbols) are
known. With a drawing machine (for example, lottery or bingo), the
total number of numbers/balls, their value interval, the number of
numbers/balls to be drawn, and so on are likewise known.
 The gambling mathematics knowledge
may be acquired by gamblers via instructional means
(gamblingmathematics courses in schools or private organizations,
experimental interventions) or specific media (books, journals,
magazines, and websites). Of course, the structure and content of
such gamblingmathematics resources vary and the existent courses
usually follow the curricula of regular Introduction to/Basics of
Probability and Statistics classes in postsecondary schools, with
the focus on applications of these disciplines in gambling.
Regarding the latter category of resources, the plethora of popular
literature on gambling mathematics published in the last decade
raises the necessity of critical selection and professional
certification when it comes to a recommendation. This is because
such commercial publications serve various scopes, wide or narrow,
and the information delivered by them can be useful even if
incomplete, but also misleading (as is the case with most of the
socalled “how to win” or “strategy” titles, in which the
mathematical information or systems described are not mathematical
at all). In any case, credentials of the authors and publishers of
such publications must be verified.
 This website provides you with
basic information on gambling mathematics
for the most popular games (especially probability results).

Further research is needed to establish the optimal content and
organization of the basic mathematical information with respect to
the ethical obligation and whether it can be comprised in the form
of warning messages similar to the warning messages used in the
prevention of other addictions. Projects forthcoming such research
may be devoted to the development of the optimal informative modules
and the technical ways of exposing them.

References
Barboianu, C. (2013). The mathematical facts of games of
chance between exposure, teaching, and contribution to cognitive
therapies: Principles of an optimal mathematical intervention for
responsible gambling. Romanian
Journal of Experimental Applied Psychology, 4(3), pp. 2540.
Barboianu, 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, 29,
pp.123.
Turban, E., Aronson,
J. E. & Liang, T.P. (2004). Management support
systems : an overview. Decision Support Systems & Intelligent
Systems, seventh ed., pp.223. Upper Sadle River: Prentice Hall.
This entry should be cited as:
 Barboianu, C.
(2014).
InformativeEthical Contributions of
Mathematics to Problem Gambling.
Retrieved from
http://probability.infarom.ro/ethical.html.
back to Problem
Gambling index
Sources 
The
content of this section is based on resources from our
Articles and Books
sections, as well as other published research. 



