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Using Videogame Poker to Learn Probability
Research Proposal
Submitted by
Adam R. Carberry
May 2, 2005
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Table of Contents
Abstract
2
Introduction
3
Research Question
4
Research Goals
4
Technology Description
5
Research Methods
8
Sample
8
Design
8
Data Collection
9
Data Analysis
9
Deliverables
9
References
10
Appendices
11
1
Abstract
Students today are more interested in their video gaming systems than they are
about schoolwork. One way to combat this plague is to teach students in a way that
seems like a game. In this study the mathematical concept of probability is introduced
through this ideology via the popular game of poker. Using such a game addresses the
need to make learning more interesting and fun while also making learning more inquirybased and discovery oriented. Students can learn about permutations, n-factorials and
probability all while playing a game and learning strategies based on these concepts
(Packel, 1981).
2
Introduction
If you have 40 students in a class and none of them understand the mathematical
concept of probability, what is the probability of randomly selecting a student who cannot
do probability problems? The answer in this question when calculated is one, but it
shouldn’t be the final answer. Why? The question should be responded to with another
question asking why is it that students are having difficulty with probability. Is the
concept too difficult? Are teachers teaching it ineffectively? What is the reasoning
behind all the difficulty? The answer is three-fold lying in the teaching approach, the
inability to consider all possibilities and the lack of interest (Peard, 1996). As it is with
many subjects, students are asked to memorize a number of equations. These equations
are then in turn used to solve problems, which have no real life bearing for the students.
Learning in this sense is also designed in a way that focuses on knowing the equation as
opposed to understanding the equation. As a result the operation becomes mechanical
and just accepted without thought or reasoning (Garfield & Ahlgren, 1988).
In order for students to learn, understand and retain probability more efficiently,
there are three main changes that need to occur:
1) a learner-centered approach to teaching should be employed
2) understanding should be integrated along with content
3) content should be related to real life to spark interest
Through the use of games and technology, these three changes can be achieved
resulting in a better understanding of probability (Beasley, 1989; Miller, Charles, Vern,
Heeren & Hornsby, 1997). This proposal looks to investigate the specific integration of
videogame poker as a new approach to learning probability (Emert & Umbach 1996).
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Research Question
1. Can the game of poker assist students in learning the concept of probability?
Research Goals
Implementation of videogame poker to improve learning of probability looks to
incur three changes: 1) create a learner centered environment for learning probability, 2)
teach understanding along with content and 3) spark interest.
To use a learner-centered approach requires that students have the ability to
experiment and figure out many concepts on their own. Discovery of “new” ideas gives
meaning and a sense of possession to the students. A higher number of students thrive in
this environment as compared to rote memorization typically enforced in a teachercentered atmosphere. Through the use of a game such as poker, students will be
intrigued to play the game and learn what they can do in order to perform better.
Along with allowing students the ability to work on an inquiry-based level,
students will be taught reasoning behind the theories. This can be accomplished by
students formulating their own hypotheses/equations and determining why they work or
don’t work. This method will combat the lack of understanding correlated with a student
who memorizes an operation or conjecture. It is evident that understanding is not only
essential in order to perform a particular task, but understanding leads to a much higher
retention rate of concepts (Ramsey, 2002).
For the previous two changes to be sincerely effective, students need to be
interested in the subject. Students don’t care about the probability of choosing a red
marble over a blue marble. They are however interested in games. Poker is just one
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game that is fun and interesting to all age levels. The benefit to poker over other games
is that it requires a high level of thought, understanding and knowledge of probabilities.
Technology Description
The poker videogame that will be used in classrooms will be a hybrid of what can
be bought commercially or used online. The first alteration will be three designed levels
of play. The first stage will be an introductory level. In this level, students will inquire
about possible permutations using playing cards. Users will be presented with tasks that
ask how many possible combinations are possible. The program will propose a number
of questions to the students making them focus on what is required for one permutation:
1) When filling the first empty slot, how many possibilities do you have? (4)
2) When filling the second empty slot, how many possibilities do you have? (3)
3) When filling the third empty slot, how many possibilities do you have? (2)
4) When filling the final empty slot, how many possibilities do you have? (1)
Students will be taught that they can determine all the possibilities by making a chart but
that their technique is tedious and impractical if there are a high number of combinations.
The teacher can then ask the students to make some broad generalizations.
Following the first introductory stage of discovering permutations and
determining a number of broad generalizations, a second intermediate stage will be
presented to give the students problems to solve and to introduce the concept of the nfactorial. These slightly more difficult problems will lead students to discover that in
order to determine the desired number of permutations they need to determine the total
number of permutations and remove the permutations that are repeats through a
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mathematical calculation. Students’ previous generalizations for one permutation will be
modified into a more systematic way identifying with the concept of n-factorials:

n ways of picking the first slot

(n − 1) ways of picking the second slot

(n − 2) ways of picking the third slot

1 way of picking the last slot
Once the concept of permutations and n-factorials has been discovered by the
students they are ready for the third and final stage. In the third stage, students are
introduced to probability and the actual game of poker. With less instruction than the
previous two stages, students are shown that poker is a game of 52-cards where players
bet based on a five-card hand. Students are shown the types of hands possible and then
asked to determine the likelihood (probability) of obtaining one of those hands in a 52card deck. Students are asked to produce Table I.
Table I: Poker Probabilities
Hand
# of Ways
royal flush
4
0.000002
0.0002
straight flush
36
0.000014
0.0014
4 of a kind
624
0.000240
0.0240
full house
3,744
0.001441
0.1441
flush (not a straight)
5,108
0.001965
0.1965
straight (not a straight
flush or royal flush)
10,200
0.003925
0.3925
3 of a kind
54,912
0.021128
2.1128
2 pairs
123,552
0.047539
4.7539
1 pair
1,098,240
0.422569
42.2569
nothing
1,302,544
0.501179
50.1179
total
2,598,960
1
100
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Probability Percentage (%)
The stage then allows for students to play the game of poker within their class in a
manner which allows the teacher to monitor the activity. Each student is presented with a
hand of cards that the teacher can see. Before students can bet, they are asked to
determine and input the probabilities relating to their particular hand.
Because this approach is discovery based, throughout the game students will be
introduced to common terms involved with probabilities. Terms defined will include the
terms permutation, n-factorial (n! = n (n − 1) (n − 2) (n − 3) . . . 1) and probability. After
it has been shown that the students have at least a basic understanding of how to calculate
probabilities, common notation used with determining the number of combinations will
also be related in order to allow the students to understand common conventions. Here
are three notations used to represent the number of permutations:
1)
nCr
2)
C (n , r)
3)
 n
 
 r
where n is the number of different distinct objects that can be chosen and r is how many
objects are chosen (C is simply to identify the function as “choosing”). Notation should
not be introduced earlier to avoid confusion on the part of the students. Notation will
simply be described as a short hand notation of what they have been doing the entire
time.
Example questions and screens for the program can be seen in Appendix I.
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Research Methods
The following methodology is designed to determine the advantage of using video
poker games to teach probability over standard teacher-centered techniques.
Sample
The following study will be conducted in two 3rd or 4th grade mathematics
classrooms. Both classes, containing approximately 30 students per class, will be taught
by the same teacher. One class will be taught the concept of probability using
standardized teaching techniques (control group) while the other class will be taught
using videogame poker (test group).
Research Design
The two classes will each be taught probability. Students in the control group will
be taught probability through the use of a mathematics textbook. As with standard
teacher-centered methods, the students will memorize the equations and definitions
incorporated with probability; do examples (in class and at home) and take quizzes and
exams on the material.
The students learning probability in the test group will be presented with a
number of tasks using the poker videogame as opposed to performing a number of
repetitive pencil and paper calculations. Using the poker videogame, students will
discover permutations, n-factorials and probability on their own, at their own pace. As
their understanding of the concepts grows, they will advance in stages to a point where
they are strictly playing the game of poker allowing them to practice their probability
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calculations. After completion of the videogame stages, students will be tested to
determine their knowledge of probability.
Data Collection
The groups will each be given the same exam in order to determine the ability to
perform probability related calculations. These grades will be used as quantitative data.
Both groups will also be sporadically video-taped to analyze the ways in which the
students interact with their teacher as well as with the material. A select number of
volunteer students will be interviewed from both groups to gain more insight into their
scores and how they felt about learning probability.
Data Analysis
Analysis will be conducted on the three sources of data: test grades, video-taping
and interviews. Grades between the control and test groups will be compared to
determine which approach was more effective at teaching probability. Video-taping and
interviews will be coded to identify good and bad language related to learning
probability. The coded videotapes and interviews will be correlated to the exam grades
to gain more insight into understanding the test results.
Deliverables
From this study I plan to publish results showing that the use of videogame poker
can teach students the mathematical concept of probability better than standard
methodologies.
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References
Beasley, John D. (1989). The Mathematics of Games. Oxford, England: Oxford
University Press.
Emert, J. and Umbach, D. (1996). Inconsistencies of "wild-card" poker. Chance
9(No. 3):17-22.
Garfield, J. and Ahlgren, A. (1988). Difficulties in learning basic concepts in
probability and statistics, Journal for Research in Mathematics Education, 19, 44-63.
Miller, Charles D., Vern E. Heeren, and E. John Hornsby, Jr. (1997).
Mathematical Ideas. 8th ed. Reading, Massachusetts: Addison-Wesley Educational
Publishers, Inc.
Packel, Edward W. (1981). The Mathematics of Games and Gambling.
Washington, D.C.: Mathematical Association of America.
Peard, R. (1996). Difficulties teaching probability, Teaching Mathematics, 21(1),
20-24.
Ramsey, James B. (2002). The Elements of Statistics with Applications to
Economics and the Social Sciences. p. 215-219. New York, NY, USA: Duxbury Press.
http://mathforum.org/library/drmath/sets/select/dm_poker.html
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Appendix I: Example Problems
Stage 1: Introductory
Example: Students are given 4 cards that all read the same number but are obviously
different suits (: hearts, : diamonds, : spades, and : clubs). The students are asked
to determine the number of possibilities of arranging the 4 cards in the below boxes
(work can be done on paper and imputed into the game).
   
Table I: Possible permutations for four choices.
1
2
3
4
5
6
7
8
9
10
11
12
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
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Stage 2: Intermediate
Example: Students are given the same four cards as before with the same value but 4
different suites. Students are asked how many different ways they can make a 4 of a kind
(Table IIa), a 3 of a kind (Table IIb) and a pair (Table IIc) with the 4 cards given? Once
they determine the answers are 1, 4 and 6 respectively, a group discussion asks how they
came to their conclusions?
Table II a: 4 of a kind possibilities,

1

Table II b: 3 of a kind possibilities;
2
3
4
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4!
=6
2!2!
1
2
3
4
5
6

4!
=4
3!1!

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
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1
Table II c: pair possibilities,
4!
=1
4!1!

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Stage 3: Advanced (Actual Poker Play)
Figure 1: Complete odds sheet which can be calculated by each student based on a 52card deck.
Figure 2: Calculated odds based on the individual game being played.
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Figure 3: Teacher’s screen allowing for the teacher to analyze how the students are
playing.
Figure 4: Final poker table where students can just play.
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