MDM4U Probability Games Project
Purpose:
The purpose of this project is to allow students the opportunity to
demonstrate their understanding of permutations, combinations,
experimental and theoretical probability, and discrete probability distributions.
Overall Course Expectations Covered
 Solve problems involving the probability of an event or a combination of events for
discrete sample spaces
 Solve problems involving the application of permutations and/or combinations to
determine the probability of an event
 Demonstrate an understanding of discrete probability distributions, represent them
numerically, graphically, and algebraically, determine expected values, and solve
related problems from a variety of applications
The Assignment
Students are to create an original, interesting, easy-to-play, and profitable game involving
dice, spinners, cards, or any other reasonable item. The outcomes of your game should
depend ONLY on the element of CHANCE.
Part 1: With a partner (max 3/group); prepare for the Game Fair
 Develop a game and the rules
 Conduct experimental trials and record data (min. 100 plays of the game)
 Discuss and develop calculations for theoretical probability values
Part II: Alone; Write a report of your Game
 Create graphs
 Write an analysis of the game with mathematical calculations
shown. Follow the Report Instructions attached.
Things to look for…
 Use of experimental probability
o Are the devices used (dice, coins, spinners, etc.) to simulate the event “good”
devices (ie. Do they produce random outcomes? Verify!)
o Playing the game over and over again (at least 100 times) and keeping track of
important events
o Graphs/diagrams/charts depicting the experimental probability (probability
distribution) of the event(s) along with the expected outcomes
 Use of theoretical probability
o Use of permutations and/or combinations where applicable
o Use of Venn diagrams/tree diagrams/Pascal’s triangle where appropriate
o Use of probability distributions to aid your calculations
o Use of graphs/diagrams/charts depicting the theoretical probability of the
event(s)
 Analysis of the results of experimental and theoretical probabilities
o Are they similar? Why or why not? A detailed explanation is required here.


Determining the expected value/winnings for your game
o Is the game fair for all players? Justify your answer.
Game strategies
o Is there a winning strategy for playing your game?
Rules for “Games Fair” Games
 Each game will require ALL participants to pay either one or two ‘DATA DOLLARS’
 ALL prizes must be payable in full ‘Data Dollars’ (i.e. in one dollar increments. For
example, a prize cannot be $1.50 or 75 cents)
 Operators may not charge any further fees after the player has paid his initial $1 or
$2 game fee. (For example, a player cannot land on a “Pay another $2”)
 The operator must post the expected value for his or her game, as well as the
probability distribution for the possible prizes (winnings)
Games Fair:
The high stakes Games Fair will take place over two days. On the first day of the Games Fair,
half of the class will be players, the other half will operate the games they have created. On
the second day, the roles are reversed.
Operators:
On the day that you operate your game, you must have DISPLAYED






A description of how your game is played
A list of items needed to run your game
A chart showing how a player can win and how much a player can win
A chart showing the theoretical probabilities of all possible winning amounts
A player's theoretical expected value
Calculations showing how you determined the theoretical probabilities and the
theoretical expected value
You will also need some kind of tally chart in which to record every outcome for each time
your game is played.
Players
On the day you are playing, you will be also be critiquing the games. You must play each of the
games a minimum of 5 times, and provide a detailed critique of each.
Each player must play every game at least three more times (more if possible) so that each
student collects enough data for his or her report.
WINNING!
On Games Fair days, each player and each operator will receive an initial thirty ‘Data Dollars’.
If an operator or player no longer has enough ‘Data Dollars’ to award a prize or continue
playing, bankruptcy is declared and $30 is borrowed from the ‘Data Bank’ (Your teacher). At
the end of each day of Games Fair, the player and the operator with the most ‘Data Dollars’
are declared winners. Bankrupt players and/or operators are not eligible for a prize. There
will also be a “Player’s Choice” award for the game the players liked the best.
Disqualification:
If a player suspects that a game operator has not quoted the theoretical expected winnings
accurately, he or she may challenge the game to the ‘Bank Manager’. The ‘Bank Manager’ will
then check the operator’s chart showing outcome probabilities and expected value. If the
‘Bank Manager’ calculates that the players expected value is not correct as quoted, the
operator must continue to operate his or her game and collect data, but will not be eligible to
win.
MDM4UI
Games Fair: Player Critique
Game Name: _______________________
Evaluated by: _______________________
Game Operator(s):____________________
Very Clear: No problems understanding what has been displayed
Clear: One or two questions/assumptions needed to understand what is displayed
Not Clear: Three or more questions/assumptions needed to understand what is displayed
Game Display
Very Clear
Clear
Not Clear
Missing
Description
play the game
3
2
1
0
Includes how to play the game and what items are needed to
“How to Win” Chart
3
2
1
0
“How Much You Can Win” Chart
3
2
1
0
“Theoretical Probabilities” Chart
winning amounts
3
2
1
0
Should show the theoretical probabilities of all possible
Player’s Expected Winnings
3
Calculations shown
winnings shown
3
2
1
0
Calculations for all theoretical probabilities and expected
Overall Impression
2
Outstanding
3
Pretty Good
2
1
0
OK
1
Total: __________/21
Suggestions for Improvement:
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
MDM4UI
These descriptions are
from the rubric
distributed in class
Knowledge of experimental
and theoretical probability
of simple events
Knowledge of Counting
Techniques
Knowledge of Probability
Distributions
Selects appropriate tools
and strategies to solve
problems
Makes connections
between mathematical
concepts of probability and
the analysis of a simulation
of a game of chance
Selects and applies
problem solving strategies
to solve problems and
make connections to a
simulation
Applies reasoning skills to
justify conclusions and
plan and construct
mathematical arguments
Expresses and organizes
ideas and mathematical
thinking/justification using
visual and written forms
BONUS
Peer critique(s) of games
appropriate
Game Fair Report Assessment
Name:
Not
Demonstrated
(+ 7 errors)
Limited
/Few
(5-7
errors)
Some
(3-5
errors)
Considerable
/Most
(1-3 errors)
High
Degree
(0 errors)
0
1
2
3
4
0
1
2
3
4
0
1
2
3
4
0
1
2
3
4
0
1
2
3
4
0
1
2
3
4
0
1
2
3
4
0
1
2
3
4
0
1
2
3
Not
Available
Teacher Evaluation of Displayed Game: ________________/21
Teacher Evaluation of Report: ____________/32
TOTAL: _______________/43 = ______________%