Pre Calculus
Probability group project
A group of 2-3 students and a willingness to have fun and think outside of the box.
Task:
Your task is to use your knowledge of probability, expected outcomes/rate of returns and what is fun to you and
come up with a carnival game of chance for our class. Your game needs to be based on probability, not skill.
(no bean bag tosses etc.) It cannot be a game that already exists - you must create a unique game. The game
should take a relatively short time to play, so it can be played several times in class. You must be able to
explain the probability of your game so don’t make it too complicated.
The goal is to create a fun game that your peers will want to play. You will want to come up with a game that
has a positive expected value for the house (you) but one where the players feel like they can win too. You will
decide how many tokens the game will cost. Prizes/payouts must be clearly visible so the participant knows
what they could possibly win.
You will be judged by your peers and the teacher. Carnival day is Thursday, March 29th.
The Write-Up
1. Introduction - Provide an overview of your game. (1 Per Group)
• What type of game is it?
• Where would you play this type of game?
• How much does it cost to play?
• What are the prizes if you win?
2. Instructions - Step-by-Step instructions for how to play the game. (1 Per Group)
3. Game Description – What do you need to play the game? (1 Per Group)
• List all materials needed to play (dice, spinner, darts, ball, etc.)
• Draw picture of your game board, if necessary
4. Probability Analysis (1 Per Group)
• Create a probability chart for each possible outcome and compute the payoff.
• Show the mathematical calculations for the expected value of winning the game.
• Is the game fair? If the game is not fair, how could you change the game to make it fair?
• Write up the actual payoff that occurred during the carnival. Show the number of trials and what
happened and compare that with the mathematically expected return of your game.
• Calculate what you would expect to make/lose if your game was played 100 times.
5. Reflection – Each student must write a 1-page reflection (1 Per Person)
• What were your overall feelings about this project?
• Did this project help you understand the probability any better?
• How did your group work together?
• Relevance: What have you learned about “Fair Games”? What is your opinion about Las Vegas and
the gaming industry? Do you think it’s fair to have establishments designed for people to lose
money? What is your opinion on the lottery? Would you advise your grandmother to play? What
do you think about gaming casinos?
Your responsibility as a carnival participant:
1.
2.
3.
4.
Write down the name of the game you are playing. (you must try at least 5 different booths)
How many times did you play the game? (1-5)
What was the value of the prizes/money you walked away with? Or how much money did you lose?
General impressions of the game.
Your responsibility at the booth:
1. Write down every trial and the outcome of the trial. (you need to keep track of this while you man the
booth).
2. Be friendly and encourage people to try your game.
To turn in (April 3rd start of class):
1. The Write-Up [30 pts]
2. Packet of all members tally sheets. [5 pts]
3. Packet of all members actual payoff work that occurred while they were at the booths. [5 pts]
Tally Sheets
Name of the game:
Number of times I played:
Net result of the trials:
Overall impressions of the
game:
Name of the game:
Number of times I played:
Net result of the trials:
Overall impressions of the
game:
Name of the game:
Number of times I played:
Net result of the trials:
Overall impressions of the
game:
Name of the game:
Number of times I played:
Net result of the trials:
Overall impressions of the
game:
Name of the game:
Number of times I played:
Net result of the trials:
Overall impressions of the
game:
Name of the game:
Number of times I played:
Net result of the trials:
Overall impressions of the
game:
Grading
Rubric:
CATEGORY
Game
Instructions
Group WriteUp
Probability
Analysis
Individual
Reflection
Neatness and
Organization
5
4
3
2
Students create a fully
functioning game that
students can play. They
bring all of the game
materials to class.
Instructions are clear
and easy to follow. The
game can be played by
others without referring
to the game creators for
help.
Group has
comprehensive writeup including:
introduction,
instructions, game
description and
probability analysis.
The write-up has been
thoughtfully prepared
and provides insight
into the actions of the
group.
Group provides
accurate analysis of the
math behind their
game. The idea of a fair
game is clearly
explained in terms of
their project and an
alternative for making
their game fair is
presented.
Students create a game
that students can play.
There may be slight oversights, but overall the
game can be played.
Instructions are
somewhat clear and easy
to follow. The game can
be played by others with
minimal interaction with
creators of the game.
Group has write-up
including: introduction,
instructions, game
description and
probability analysis. The
write-up provides some
insight into the actions of
the group.
Students create a
game, but it cannot
be played in class.
Students have an idea
for a game.
Group has written
instructions but
they are unclear
and a verbal
description of the
game is necessary.
Group has an
incomplete writeup including some
of the following:
introduction,
instructions, game
description and
probability
analysis.
Instructions are
incomplete.
Group provides
somewhat accurate
analysis of the math
behind their game. The
idea of a fair game is
explained in terms of
their project. An attempt
at providing an
alternative for making
their game fair is
presented.
Reflection attempts to
explain students thought
process during the
project. The relevance of
the project is described.
Group provides
some analysis of
the math behind
their game. The
idea of fair game is
mentioned.
Group attempts some
sort of analysis of their
probability.
Reflection attempts
to explain students
thought process
during the project.
Some attempt at a
reflection is made.
The work is presented in
a neat and organized
fashion that is usually
easy to read.
The work is
presented in an
organized fashion
but may be hard to
read at times.
The work appears
sloppy and
unorganized. It is hard
to know what
information goes
together.
Reflection clearly
explains students
thought process during
the project. The
relevance of the project
is clearly described.
The work is presented
in a neat, clear,
organized fashion that
is easy to read.
An attempt at a writeup is made.