Probability?
Deal Or No Deal
Briefcase Presenters
•
•
•
•
Violette Espinoza, Rickard’s MS
Sonia Kimbrough, Forest Glen MS
Wendy Moskowitz, Taravella HS
Lisa O’John, Forest Glen MS
Goals of Presentation
- Students are given the opportunity to explore
probability and mean in a fun and familiar
real-world context.
- Students will apply mathematical
reasoning to everyday decision making.
Florida Sunshine State Standards
New Standards
• MA.7.P.7.2
• MA.7.A.3.2
• MA.8.A.6.2
Let’s Play a Game!
For Example
Game 1
First Suitcase
$10
Second Suitcase
$20
Third Suitcase
$30
Game 2
First Suitcase
$5
Second Suitcase
$10
Third Suitcase
$45
Game 3
First Suitcase
$0
Second Suitcase
$0
Third Suitcase
$60
Formula Intuitively
Game 1
Median
10  20  30
 20
3
Game 2
5  10  45
 20
3
Game 3
0  0  60
 20
3
20

10
0
Which game is most skewed and why?
What is Expected Value?
Expected Value (EV) represents
how much money one can
expect to win or lose in a game.
The Expected Value is also known
as the mean.
A Mathematical Breakdown
Game 1
1 
1 
1 
E(V )   10   20   30
3
3
3
1
Factor out .
3
Therefore, we will get the following :
1
10  20  30  20
3
A Mathematical Breakdown
Game 2
1 
1 
1 
E(V )   5   10   45
3
3
3
1
Factor out .
3
Therefore, we will get the following :
1
5  10  45  20
3
A Mathematical Breakdown
Game 3

1 
1 
1 
E(V )   0   0   60
3
3
3
2 
1 
E(V )   0   60
3
3
Therefore, we will get the following
2
1
0  60  20
3
3
:
How to apply formula to
Deal or No Deal
• Deal or no Deal is a chance-based TV show.
• A player is given a gallery of 26 closed, moneyfilled briefcases.
• Ranging in value from $.01 to $1,000,000.
• The game is simple because there is no
content knowledge involved, but
understanding EV can help a player decide
what to do.
Formula for Expected Value of
Deal or No Deal
26
E(X)   x i * P(x i )
i1

Formula of EV
26
EVevent   x i * P x i 
i1
What do these symbols and words mean?
∑ = sum
xi = represents the amount of money in each suitcase
at that given moment.
P(xi) = the probability of the outcome happening.
Formula for Expected Value of
Deal or No Deal
26
E(X)   x i * P(x i )
i1
1
x1  .01  P(.01) 
26

1
x 2  .1  P(.1) 
26
1
.01*
+
26
1
.1*
+... +
26
1,000,000 * 1
26
          
$131,478  E(X)
How to apply formula to
Deal or No Deal
This total represents the average or mean of
what a player can win. This number is the way
that contestants can determine if the banker’s
offer is reasonable.
Worksheet for Students
• This worksheet can be used to calculate the
Expected Value at any round of the game.
• An Excel worksheet can also be used.
Let’s Play a Game!
First Question?
• 1. What role does “your briefcase” play in
Computing the EV in the game as a whole?
Answer:
The briefcase is still part of the EV, but the value of the briefcase is unknown.
Second Question?
• 2. How do you compute the EV after each
round in Deal or No Deal?
Answer:
We take the sum of all the opened cases, and then subtract it from the total
amount ( which is $3,418,416.00). We then divide the amount by the
remaining unopened cases.
Third Question?
• 3. How does the EV change throughout
game play?
Answer:
The expected value changes based upon the remaining values of unopened
cases.
Fourth Question?
• 4. How do the Banker’s offer and the EV
compare following each round?
Answer:
The Banker’s offer is generally lower than the EV.
The patterns that we analyzed was a 70% decrease of the EV within the first
2 to 3 rounds. As we continued to play,
Fifth Question?
• 5. During which period does the Banker
want you to deal or no deal?
Answer:
The banker usually wants you to accept the deal early in the round.
References:
1.) www.ithaca.edu/faculty/cduncan/311/pascallong.doc
”The Expected Value Theory of Rational Choice”
2.) “Winning Big Money”, Mathematics Teaching
in the Middle School, Vol.14, No.6, February 2009
SOME MATH JOKES
Teacher: “Who can tell me what 7 times 6 is ?”
Student: “It’s 42!”
Teacher: ”Very good!- And who can tell me what 6 times 7 is?
Same Student: “It’s 24!!”
Q: How does a mathematician induce good behavior in her children?
A. I’ve told you n times, I’ve told you n+1 times….
Mathematicians never die—the only lose some of their functions!
Q: What does the little mermaid wear?
A: An Algae-bra.
THE END
⏎
MA.7.P.7.2: Determine, compare and
make predications based on
experimental or theoretical probability
of independent or dependent events.
⏎
MA.7.A.3.2: Add, subtract, multiply and
divide integers, fractions and
terminating decimals and perform
exponential operations with rational
bases and whole number exponents
including solving problems in everyday
contexts.
⏎
MA.8.A.6.2: Make reasonable
approximations of square roots and
mathematical expressions that include
square roots and use them to estimate
solutions to problems and to compare
mathematical expressions involving real
numbers and radical expressions.