
Deal or No Deal? Expected Value, Utility Theory, and the Role of the Banker
Marsha Davis, Michael A. Jones, Brittany Shelton & Jennifer M. Wilson

Mathematics Topic: Probability 
Application Areas: Various 
Prerequisites: Students need to be familiar with function notation and
basic ideas about probability. 

This PullOut consists of three activities.
The context for Activity 1 is a school’s
fundraising carnival. Students calculate
the expected winnings for each game
and then determine which game should
be the preferred game from the player’s
point of view. This context is briefly
revisited at the start of Activity 2.
Some
players might be attracted to the spinner
challenge from Activity 1, a game in
which players lose, on average, over a
dollar per game. That’s because the
spinner challenge has the highest maximum
payout of all the carnival games
and some players are willing to take the
risk for a chance at getting the highest
payout. In Activity 2, utility functions
are introduced as a tool to quantify how
much someone values money.
The
shapes of utility functions’ graphs give
students clues about whether a person is
riskaverse, riskneutral, or riskfriendly
toward money. In Activity 3 students
apply what they have learned about
expected value and utility functions to
the game Deal or No Deal. Together these
activities introduce a framework to
think about decisions under conditions
of uncertainty that can be applied to any
reallife (business, political, testtaking,
etc.) situation.
These activities address the following
standards from the Common Core State
Standards for High School Mathematics: SMD.5, FIF.1, FIF.2, FBF.4(a), FBF.4(c)
