Today we watched an episode of Deal or No Deal in my Algebra 2 class. It worked out really well.
First, I asked a student to explain the premise of the show. Each contestant chooses a briefcase from 26 possible cases being held by models. Each case contains a certain amount of money ranging from $0.01 to $1,000,000. But nobody knows how much is in the chosen case. The contestant then picks other cases to open. The amounts in these cases are revealed which narrows down the possible amounts in the first case. Throughout the show the “banker” offers the contestant a certain amount of money to “buy” the case back, and Howie Mandel asks the question: Deal or No Deal?
While they were watching I asked the students to come up with reasons why the contestant should take the deal and reasons why she shouldn’t. I also asked the students to state whether or not they would take the deal.
(I know now to clarify that I expect the reasons to be mathematical. . . Students said things like, “Because she is stupid.” One student even concluded that the low amounts of money are in the cases being held by the ugly models!)
Anyway, the show offers an introduction to a whole host of mathematical topics. The most obvious is simple probability. The chance of picking the million-dollar case is 1 out of 26. However, other probabilities change as the game progresses.
If low amounts are revealed when opening cases, the banker’s offer goes up. As higher amounts are revealed the offer goes down. So the contestant wants to reveal lower numbers. For every round students could calculate the probability that the next case opened will increase the offer.
Students could also try and predict the banker’s offer. This introduces the more complicated concept of expected value which is basically the average of the amounts left. As the game nears the end the banker’s offer is very close to the expected value for the remaining numbers.
The show is also an interesting glimpse into psychology. Even though Howie says the banker wants the contestant to take the offer, it is clear that the early offers are low and they want the game to continue. Students could discuss how they would factor psychology into their calculations.
Finally, I showed students how to greatly improve their odds on the Lucky Case Game. (But I will have to save that for a future blog entry.)
Overall, it was a lot of fun and the students really got into it.
Update: I now have a Squidoo lens dedicated to Deal or No Deal.