Write Angles

May 24, 2006

Deal or No Deal: Lucky Case Game

Filed under: Deal or No Deal,Math Videos,Puzzles/Games — Damon @ 6:50 pm

Yesterday I was showing students how to improve their odds at the Lucky Case Game. Today I realized they can’t play because they’re not old enough. Oops. You have to be 18.

So today I put a notice on the board forbidding them to play. (And they always read and comply with the notices on the board!) So if you are 18 or older continue reading to find out how to “beat the house” on the Lucky Case Game.

First of all, you should never use your cell phone to enter. They charge 99 cents per text message. You can enter 10 times online for free at Deal or No Deal.

About halfway through the show they display a bar graph showing the numbers that the rest of America is choosing. (Which is somewhat presumptuous–assuming that all of America is watching and entering the contest.) The key to improving your odds is in this bar graph. There is usually a number that is being chosen less often. I recommend waiting until you see this bar graph and then entering 10 times and choose the number(s) the “rest of America” is not picking.

Two things have to happen to win the 10,000 dollar prize. One, they have to pick the same number you choose. The probability of that happening is 1 out of 6. Two, they have to randomly select you out of the millions of people that chose that number. If ten million people chose that number the probability of picking you is 1 out of ten million. When these two probabilities are multiplied the final probability is 1 out of 60 million. If you pick the number that only 1 million people choose your odds become 1 out of 6 million. That’s 10 times more likely!

Okay I won’t be retiring in order to spend more time playing the lucky case game.

Update: I now have a Squidoo lens dedicated to Deal or No Deal.


May 22, 2006

Deal or No Deal in Math Class

Filed under: Deal or No Deal,Math Videos,Puzzles/Games — Damon @ 8:23 pm

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.

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