Deal or No Deal?

This is going to be a busy week. Grades are due, report cards need to be run, conferences held, course selection sheets distributed and collected. I am way behind on my grades, and I am still working on the final exam schedule. Plus my high-speed kit should arrive, and that will get my immediate attention.

But there is something I am looking forward to: my combinatorics* class is taking a detour into probability and expected value, culminating with some simple analysis of the awful game show "Deal or No Deal." I like this description:

it is one of the more brain dead game shows created. At the beginning of the game, a contestant stands in front of 26 models holding briefcases in their hands. Each briefcase contains a particular dollar amount, ranging from one cent to one million dollars. The contestant picks a briefcase but does not get to look at the dollar value in that case. She then proceeds to pick a half dozen briefcases, the dollar values of which are revealed. As each case is picked, its dollar value is removed from the board of potential winnings. Once the first six cases have been chosen, a fictitious "Banker" is asked what price he will pay in exchange for the case held by the contestant (this is perhaps the most glamourous job ever held by a statistician …). In theory, the Banker knows no more about the contents of the contestant's briefcase than does the contestant herself. If the six cases eliminated were all low numbers, the Banker will offer a number in the tens of thousands of dollars. If the cases revealed high numbers, however, thus indicating a higher likelihood that the contestant holds a low dollar value in her chosen briefcase, the Banker will offer a buyout of mere thousands. The contestant then has to choose to take the offer based upon the information available or risk potential losses while turning over some more cards. The case picking and Banker offers continues until the contestant either takes an offer from the Banker or has chosen all of the cases and gets to reveal what is in the briefcase she originally picked.

*Combinatorics? In my school students are required to take math every year (New York State requires only 3 years of math). In senior year most take precalculus or calculus. Some, however, met their match in trigonometry. For those students we provide discrete electives for senior year. Also, there are other students who want a discrete elective in addition to their regular math. So we provide (and yours truly teaches) a discrete elective each term. In the fall it was logic, now it is combinatorics (basically – counting, not accounting).

Combinatorics Links (simplest first): Wiki link, The Mathematical Atlas Link, Mathworld Link

So, this game show is a bit of a detour, but I have been given lots of leeway. I am trying to decide if I actually need to show an episode in class (that would be the week after this one). And when we are done, I will post the results of our simple analysis. (The real world is more complicated, but at least they will have an engaging complication).