Deal or No Deal?

During Winter Break, I watched an unusually high number of game shows since my grandmother, who loves game shows (and cheesy Indian soap operas), was at home. The most interesting one, by far, was Deal or No Deal (http://en.wikipedia.org/wiki/Deal_or_No_Deal). Why? Because I can’t figure out if the show is pure genius or pure stupidity.

On the one hand, the game is just a measure of contestants’ risk tolerance. When more briefcases with large dollar amounts are opened, the probability that the contestant possesses a briefcase with a low dollar amount is higher; and vice versa. Contestants usually choose to reject the first few offers, either out of greed or a love of being on TV.

On the other hand, the genius of the show might be in how the deal is calculated. The deal seems to be computer-generated; if so, the Banker is there only ‘for show’. At first, I thought that the deal was just the expected value of the remaining amounts. The expected value is the remaining dollar amounts x the probability that they will be selected. But, this turns out not to be the case. I sat with my laptop and Excel open a few times while watching the show and the deal turned out to be lower than the expected value. Clearly, a more advanced algorithm is at work. The algorithm probably changes, as do the rules of the game, from time to time.

To his credit, Howie Mandell is an entertaining host. And while most game shows are high energy (The Price is Right, Family Feud, etc.), this one is larger than life given all its melodrama. But to me, nothing is more satisfying than watching a greedy contestant reject a deal and end up with a low amount. It’s like watching NASCAR for the car crashes!