Deal With It

Many people have heard of the game show, Deal or No Deal, but it seems few have seen it from beginning to end. It stars Howie Mandel, who was a comedian in the distant past, and often acted like this little kid. Since then, he's shaved his head, and gotten extremely paranoid about people touching him. Either he's over it, or he's particularly masochistic by being a game show host.

I've probably blogged about it, but I'll just spend this entry on the rules, which seems to defeat folks. I figure this might help me explain it again if I have to.

First, there are 20 briefcases. Inside, there is a label (think of it as a card, if you like) with an amount from say 5 dollars up to 1 million dollars. You are the contestant, and you're goal is to win as much money as possible. Your goal is to pick the suitcase with a million dollars in it (it's not really your goal, but we'll get to the actual goal in a moment).

At this point, you pick out one briefcase. Admittedly, you only have one chance in 20 to guess correctly. Furthermore, although you have selected it, you don't get to open it.

Next step. There are 19 women, each standing by the remaining 19 briefcases (the women are somewhat incidental to the show--the idea, presumably, is the show is actually pretty dull, and so pretty women help spice it up). You will go through several rounds.

In each round, you pick some number of briefcases. To make it easy, each briefcase has a number from 1 to 20. Note: you have one of the twenty with you.

Thus, in the first round, you are told to pick 5 cases. Here's the key. Those 5 cases are eliminated from the game. That's usually the confusing part. People don't expect the selection to be eliminated.

For each case you pick, the case is opened up, so you see what amount is inside, and therefore, what amount has been eliminated. Thus, if you see $100, it's been eliminated. There's a huge board showing which amounts have not been eliminated and which have. Contestants typically want eliminate the smallest amounts.

So far, the game seems silly. You are eliminating cases, but to what end?

This is the part that makes it interesting. Each time you eliminate some cases, there is a banker who bids an amount. That amount is typically much smaller than the largest amount on the board. Indeed, it typically is less than the average amount of all remaining amounts you could possibly win. Say, there is 10, 50, and 100 dollars still remaining. The banker is likely to bid less than about 50 dollars, which is the average of the three.

Notice you still have a chance to win 50 or 100 dollars. So the question is, do you take the amount the banker is offering, or do you continue to eliminate more cases, hoping the smaller amounts disappear, and the banker will make a higher bid.

The rules are a bit fuzzy when it comes down to the case you are holding. Since the odds are pretty small that you have picked the million dollar case, the contestant almost never waits until they get to their case at the end. They almost always accept the bid of the banker, especially after they've made a mistake and the bid has gone down because they have picked a case with large amounts and eliminated it.

My guess is that if it ever came down to two cases: one by a woman, and the one you picked, they would make you decide whether to take the banker's bid or to open the case by the woman (thus eliminating and picking your own case). I had thought maybe you could pick the other case's amount, but that wouldn't be so consistent with the rules.

The reason people with math backgrounds find it silly is because the contestants clearly don't know how to compute the odds or the expected value, so they simply run on gut feeling, and often go on far beyond what they should.

My rule of thumb is that if you ever reach 200,000, stop. You're good. Even low 100,000 is pretty good. Of course, you can look at odds and such, but it's amazing how many people want to go for half a million, even though only two cases have at least that amount.

Anyway, those are the rules of the game.