I suspect the number is somewhat arbitrary. You want an even number, so the board will look nice. I suspect the amount of floor space in the studio for the models is also a factor.

]]>Or is that just what fit easily on their board with the desired font size?

]]>WRT the amount that the banker offers, there have been a lot of discussions in various forums about his algorithm. It is based on the expected value, but with a bias. Towards the beginning of the game, the amount offered is significantly less than the expected value. As the game progresses, the offers approach the expected value. If a contestant holds out to the very end, the last few offers sometimes actually exceed the expected value by a small amount. The idea here is that they don’t want contestants taking the early deals (since it makes for a boring show), and they want the contestants to have to make really hard choices near the end of the game (the agonizing over decisions, and the resulting conversations keeps things interesting for the audience.)

There is, however, a certain amount of randomness to the biassing. Identical configurations of the board do not result in identical offers. I think this is purely random, just to keep the game unpredictable, but some believe that the variation is deliberate, in order to keep the more-interesting contestants on TV longer than the less-interesting ones.

The algorithm used for the TV show is not known, but the algorithm used for the NBC on-line version is well documented. It was a fixed non-random formula until recently. Today, it’s a random percentage of the expected value (with the random-percent envelope increasing as more cases are removed.) You can see the details here.)

(No, I don’t watch the show that much, but my brother frequents several math and gaming newsgroups, and this was a frequent topic for discussion when the show was first on the air.)

]]>Of course, it’s a bit of a catch 22 if you were trying to stack the deck. If you put the high numbers in the “good/popular” places, whether it be by model or number, there is a better chance of knocking out high values, but a better chance of having one in your case too. LIkewise the question of do people keep what they like or pick what they like.

Thus I don’t think they could gain much by trying to “stack” the deck. Too many human nature variables.

]]>The next obvious question is, do the producers of the show know these general preferences, and do they factor that into their decision (or pseudo-random algorithm) of which models start out with which dollar amounts? Would they try to create perceptions that certain models always (or at least often) have low dollar amounts (good news to the contestant who picks them)? I wonder…

]]>one thing I notice is that they try to make the bankers offers seem so taylored and personal, based on his measure of the person, but I think they are computed straight off some actualrial formula. They practically admit this when they do the hypatheticals once a person has picked a case. You would have picked case X, the amount in that case was Y, and the offer would have been Z.

Another side note of sociology interest is the models. Totally gratuatous eye candy, right? Not necesarily. Just as some people have lucky/favorite numbers, I’ve seen some contestents with opinions about the models themselves. One guy the other week wasn’t selected cases by number, he was calling out the model’s name. Each time Howie would have to mention the case number so the audience would know what he had selected. Until then, I didn’t really realize that the models always stayed in the same place, but since then I can see how avid watches would come to learn the personalities of the various models and that could have meaning for them.

]]>On the one hand, it’s a simple case of computing expected value. The person offering the money is “playing the game” every week for dozens of weeks, so all he has to do is offer enough so that, in the long run, they can pay the advertisers. The law of large numbers guarantees that they will make up for any short term losses in the long run; which is the same reason that casinos make money.

So this guy offers the contestant a little less than the expected value of the game at that state. It’s always a winning proposition for him.

But the contestant only plays the game once. They have to balance the opportunity to win the payoff of a lifetime, and the thrill of risking a “loss” (which does have its own subjective value). They don’t have a long run strategy. It’s interesting.

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