Deal or No Deal

[JoeImp]

I've recently watched a few episodes of this game show called 'Deal or No Deal.' If you don't know the game, go look it up, not going to explain it. Anyways, I decided to try and figure out a formula for computing how much the banker will offer. After doing some math, I googled around and found out that a number of people are also trying to do the same thing.

This page has some data for three different contestants (The last three tables/graphs.) http://wizardofodds.com/askthewizard/tvgames.html . Be warned that there's some computations and speculations on that site, if you wanted to try and work it out yourself first.

If someone else is bored, try computing a formula yourself. Don't read any farther if you're going to.








[SPOILERS]

First of all, I tried computed stuff using both data from the site I linked to and from the online game. The online game uses a strict formula, with a random multiplier for each game. Not going to go into that. For the actual show though, I believe they use a strict formula, but the banker randomly raises it higher or lower depending on how the contestant is doing, what he feels like giving the contestant, if he can get ratings up a bit, etc.

One way people have said to compute the estimated offer is by taking the amount of cash left in play, and just dividing it by the number of cases left. Most people believe this is an accurate estimate, I believe otherwise.

Here's a graph of the estimated offer calculated this way, vs the actual amount offered, with the data from that site above.

http://www.rit.edu/~jci7794/regressed_1.jpg

You can see there's a bit of correlation, but not much. Only accounts for 68.9% of the variation.

--

Now the way I came up with to calculate the offer, is by this formula:

Offer = (Cash left in play/Cases Left)(1/Number of cases to choose next)

The first round, the contestant has to pick 6 cases, next round 5, etc. That's what the 'Number of cases to choose next' means.

Here's a graph of the estimated offer calculated my way, vs the actual offer.

http://www.rit.edu/~jci7794/regressed_2.jpg

As you can see, the regression is a lot better. Accounts for 92.2% of the variability. I believe the other 7.8% is from the randomness of the banker, as stated above.

So the sum of all my research has come up with that formula for the regressed line at the top of the graph. 4595 + .6702(Estimated Offer(2)). Can anyone else get a line that accounts for more than 92.2% of the variability?

[/SPOILERS]

Why I'm spending some of my vacation doing statistics, I don't know. Pretty bored I guess.

[Weregoose]

I watched the show tonight (where the banker got a pie in his face) and had almost the same line of thinking, so I wouldn't worry. ;)

This provides a good response to question number three in this topic: Click

[myfavcolorchanges]

Wow, I was curious about that.
Thanks.