deal or no deal

[Rocco Moretti]

rbt wrote:

> The TV show on NBC in the USA running this week during primetime (Deal 
> or No Deal). I figure there are roughly 10, maybe 15 contestants. They 
> pick a briefcase that has between 1 penny and 1 million bucks and then 
> play this silly game where NBC tries to buy the briefcase from them 
> while amounts of money are taken away from the list of possibilities. 
> The contestant's hope is that they've picked a briefcase with a lot of 
> money and that when an amount is removed from the list that it is small 
> amount of money not a large amount (I categorize a large amount to be 
> more than 100,000)

Well, if the contestants' choices are truly random, and they stick with 
their first choice all the way to the end, each contestant wins, on 
average, $131 477.54 (sum(amounts)/len(amounts)).

Assuming that the buyout offer is always less than (or equal to) the 
average of the still-available amounts, NBC will (on average) never have 
to pay out more than ~$132k per contestant. Likely they'll pay out less, 
because most people will get nervous before the very end, and will take 
the low ball offer NBC is fronting.

What I would really like to know, is how they calculate the offer. 
Obviously, they set the upper limit at the average of the still standing 
offers, but I wonder if and how they take subsequent rounds into 
consideration. Is there a "Monty Hall" 
(http://en.wikipedia.org/wiki/Monty_Hall_problem) type consideration 
that needs to be taken into effect as cases are eliminated?