# How does the banker calculate his offers in the tv show Deal or No Deal?

Asked by

Perchik (

4982)
February 11th, 2008

I assume it has to be something with expected value of the person winning, but I cannot figure it out. Does anyone know this formula?

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## 10 Answers

Yeah I’d really like to understand this too. You’re right though, its got to be some sort of statistical function of the amount player has already acquired, the amount remaining and the number of cases that remain.

After poking around the internet there doesn’t seem to be a solid answer. It’s something like the statistical mean * (turn number /9 ) but that doesn’t seem to be the case always.

According to Wikipedia, the offers are based on (but usually aren’t exactly) the arithimic mean (average) of all the remaining values.

There’s got to be an algorithm that defines “based on”. Usually the offers are at least 20% off of the mean of the remaining values.

Maybe it is just TV “hocus pocus”. I mean, who says they are actually doing real math there? We would never know. There are those times when the person “Takes the deal!!” and then Howie asks what the next cases he/she would have picked. The offers the banker gives make no sense to me at that point. It is all just show, to make the person/fans think he/she could have won more. Oh wait… not that I watch that show. ;-)

well it’s actually that part that makes me think there’s a formula. NBC obviously wants to give away as little money as possible while keeping the image that they make somewhat fair deals

If the offers on the show were based upon a simple algorithm, we would have a very boring show on our hands. In order to stay somewhat unpredictable they probably generate a random amount within a given tolerance of the expected value. My guess is that tolerance grows or shrinks based on the person playing. They use trends and tendencies to determine the structure. Most of the people on that show tend to be outgoing which I would assume would suggest they are riskier. Plus they are being watched nationally so they have added pressure of wanting to please an audience. etc. Every factor about the contestant probably helps determine the range of the offer, but the strongest factor is definitely the expected value and the min – max range left on the board. This show is actually providing a dream study of risk tolerance for individuals from an economists prospective. I think the banker is actually doing a little experimenting to see what people are willing to pass up. If I was writing my undergrad econ thesis now, I would be very tempted to gather data based on decisions made by different races, genders, regions, etc. on this show.

there must be a formula of some kind. i do not know math in any sense so i am going to give a few links. maybe the math whizzes will get it. all i know is HOW can you offer TWELVE $1 million slots on the board and people STILL lose? i would say basically it is impossible to win the million. even though there are only 26 cases, human fear tends to end the contest early.

Enter probability theory, and more specifically, the value that you can expect to earn based on the number of remaining suitcases and their associated dollar amounts. Not surprisingly, this is astutely named – wait for it – the expected value.

http://www.pearsonified.com/2006/03/deal_or_no_deal_the_real_deal.php

Deal or No Deal: Gambling With Math!

http://www.mydollarplan.com/deal-or-no-deal-gambling-with-math/

Meanwhile in Deal or No Deal nothing is predestined. Let’s assume on Deal or No Deal the amounts remaining were $0.01, $1, and $1,000,000. With three cases left it IS possible that the opened case will contain the million dollars. The following table shows the possible outcomes with three cases left. Remember, the player can not open his own case.

http://wizardofodds.com/askthewizard/tvgames.html

Beating the Banker: Game Theoretic Applications in Deal or No Deal PDF

http://www.isveum.com/research/DoND.pdf

Deal or no deal formula

http://www.davegentile.com/stuff/Deal_or_no_deal.html

The key to the winning strategy is to decide on the respectable take-home payout you’re after, and Accept the Deal when you have only one lottery prize left on the board. As long as you have two big prizes left, you can open another case and still have a reasonable offer

http://sourcery.blogspot.com/2006/03/how-to-win-on-deal-or-no-deal.html

Since the range of possible values for cases is known at the start of each game, how much the banker offers at any given point changes based on what cases have been eliminated. To promote suspense and lengthen games, the banker’s offer usually strays from the expected value dictated by probability theory, particularly early in the game.[1] However it is not uncommon for the bank’s offer to exceed the player’s expected value very late in the game.

http://www.answers.com/topic/deal-or-no-deal?cat=entertainment

It is **not** human fear, as you say, that ends the game early. On any given turn, if the bankers offer exceeds the statistical expected value, you should walk. The expected value (arithmetic mean) is called that, because that is the value that you should expect to win. If you are offered more than the expected value, you should take it and leave. Example, if you’re told that you can flip this coin. Heads you win nothing, tails you win 10$. Or I’ll pay you 6$ to not flip the coin. IN theory you shouldn’t flip the coin (because your expected value is 5$.)

However on deal or no deal, human greed takes over logic. Last night the lady was offered 266,000 $ and then the banker offered to double that, if she kissed a frog. Her expected value at this time was right at 275k. She was being offered 532k (if she kissed the frog.) But she was so sure that her case contained 1mil, that she gave it up. She ended up wiping out the remaining 3 million dollar cases, and ended up leaving with 166k. No logic, just greed.

I agree there’s a degree of teasing in the offers, beyond statistical risk.

Now, the show **I** would like to see would be “1 vs. 300”, where you match wits with a horde of Spartans!

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