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about deal or no deal
Deal or No Deal is a television game show format owned by Dutch-based production company Endemol, known for creating such shows as Big Brother. The basic format of Deal or No Deal consists of a number of cases (usually 26, but varies in some countries) each containing a different amount of money. Not knowing the sum of money in each case, the contestant picks one case which potentially contains the contestant's prize. They then open the remaining cases, one by one, revealing the money they contained. At predetermined intervals the contestant receives an offer from the bank (run by "The Banker") to purchase the originally chosen case from the contestant, the offer being based on the potential value of the contestant's case. The contestant must then decide whether to take the deal from the bank, or to continue opening cases. If the contestant decides not to take the deal and reveals low value cases, then the next bank offer is likely to be higher (as the contestant's case is proven not to contain these low values). Alternatively, there is risk in revealing higher values, lowering future offers from the bank. This feature makes for an exciting and suspenseful game.

The format of Deal or No Deal varies in each country. In the UK version, for example, contestants choose from 22 boxes rather than 26 briefcases. The concept of pitting a contestant against an in-house adversary (in this show, the Banker) is unusual, though not unique, among game shows.

Will someone win the top prize?
It is interesting to consider the likelihood that a contestant will actually win the top prize in a case. In the following discussion, "$1,000,000" represents the top prize value (as is the case in the United States), and the number of boxes in the probability model is equal to 26 (as per the US version). This number varies depending on the location of the show.

In order to win $1,000,000, one must

choose the right case, and
must never accept a deal.
or

keep the million dollars on the board with 2 left and
switch cases at the end of the episode
A contestant chooses the right case with probability 1/26. However, deals near the end of the game usually

are closer than usual, but still less than the expected value of the remaining cases, but
accurately account for the contestant's risk tolerance in determining the difference between the deal and expected value of the remaining cases.
The following example illustrates the need for the banker to assess the contestant's risk tolerance. Imagine if there are two cases left, one with $1,000 and one with $1,000,000 (i.e. high variance). The banker is contemplating how much to deal. If the contestant is, for example, a billionaire, a $400,000 deal would probably not be accepted as it is far below the mean value of $500,500. That same $400,000 deal would be very attractive, however, to a contestant living in poverty.

This article is licensed under the GNU Free Documentation License.
It uses material from the http://en.wikipedia.org/wiki/deal or no deal.

External links
Australian version, on [Seven]
French version, from TF1
Bulgarian version on Nova Television
German version on Sat.1