Deal or No Deal is the name of several closely related television game shows, the first of which (launching the format) was produced by Dutch producer Endemol. It is played with 26 cases with certain sums of money. The Player chooses a case to knock an amount of money off the board.

Gameplay
Deal or No Deal is played in many different ways around the world. Many different countries have their own version or versions of the show, each with version-specific twists on the same general format. The general format is described here.

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The central game of Deal or No Deal involves a contestant, a banker, and a host/presenter who acts as MC for the game. The game revolves around the opening of a set of numbered boxes each of which contains a different prize (cash or otherwise). The contents of all of the boxes are known at the start of the game, but the specific location of any prize is unknown. The value of each of the boxes is indicated by a label or card sealed within it.
The contestant claims (or is assigned) a box to begin the game. The box’s value is not revealed until the conclusion of the game.
The contestant then begins choosing cases to be removed from play. The amount inside each choice is immediately revealed; by process of elimination, the amount revealed cannot be inside the player’s chosen box. Throughout the game, after a predetermined number of boxes have been opened, the banker offers the contestant an amount of money and/or prizes to quit the game, the offer based roughly on the amounts remaining in play and the contestant’s demeanor. The player then answers the titular question, choosing:
“Deal”, accepting the offer presented and ending the game, or
“No Deal”, rejecting the offer and continuing the game.
This process of removing boxes and receiving offers continues, until either the player accepts an offer to ‘deal’, or all offers have been rejected and the values of all unselected boxes are revealed. The player wins the value of the deal taken, or if no deal is taken, the contents of the player’s box.
Should a player end the game by taking a deal, a pseudo-game is continued from that point to see how much the player could have won by remaining in the game. Depending on subsequent choices and offers, it is determined whether or not the contestant made a “good deal”, i.e. won more than if the game were allowed to continue.
Since the range of possible values is known at the start of each game, how much the banker offers at any given point changes based on what values have been eliminated. To promote suspense and lengthen games, the banker’s offer is usually less than the expected value dictated by probability theory, particularly early in the game[1]. Generally, the offers early in the game are very low relative to the values still in play, but near the end of the game approach (or even exceed) the average of the remaining values.
Only a few people have ever won the top prize on any version of the show (see table below). For a contestant to win the top prize the player would have to select the case containing the top prize and reject every offer the banker makes during the game. While the chances of a player selecting the top prize are reasonable (4-5% depending on how many amounts are in the game), the chances that a player will be able to turn down a number of inevitably large offers to win that top prize are much smaller.
International versions
Various versions of Deal or No Deal have between 20 and 26 prizes in the game; some versions have only cash values, others include prizes such as a car or booby prizes. For instance, there are 26 cases in the prime time U.S. version, containing cash values from 1 cent to $1,000,000. The daytime U.S. version only has 22 values, ranging from $.01 to $500,000. Alternately, the Australian version has 26 values from 50 cents to $200,000, but includes a car as one of its more valuable prizes. The U.K. version of Deal or No Deal has 22 boxes which contain anything from 1 penny to £250,000.
The stopping points at which the Banker places an offer vary wildly from format to format. In a small number of variants, the Banker knows the locations of the prizes.
In some versions, a player who rejects all offers is given the option to swap the initially selected case for the last unrevealed case before revealing the contestant’s final prize. Some versions even allow the banker to offer the opportunity to swap in lieu of a cash offer during game play.
Some versions occasionally add side games, with or without impact to the central game.
There are also scores of variations in presentation otherwise having little or no effect on the central game.   
Worldwide, the largest active-play offer made (after adjusting for exchange rates) is €1,495,000 on Dutch version Miljoenenjacht, offered on November 13, 2005. The offer was accepted, and stands as the biggest win in the history of the format, despite many versions (either occasionally or permanently) having higher top prizes.
Scientific research
Deal or No Deal has attracted attention from mathematicians, statisticians, and economists as a natural decision-making experiment. A team of economists has analyzed the decisions of people appearing in European and US episodes of Deal or No Deal and found, among other things, that contestants are less risk-averse or even risk-seeking when they have seen their expected winnings tumble. In their follow-up article they find that contestants behave similarly in ten different versions of the show, despite large differences in the amounts at stake; amounts appear to be evaluated in relative terms, for example in proportion to the initial average, and not in terms of their absolute monetary value. The research project received a great deal of media attention, appearing on the front page of The Wall Street Journal on January 12, 2006 as well as being featured on National Public Radio in the United States on March 3, 2006.

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