Understanding Deal or No Deal
Deal or No Deal has been a global television hit since the original, Dutch version of the show launched in 2000. It's simplicity appeals to a wide audience, and economists have praised the format as a prime example of natural decision making processes and game theory. As well as being re-made for TV in countless countries, Deal or No Deal has found great success online.
It is the latter format which is currently finding fans at popular gaming websites like Sky Vegas. At Sky's deal or no deal, you are presented with 26 boxes, each containing a different cash value. At the outset, you must pick one box to remain unopened until the end. The aim is to pick the box containing the top prize. A series of rounds follow during which you must open the remaining boxes to reveal their contents.
At the end of each round, the Banker will make an offer for your box, which you either accept or decline. Anyone who has seen the TV show will be familiar with the lurking presence of the banker, who phones contestants during play to make an offer. If the phone rings, the banker will make an offer of a guaranteed cash prize in exchange for the amount about to be won. Players must test their nerve and choose 'deal' to accept the banker's offer, or 'no deal' to refuse the offer and return to the game.
The online version allows for much the same probability calculations as the hit show. One basic strategy is for contestants to act in a way that maximizes the expected value of the prize. For instance, a contestant can calculate the average value of unopened cases, and accept any offer from the banker which is greater than that value, and declining it is less. Notably, the offers from the banker rarely exceed this value! Thinking from the perspective of the banker is a vital part of understanding the game theory approach to DoND.
As in real life, people have widely differing degrees of risk tolerance. This tolerance also changes as the value of the potential prize grows, since most people evaluate the utility of the money rather than the absolute value. So, for instance, if a player stands to win £300,000, the utility of that money is worth much more than the next £500,000, so their primary concern is with winning the £300,000.
Needless to say, these amounts of money are in a different league to the online version of the game. But the Skyvegas.com Deal or No Deal game is still a fun distillation of a true cultural phenomenon - one that number crunchers and statisticians will have endless hours of nerdy fun evaluating - and hopefully winning some cash from!