Monday, February 27, 2006

Deal or No Deal Redux

The NBC game show Deal or No Deal resumes with new episodes tonight. I described the game when it first ran in December where we discussed the game from the player's perspective. Now let's look at the game from the view of the Banker.

Suppose the Banker always offered the expected value of the remaining cases. Could a player somehow make smart choices to increase his or her expected winnings? No. Let X be the random variable representing the value of the briefcase held by the player. Let Y be the random variable describing the briefcases open so far. A well known equality states E(E(X|Y))=E(X), i.e., the expectation of the expected value of the briefcase given the current game situation is just the original expectation of the briefcase. Any strategy by the player will yield exactly the same expected winnings, about $131,477.54.

Usually the Banker gives an offer below the current expected value of the briefcase. Why? As I mentioned in the previous post, the players are risk adverse and may accept a smaller guaranteed amount now. But more importantly a lower amount will increase the chances that a player will not accept the deal and play longer. The Banker pays an expected $131K per player not per episode and thus pays out less per episode the longer each player plays.


  1. I wonder if an "insurance" company could win by insuring the candidates $100,000, and, in exchange, requiring them to eliminate all but one suitcase and giving that amount to them (the insurance company).

    Does anyone know the actual average winnings of contestants?

  2. During the game, viewers at home can play:

    There are six cases, and one of those contain $10,000. Viewers can vote for which case contains the money. In theory, the $10,000 is equally likely to be in any one of the six cases. About half way through the show, viewers can see how the rest of America is voting and for some strange reason, the distribution is always bell shaped.

    It seems very strange.

  3. i would like to vote for case number 4 on the 10,000 case my name is betty bevil 178 pr 4283 decatur texas 76234

  4. I would like to know how to send in the entry for the $10,000 contest on Deal or no Deal. I put in 59595 and hit ok. Then I put the case number I chose in the body of the message. I get an answer back saying that my entry is invalid and I have to put the letter of the case in. How can I do that when the cases are numbered and not lettered?

  5. I would like to know how to qualify for the show Deal or no Deal? I would love to be on the show and try to win the millon dollars.My husband and I want to buy a ranch that is 500 acres to help unfortune people get back on their feet and start a fresh new life.
    Thank you for taking time to read my comment.

  6. can anyone please tell me what the winning case was for the 10,000?

  7. Is there a telephone number to call instead of a text message for the $10,000 contest?I would also like to know how you get on the show, its fantastic
    Thank you.

  8. Er... the correct phrase is "risk averse"