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Deal or No Deal

I happened to catch a new game show on TV last night called Deal or No Deal after seeing an incredibly long line of people queueing on the sidewalk for open auditions to be contestants on my way home from dinner. The show itself is incredibly boring, but the mechanics of the game are kind of interesting.

The game starts with 26 briefcases, each of which represents a dollar amount, running from one cent to one million dollars (or in the case of last night’s show, two million dollars). The game begins when the contestant picks one of the briefcases, which contains the amount of money they’re playing for. The contestant then chooses other briefcases to open, revealing amounts of money that they didn’t pick. Periodically the “banker” calls then and offers them money to stop playing, based on the amount of money still in play.

Once the person has picked their initial briefcase, they eliminate five or six other briefcases, then the first offer comes in. On last night’s show, contestants never eliminated the big dollar amounts in this first round, so with the person having a 1 in 20 chance (or maybe 1 in 19) of winning the big money, the bank offered something like $23,000 to buy them out. As they eliminated briefcases without revealing the top prize, the amount offered by the bank would go up. In one of the games, the person got to a point where there were four briefcases left and the two million dollar prize had not been revealed. They got a buyout offer of over $400,000, took it, and learned that their briefcase had $5 in it. Good choice.

What I haven’t figured out yet is whether the banker is trying to cheat people or whether the game is really just about tolerance of risk. In other words, are the offers fair given the amount of money left in play? If every offer is fair, then the only question is how much risk you’re willing to accept. Each time you open a briefcase, you chance removing a big amount of money from play and causing the banker to adjust your offer downward. On the other hand, removing a small amount will get you a higher offer. If some of the offers are unfair, then there’s math involved in determining whether or not to take the offer.

The game Web site doesn’t reveal how the offers are calculated, but the calculations I did in my head make it seem like the offers are fair, so the game is about a contestant’s willingness to gamble. (The odds are completely set, obviously.) I wonder how many of the players know that?

11 Comments

  1. The offers, which start out on the low side, seem to trend towards an amount that is the average of the remaining possiblities. When it gets down to, say, the last five cases and the unrevealed money totals about $1,500,000, then a fair offer would be about $300,000 (I think), though the banker seems to stay a little under that.

    It would be interesting to see a comparison of this and the Monty Hall Problem, where the person opening the unpicked cases KNOWS where the big prizes are.

  2. Assuming this is the same format to the UK version, the banker has an agenda to reduce the amount of money paid out. He will make offers based on risk calculations on the number and value of boxes available, the current state of the board and a personality assessment.

    The trick to the game is knowing which deal is optimal for you.

  3. The Wikipedia article has a good section on optimal strategy.

    What annoys me about Deal Or No Deal is the way that the presenter has to drag out the duration of the show, introducing the idea of “luck” to the contestants. Since the allocation of amounts to the suitcases/boxes is random, you might as well open them in numerical order. All the chat is just flim-flam.

  4. DEAL OR NO DEAL IS MINT

  5. There is not much into this game in terms of an optimal strategy; Basically, if the banker offers you more than the fair value, it is mathematically “better” to deal; However, the other aspect is the real “money value”; For many there is some threshold they wish to earn; For example if the contender is offered 200K, he is more likely to deal even if the banker offer was below the fair value. On the other hand in the range of 20 K nobody would like to deal even if the offer was more than fair value,

    Also, there is no comparison with Monty hall problem since in this show, the host never gives away any free information; there is no advantage switching the cases at the end;

  6. LOVE THE SHOW WOULD LOVE TO BE ON THE SHOW.

  7. i believe that no deal is a big hoax and are cheating people in a big way. What i have come to know from the internal sources that all the briefcases have bluetooth devices attached to it and when a person choose any briefcase the people in the background change the amount with the help of bluetooth device. Notice the amount in the briefcase is under a slip and small rollers can do the magic….. well so remember there is no shortcuts to hard work or neither to get big sum. One more thing nothing is free in this world… someone has to pay for the resources which are given to the people for free.. thanks….

  8. Mr conspiracy theorists Thelma your really dumb. You realize how fast that information would get out if that was the case. There was one game in the history of Television that was a fix and it was Quiz Show. So many people got fired for that sham of a show that any television producer would have to be nuts to try to fix another show. Also the whole fix on Quiz Show was they were given the answers to make it easier not harder. You think 26 girls are under the influence of NBC so much that they won’t say a word i doubt it. Why don’t you leave the south and head north you might actually learn something.

  9. This show is a hoax. The people are actors, the money may or may not be real and they aren’t competing so it’s not against any law. You are all just duped… Deal or no Deal…

  10. It is obvious that the case values are changable behind the scenes…. it’s just too coincidental that they “lead them on” [them being the contestant] up to a critical point where they could lose everything, and whatever case they pick, they happen to lose everything. The beginning few shows of any new gameshow make it look better than it is because they give away bigger amounts… same as the Who Wants to be a Millionaire show… the less viewers there are, the harder the questions are and nobody could possibly get $1million…. since the first 2 or 3 weeks of Deal or No Deal I havent seen anyone win more than $100,000…. phishy.

  11. Dont know what you lot have got going on over there in the states, but our Deal or no Deal is so much better.

    No Hoax, ours is just done with boxes, so none of this “bluetooth” bollocks

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