Deal or No Deal

I cannot help but be fascinated by the NBC game show “Deal or No Deal.” For those of you who are unfamiliar with this show, the format is as follows:

Contestant randomly selects a briefcase among a good number of briefcases (20-30, I forget how many). For the remainder of the show, this will be the contestant’s briefcase. In each briefcase is a different monetary value ranging from $.01 to $1,000,000.

The trick is that the contestant never knows (until the end) the value in his/her briefcase, but is allowed to open other briefcases to discover what values the briefcase does not contain. After each round of opening cases, a “banker” will make an offer to purchase the contestants briefcase for a certain sum. These offers are part of what makes the game interesting to watch.

When an offer is made, the player is given the choice to take the offer and end the game, or to continue selecting briefcases and revealing more information. Should briefcases that are opened contain high values (thus, the high values could not be in the contestant’s briefcase), the subsequent offer will decrease and visa versa.

Now what I find intriguing is this: at each step of the game it would be possible to calculate the expected value of the cases and determine whether the offer is higher or lower than the expected value (in the first couple rounds, the offer is always significantly lower). But in greater rounds, some players will turn down offers which are greater than the expected value: they are truly gambling with large sums. This is strange (if not irrational behavior for someone who would have a good use for the money). For example: The available values may be: $25,000 $50,000 $100,000 and $1,000,000. The average of these values is $293,750… but the player may turn down and offer of $350,000 in hope that they will eliminate yet another low value, or have the $1,000,000 value in their case.

As it turns out I’m not the only one interested in this topic, I found a very interesting academic paper written about the behavior of contestants on the European versions of this show. I’ve read about half so far, and it wonderfully explains why people do not always act as we predict they will:

http://papers.ssrn.com/sol3/papers.c...ract_id=636508

Anybody else watch this show and enjoy it (or just find it interesting) as I do?

[Beebs]

http://www.nbc.com/Deal_or_No_Deal/game/
Here's the online version I was talking about, and like you said the offers are often based more on psychology than expected value, because most people don't think in terms of expected value. Plus I think the producers offer intentionally good deals at times because the audience doesn't want to see too many people lose.

[Orgazmo]

I watch the show any time I find it on...and often try to figure out why the fuck people make some of the choices they do.

Thanks for the paper. Looks very interesting.

[Ugly Bastard]

Like Orgazmo, anytime I see this show it makes me completely puzzled about how stupid people are. Once I was watching it with my mother. It came down to like two briefcases one with 75,000 and one with 100,000. The guy was offered 85,000 for his briefcase and my Mom was going on and on about how they should just take that offer and be happy. I tried to explain to her the expected value of everything, and that if the contestant took this deal several times in their life, they would be giving up $2,500 in value each time, but my Mother is very illogical, and each time she just kept saying "Oh, just take the money and quit risking it!" Anyway, point of the story is, it pisses me off how illogical some people are.

Oh but UB, if expected value were everything you wouldn't buy insurance would you?

You're forgetting a great chunk of the theory, risk aversion.

[Ugly Bastard]

Right, but risk aversion has nothing to do with settling for 85k when you're dueling between 75k or 100k.

Ummm, yes it does.

[Ugly Bastard]

What person on this show is going to say "oooh I better take the -EV settlement for 85k 'cause I risk can't missing on the 100k and having to take 75k!"

No one says that. Risk aversion is a moot point in this example. Only in some extreme circumstance is someone going to view taking the 85k as a clear decision to avoid having to settle for only 75k.

Risk aversion becomes a good conversation if someone is being offered 300k rather than flipping a coin for 20k or 1M.

No, UB, you are wrong. Just take my word for it. Many people would take a guarenteed 85k over a 75-100k chance. Even you may do so if given the actual opportunity. Sure, maybe you wouldn't. But lets say you have a family and kids who would really, really like that extra 10k. In that case, you have high risk aversion, and you may take the 85k option.

I'm talking about risk aversion in a technical sense.

Edit: Essentially the 85k issue breaks down as follows:

75k is guarenteed, so forget it... the real gamble here is 10k vs. 0 or 25k... would you turn down $10 thousand for a 50-50 flip where 50
% of the time you get 0 and 50% of the time you get 25k? The answer depends on your level of risk aversion. For many people, the initial 75k would make them less risk averse, so they may go ahead and gamble on the 2nd portion. But some people will still be risk averse even after the initial 75k, in which case they will take the guarenteed value.