[Computational Complexity] Deal-No Deal: MORE \$ = LESS Interesting

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• I caught an episode of DEAL-NO DEAL recently (see this for a description). The math behind this game has been described in blog postings of Lance (see this as
Message 1 of 1 , Oct 1 2:51 PM
I caught an episode of DEAL-NO DEAL recently (see this for a description). The math behind this game has been described in blog postings of Lance (see this as well as the above link)The episode I saw showed something wrong (at least in my opinion) with the way they are promoting the show during premiere week. They have upped the amount of money to be a max of \$4,000,000 (instead of \$1,000,000). I saw the following (this might not be quite accurate but makes the point)There were 6 numbers left:
1. \$5,000
2. \$10,000
3. \$20,000
4. \$100,000
5. \$1,000,000
6. \$4,000,000
and the bankers offer was \$700,000. \$700,000 is so large and so life changing that the decision to take it (which she did) is rather obvious. Even the audience WAS NOT yelling `NO DEAL! NO DEAL!' like they usually do. To exaggerate this, imagine if the top amount was \$40,000,000 and your dilemma was whether to take \$7,000,000 or risk it to maybe do alot better but maybe do alot worse. YOU WOULD TAKE THE \$7,000,000. (or at least I would).A question like `would you take \$70,000 or take the chance that you get \$400,000' is mildly interesting. But the \$700,000 is to large to not take. Hence the game gets less interesting mathemtatically.Given a persons utility function (or something like it) what would be the optimal max amount (and optimal set of amounts) to maximize the games INTEREST? This question might be interesting.

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Posted By GASARCH to Computational Complexity at 10/01/2007 04:50:00 PM
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