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

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  • GASARCH
    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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