I caught an episode of DEAL-NO DEAL recently
for a description).
The math behind this game has been described in blog
postings of Lance
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:
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.
Posted By GASARCH to Computational Complexity
at 10/01/2007 04:50:00 PM