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• ## [Computational Complexity] A Bad Deal

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• Bill Gasarch is on vacation and he had given me (Lance) a collection of posts for me to post in his absence. But then I got email from Tal Rabin who wants to
Message 1 of 1 , Dec 21 12:07 PM
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Bill Gasarch is on vacation and he had given me (Lance) a collection of posts for me to post in his absence. But then I got email from Tal Rabin who wants to get the word out about the Women in Theory workshop to be held in Princeton in June. Done. Now back to your regularly scheduled post from Bill.
I don't usually watch Deal/No Deal. I like some of the interesting math or dilemmas it brings up, but the show itself is monotonous. As Host Howie Mandel himself says "we don't ask you a bunch of trivia questions, we just ask you one question: DEAL or NO DEAL!" Here is a scenario I saw recently where I thought the contestant made the obviously wrong choice.
1. There are two numbers left on the board: \$1000 and \$200,000.
2. She is offered a \$110,000 deal.
3. She has mentioned that \$110,000 is about 5 times her salary (so this amount of money would make a huge difference in her life).
4. Usually in this show you have the audience yelling `NO DEAL! NO DEAL!' This time the audience, including her mother, her sister, and some friends, were yelling `TAKE THE DEAL! TAKE THE DEAL!'. While this is not a reason to take the deal, note that the decision to say NO DEAL is NOT a `caught up in the moment' sort of thing.
She DID NOT take the deal. We should judge if this was a good or bad decision NOT based on the final outcome (which I won't tell you). Here is why I think it was the wrong choice. Consider the following scenarios:
1. If she takes the deal, the worst case is that she gets \$110,00 instead of \$200,000.
2. If she rejects the deal, the worst case is that she gets \$1000 instead of \$110,000.
The first one is not-so-bad. The second is really really bad. Is there a rational argument for her decision? I could not come up with one, but maybe I'm just risk-averse.

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Posted By Lance to Computational Complexity at 12/21/2007 02:06:00 PM
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