My Math Forum Deal or No Deal

 May 14th, 2010, 08:24 AM #1 Senior Member   Joined: Sep 2009 Posts: 251 Thanks: 0 Deal or No Deal Now that the semester is over I can ask the question that I've been wanting to answer for about two years: How do you calculate the correct decision in the TV game show "Deal or No Deal"? http://en.wikipedia.org/wiki/Deal_or....S._game_show)
 May 14th, 2010, 09:13 AM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Deal or No Deal You posted in Probability and Statistics, so I imagine your question is really, "In Deal or No Deal, how do you maximize your expected value?". In that interpretation, it's an easy question: you average the post-tax value of the unrevealed briefcases and accept any offer at least that high. Swapping cases doesn't matter.
 May 14th, 2010, 10:29 AM #3 Senior Member   Joined: Sep 2009 Posts: 251 Thanks: 0 Re: Deal or No Deal Hi, CRG, You are right about my question. But what other way, besides maximizing your expected value, is there be to make the "correct" decision? I can't even imagine another way to make that decision. Also, I think just averaging the unrevealed briefcases is not right. Let's say your choice is to accept a higher than average offer, or open three more suitcases. Let's say there are more low valued than high valued suitcases out there. What is your likelihood of opening three small suitcases and increasing your next offer? I bet there is more to this than just an average.
May 14th, 2010, 11:26 AM   #4
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Re: Deal or No Deal

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 Originally Posted by Singularity You are right about my question. But what other way, besides maximizing your expected value, is there be to make the "correct" decision? I can't even imagine another way to make that decision.
Had you posted on the Economics and Mathematics forum, I would have discussed risk-aversion. What if five briefcases remained, four with low dollar amounts (for the sake of argument, say a penny each) and the last with a million dollars? Would you reject an offer of \$166,666.67 just because it is less than the expected value? For the sake of this exercise, suppose you're given the money tax-free.

Quote:
 Originally Posted by Singularity Also, I think just averaging the unrevealed briefcases is not right. Let's say your choice is to accept a higher than average offer, or open three more suitcases. Let's say there are more low valued than high valued suitcases out there. What is your likelihood of opening three small suitcases and increasing your next offer? I bet there is more to this than just an average.
That depends on the Banker's strategy. Do you know anything about that?

Last edited by skipjack; June 3rd, 2015 at 08:37 PM.

 May 14th, 2010, 11:32 AM #5 Senior Member   Joined: Sep 2009 Posts: 251 Thanks: 0 Re: Deal or No Deal No. I don't know anything about the banker's strategy. Hmmmm....
 May 14th, 2010, 11:39 AM #6 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Deal or No Deal Obviously the expected value strategy falls apart if you expect that the Banker may offer you more than the expected value of taking your suitcase in later periods. But if we don't know how he acts, it's very hard to say what strategy to use.

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