Stopping rule in "Deal or No Deal" game show is a simple probability problem, which you should be able to answer using your current knowledge. The stopping rule depends on how much the "Banker" offers the contestant, what are the dollar amounts associated with the remaining unopened cases including the one that the contestant is holding, and the value system of the contestant. Is he/she a risk averse or risk taker? The dilemma here, for each person, is to strike a balance between risk and greed. The same principle, i.e., risk vs. greed, applies to investing in stocks and bonds.
Let's get back to the game. There are 26 cases containing $0.01 , $1 , $5 , $10 , $25 , $50 , $75 , $100 , $200 , $300, $400 , $500, $750 , $1,000, $5,000, $10,000, $25,000, $50,000, $75,000, $100,000, $200,000, $300,000, $400,000, $500,000, $750,000, and $1,000,000.
Let's assume you are the contestant who has opened the following 6 cases in the first round: $100; $1,000; $10,000; $25,000, $300,000, $500,000.
1. What is the expected value (i.e., mean) of the remaining cases?
2. If you are a "risk-neutral" person, how much would the banker has to offer you for you to be indifferent between going to the next round and selling your case for the Banker's offer?
3. What if you are a "risk-averse"?
4. What if you are a "risk-taker"? Explain your solution in mathematical terms and words. Post a spreadsheet if you wish.