There's a board-game (well, sort of; it doesn't really have a board as such, but it comes in a box like a board game) version of Deal or No Deal. I played it once with suzimoses and my in-laws. In the board-game version, to make things interesting for other people besides the two people who are making or not-making deals, the other players "hold" the briefcases, and there are instances where they can pay a certain amount of money to guess what's in the briefcase, and if they guess right, they win the amount in the briefcase.
Since the briefcases are completely random, the maximal expected return comes from guessing the largest possible contents. And there are about 30 possible amounts, so there's only a 1-in-30 chance of winning -- but it turns out that the payments are set up so that it's virtually always a good bet if you guess the maximum possible.
It also turns out that the amount of money one can make from always mindlessly making these guesses pretty much swamps the amount of money one can make from playing the rest of the game, especially if nobody else is doing it.
Having just finished watching heros myself I have to pipe it. Deal or no deal is completely about human psychology and creating an artificial sense of urgency in each decision. I did watch most of one or two episodes and try to calculate out what algorithm they were using to come up with the offers and it did look like there was a formula to it that made some sense. I forget what it is right now. It also seemed to me that the decisions should also be made based on life circumstances. Once an offer was on the table that would make a significant difference in my quality of life I would take it vs. the chance of getting next to nothing.
One of the reasons we decided they'd never let us on the game is because we'd come prepared to do calculations - one person to check the odds, another to describe the bank offer in terms of mortgage payoff or investing return, etc. :)
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Since the briefcases are completely random, the maximal expected return comes from guessing the largest possible contents. And there are about 30 possible amounts, so there's only a 1-in-30 chance of winning -- but it turns out that the payments are set up so that it's virtually always a good bet if you guess the maximum possible.
It also turns out that the amount of money one can make from always mindlessly making these guesses pretty much swamps the amount of money one can make from playing the rest of the game, especially if nobody else is doing it.
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Deal or no Deal
Of course the best part still had to be our niece shouting out "NO DEAL!" every other turn.
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