Optimal Strategy for Deal or No Deal
When I have watched Deal or No Deal (I try not to make a habit of it) I always do little sums in my head to work out if the banker is offering a good deal. Where odds drop below "evens" it's easy to see it's a bad deal, but what would be the correct mathematical way to decide if you're getting a good deal?
There are (at least) two factors that mean that simply calculating the average of the remaining options is not enough to describe how someone should play.
Risk aversion
Someone's utility is not a predictable function of the amount of money that they win. For instance my utility from winning $\$$5 is more than 100 times my utility from winning 5 cents. However, my utility from winning $\$$100 million is less than 100 times my utility from winning $\$$1 million.
From what I hear about game-shows in general, if your performance does not make it to air, then you don't get anything. Hence you cannot just accept the first amount offered (if it turns out to be a better choice) and expect to get it, since it won't make an interesting show.