A Good Deal or No Deal Strategy

[moonman239]

You guys remember that old game show "Deal or No Deal"? You know, the one where a contestant goes for a $1,000,000 prize? Well, just for the reference, here's a little strategy I put together in case you ever find yourself playing "Deal or No Deal" with your friends:

1) For simplicity, we assume that whoever plays banker always offers the contestant an offer that = s the expected value (the average money one could expect to end up with)

2) For every round we calculate the expected value. This is done by adding up the values of the remaining cases and dividing them by the number of remaining cases.

3) We then calculate the expected amount of money lost on the round that has not been played yet.

4) If the expected value calculated in step 3 looks significantly less, it would be wise to accept the deal. Otherwise, you can say no deal with a fair amount of confidence that you will get a higher deal.

 

[moonman239]

UPDATE: Step 2 is pretty pointless in determining whether or not to say "deal" or "no deal".

 

[bpet]

For this example since there's only one shot at the prize, the law of large numbers doesn't apply, which means that expected value is not necessarily the "fair" value of the deal (a similar concept applies in option pricing theory). The optimal strategy could also vary with the individual's prize goal or risk appetite.