I wonder if anyone has done this type of analysis on the show "Deal or No Deal".

If you haven't seen it, the premise of the show is that there are 26 suitcases with various dollar amounts in side, from $0.01 to $1,000,000. The contestant picks 1 case at the beginning, and the dollar amount inside is what they're playing for. They don't get to see this amount til the end.

Then they eliminate each of the cases a few at a time, and the banker makes them offers to get them to give up "their" case. If the contestant is eliminating low dollar cases, the offer can be high. But if the contestant eliminates high dollar cases, the offer is low.

So the first thing you have to notice is that the contestant can only win one of two amounts: the amount that is in their case (determined at the start of the game), and the amount offered by the banker. The amounts in unpicked cases are not available to the player.

The other thing to notice is that (presumably) the banker has all the information while the player has none. The banker knows the dollar amount in the players chosen case, and has a computer system to tell them the statistical average amount outstanding. And this goes into how much to offer the player.

But the banker doesn't care about the statistical average - he knows what the player stands to win, he knows what's in the case. And he controls the offers. So if the player only has $10,000 in his case, the banker would be stupid to ever offer the player more than that to get them to quit.

But of course the banker needs to keep up an appearance of fairness. His offer has to be within a reasonable limit of the statistical average. For instance, if there are 5 amounts left on the board, $1,000  $100,000 $250,000 and $500,000 and the banker offers $800, it will be a bit obvious to the player and the audience what the player has in his case.

But that doesn't mean that the banker has to be at or above the average. So in the above instance, a player with $1,000 in his chosen case might get an offer of $70,000, while a player with $500,000 in his case might get an offer of $200,000.

Now this is where I'd love to see real life examples of this. Can we get copies of past shows, and see where two players both have the same amounts left and different offers? Then we can see how the offer can give the player a clue as to what is in there case.

And if anyone knows where I can find more details on how the banker calculates the offer, put a link in the comments.