Maybe this should be in GQ, but what is the algorithm for the offered deal in Deal or No Deal? It should just be the expected value, but it’s most often much less, and even occasionally somewhat more. Anyone figured this out?
This isn’t very helpful, but my WAG is that the banker manually fiddles with the numbers after getting the expected value, perhaps to jockey the contestant into going the way the banker wants them to go. It’s not much to go on, but I do recall seeing one show where the contestant picked cases 1 through 6 for their initial round, and the offer was $123,456. 
At the very least, there is an override.
Given the above, and that there is an ‘overide’ to the final amount, I am not a bit surprised.
If DOND followed pure math, everyone would know the “best play”, and the show would be even less entertaining.
I think that the overide probably favors NBC and GE. Granted the game is hard to ““win”” (in terms of the 1 million), but I think NBC knows what they are doing.
Also, I have seen shows where items in addition to cash have been offered. I think a Tractor and some Doughnuts have been part of the offer. I didn’t understand what “tractor” was doing in the sidebar, but the context came soon after.
I would like to see what NBC does, or what rule they ‘bend’ if and when it gets down to the final 2 cases, and one million is still in play. I have seen the offer to “Switch cases”, so I am sure some real interesting would occur.
There is also the factor of whether the player has “insurance”. If you have to open one case and you have the million dollars and then .01, 1, 5 and 10, picking the wrong case is a more costly error than if you have 500K, 250K, .01, 1 and 5. Even if the expected payout is better.
This is kind of friend of a friend, but this game is of considerable interest to economists and I’ve been to a couple of seminars with researchers who spent time with the Australian producers from the start of the show (the Australian version was the second and the first of that name). The producers won’t say what they do, but the researchers are confident there is no algorithm for the reasons given by BayleDomon. IIRC, they also checked using the entire run of the show and various econometric torture methods.
If there is no algorithm, how do they come up with the offer so quickly during the “play it out” phase of the game after the deal is accepted? It’s not expected value then either.
There is no “banker,” unless that’s the name of a software program. However the offers are calculated, they’re done automatically. They always have them instantly when they go through the cases after the contestant sells out. I don’t see how there can be an override.
My take is that they have general guidelines like 60% of the expected value for the first round up to 90% for the last round, but can tailor it for each situation such as making it a round number, choosing a significant offer such as $123,456, etc.
I generally can do the expected value in my head in seconds, so I don’t think the time is that much of a constraint.
It is also wrong to say that the correct decision is to keep playing simply because the expected valueis greater than the offered amount. People are naturally risk-averse and a sure thing versus an uncertain thing can have some added cost built in to the players satisfaction.
Yes, playing an optimal strategy based on expecteed value only makes sense if you play a large number of games. If you are just playing one game it makes a big difference. I know I would think differently between a board with $1M and $0.01 left than one with $700K and $300K even though the expected value is the same.