My brother is going to do a Deal or No Deal game for the staff at his business (but I don’t think he’s offering $1M). He’s trying to figure out the formula for the buyout offers made in the TV version of the game.
I imagined it would be the expected value of the remaining cases, but I haven’t watched for several months, and my brother says the offer seems to be somewhat less than the average of the remaining cases.
Does anyone know how they calculate the offers on Deal or No Deal?
I don’t know exactly but they do seem to be just a litttle less than the average of the remaining cases.
There is an onling game at the show’s offical site. You could play that and try and figure out the formula.
The early offers are much less than the expected value. The longer you go, the closer the offers approach the expected value, but never quite match it.
I could have sworn one episode had 3 cases left with an average value of 120k, and the bank offered the person 135k. I remember thinking “Jesus, take the offer!” before the contestant turned it down and played on for something like 50k.
I’m not sure there’s an actual formula that they plug in for every circumstance. Or, if there is, they might modify the value of the final offer in order to make it more dramatic or entertaining.
I believe it is expected return tempered with some risk analysis. Take for example, the situation where there are 3 cases left. One has $0.01, one has $1.00, and one has $1,000,000.00. Your expected return is close to $333,333.00, but your risk of getting (almost) nothing is 2/3. The buyout offer will thus be considerably lower than $333,333.00, and it is probably a good idea to take it.
One thing that I recall from previous threads on the subject is that there is an element of manual control so it’s not strictly a weighed average of the remaining amounts even though the number is obviously based on that.
as far as I can ever tell, the value offered is total value of cases left / 2.
That seems much too generous.
Were that to be true, then as long as the $1,000,000 case is in play, the offer would be > $500,000.
Heh. I’m playing the online version right now. There are two suitcases left, mine and one more. I either have $300,000 or $500,000.
The bank just offered me $296,600. Think I should take it?
Not exactly.
.01 .10 1,000,000 as just pointed out averages to only $333,333.37.
It’s only >$500,000 if there are only two cases left.
Surbey’s formula was “total value of cases/2” not “total value of cases/number of cases”. The former will indeed always give a value of >500,000.
You are right. Sorry BobLibDem.
And in fact, the highest offer would always be the first offer of the night, and it would get get lower with each successive pick as more and more money left the game.
The offer is always the expected value left in the cases, minus some amount that is probably chosen either based on the banker’s assumption of the player’s risk tolerance or some more complex formula. I think when the player quits and they go through the litany of “What you would have picked/what the bank offer would have been”, it’s a straight-up expectation calculation.
Don’t forget that it is in the show producer’s interest to continue the game. If the early offer is accepted, all that contestant introduction, background story, exposition, tell us about yourself, gimmick prizes, celebrity cameos and flying out the friends / family / cheering supporters of the contestant is wasted. The banker has incentive to prolong the game, therefore, the offers are a little lower to encourage the player to go longer.
As a player, the smart move after observing the inevitable rise and fall of offers is to stick to an expected value strategy. Once you get to less than 10 cases remaining, if the offer is above your expected winnings, take the offer and leave immediately.
The offer rarely exceeds expected value until the very end, and only if the choice is solely, or mostly, high values. For example, if there are only 2 cases left 300,000 and 500,000, the offer might exceed 400,000, but if the 2 cases are 500,000 and 10, the offer is likely to be 200,000 or less. I think it’s obvious why this is the case.
Bottom line, the offers are low (sometimes VERY low) at the beginning to ensure the game continues and gradually rise to meet expected value based on the risk of the contestant being stuck with one of the smaller numbers.
And Sam Stone, I haven’t seen straight up expected value even in the play through after the game is over.
I’ve watched the UK version several times.
Since we have no models holding the cases 
(it’s future contestants instead), there’s far less eye-candy, so I try to predict the banker’s offers.
Without exception, his offer is in the range 40-60% of (total value of prizes left) / (number of cases left).
He never offers (total value of prizes left) / (number of cases left), no matter how few cases are left.
So if there are 2 cases of £1 + £100,000, he will offer between £20,000 - £30,000.
If there are 10 cases left, totalling £450,000, he will offer between £18,000 - £27,000.
If the contestant has a lucky number (say 7), he may stick that in somewhere. But it won’t affect the amount significantly. So instead of offering £17,000, he will offer £17,777.
I meant the expected value for the game as a whole, not for a particular situation. So, beforehand, if I say I expect to win $150k and at a point in the game, I am offered $160k, I’ll take the offer regardless of how lucky I am feeling.
How about this as a twist on the game; have a second contestant to be the banker. Do an expected value calculation. The banker hears that number, but the contestant on stage does not. The banker makes an offer. If the offer is accepted, the banker gets to keep the difference between the offer and the expected value.
So, it’s in the banker’s interest to make the offers small, but not so small that they are all refused.
Me and a friend watch this show almost every time it comes on, partly for the money aspect, partly because of the lovely ladies.
It seems to us that this season the offers are smaller than they had been before. After quite a few cases have been eliminated, and the high numbers are still in play, it seems the offers are very low and much lower than they were in similar situations on the first season.
Has anyone else felt this way?