Deal or No Deal algorithm?

April 18, 2006 6:46 AM

Game show-filter: How is the amount of money the Banker offers the player calculated on the show "Deal or No Deal?" My friends and I typically predict the amount within $10k, but I want to know the exact algorithm. Any ideas?
posted by LouMac to grab bag (18 comments total)

I assume they add the amounts left on the board together, then divide by the number of cases left. At least, that's what we've been able to cobble together at my house.
posted by sugarfish at 6:48 AM on April 18, 2006

I agree with sugarfish, I always thought it was the average of the amounts left on the board.
posted by itchie at 6:57 AM on April 18, 2006

I think that's what they do in the end, but they have to skew it in the beginning, otherwise it would start >$100,000.
posted by cosmonaught at 7:11 AM on April 18, 2006

It's a secret. It's related to the actual "correct" value, but it's always lower.
posted by smackfu at 7:12 AM on April 18, 2006

(total left / # remaining) * variable wuss-out discount = banker offer.

This page has a bunch of information on the game, even including charts and graphs of the expected value versus the banker offer for a few episodes.
posted by I Love Tacos at 7:23 AM on April 18, 2006

In the beginning, it is much lower than the average. It gets closer to the average as time goes on. They do not want the player to take the deal early. The deal is, obviously, going to be lower than the average, since the average is the "expected value" of the remaining prizes. This is, I believe, discussed exhaustively on the web. I know it gets talked about all the time on the 2+2 (gambling website) probability forums, television without pity, etc.
posted by RustyBrooks at 7:23 AM on April 18, 2006

I don't think it's an entirely objective algorithm. I expect they do psychological evaluations of the contestants before and during the show to determine whether they need to raise or lower the offer to encourage the contestant to say "deal" or "no deal" as they would prefer to make a show more appealing to advertisers. I think the exact timing of inserting a friend of family member's opinion into the decision is made with similar goals in mind.
posted by scottreynen at 7:30 AM on April 18, 2006

I Love Tacos found the site I was looking for, so I'll just add that the banker's offer is not always lower than the average of the remaining cases. See here for an account of a game in which the banker offered almost 15% more than the expected value of the remaining cases, and contestant (rather foolishly) didn't take it.
posted by Johnny Assay at 7:32 AM on April 18, 2006

I love this show for the math, the psychology, and bald Howie Mandel.

The first several offers are always way lower than the expected value, quite obviously to encourage the player to keep going. I mean, if they went ahead and just offered > $100,000 off the bat, where would the drama be? Many would take it. But some of those early offers are just ridiculous. $8,000 when the million is still on the board?

It seems to me that the offer gets closer to the expected value towards the end of the round, and in some cases exceeds it. There may be some way to tweak the offer to fit with your view of the contestant's psychology, but I don't think it changes the amount that much. I am also not sure why they want contestants to take the deal in the later rounds.
posted by lackutrol at 7:58 AM on April 18, 2006

I hate to be the party-pooper, but my production experience with gameshows leads me to believe (IMO) that there's no math or algorithim or research or psychology involved at all. Each show has a budget, and the producers' actions all are about ratcheting up the drama, of which moments can be edited together into a final product.

On one show, they offered a contestant a pony for his little girl. Trust me, they didn't just happen to have a pony waiting backstage just in case a contestant showed up to the taping with his daughter...

The show's budget of payouts is determined by insurance requirements (the prizes are paid out by insurance companies, betting that contestants will lose more often than not). Now, the insurance guys have run some kind of an analysis to determine the premiums paid by the show overall, but that's not relevant to an individual show's budget or drama.
posted by frogan at 8:37 AM on April 18, 2006

frogan, I don't think there's any contradiction between having an algorithm and ratcheting up the drama. We seem to have a consensus that, in fact, the algorithm is designed to do just that, by offering bad deals at the beginning which no contestant would ever take.
posted by lackutrol at 9:06 AM on April 18, 2006

I agree with frogan, I don't think they have as precise an "algorithm" as you other folks are imagining. I've watched the show a fair amount, and it appears that what they offer, compared to the expected value, is just determined by the ratings they expect.

-In the early rounds, they always lowball it because the show doesn't interesting until a contestant is a little deeper into it. Nobody would watch if people were taking the deal early.
-If the distribution of the board is such that it will make for exciting TV, they lowball it (ex: if the contestant has to open one more case and all that's left are 0.05, 1, and 1,000,000, they damn sure want the person to keep playing).
-Conversely, if all the big amounts are off the board, they would actually probably give a more favorable offer because nobody wants to watch someone play when the big money's off the table. I suppose they might also try to hustle someone off the show like this if they were just plain boring, but I dunno.
posted by TunnelArmr at 9:10 AM on April 18, 2006

piggyback: is there a list of past at-home-games that shows how the distribution of how audiences have picked? I'd have expected it to be random, but I've noticed that it tends to look like a bell-curve. The middle cases, like #3, seem to get most of the picks, while the end ones, like #1, get much fewer.

Also, people on the show seem to generally be superstitious about numbers. They'll pick a number because it's the date their child was born, etc. Since I'm not superstitious, I would probably make it easier for myself by picking cases in numerical order. Pick five cases? Okay. Cases 1, 2, 3, 4 and 5. Pick two more? Okay. 6 and 7.

Is there a problem with doing this? I know their SHOULDN'T be, because the contents are distributed randomly. But according to Howie, it's not computer-generated randomness. A "third party" randomly distributes the contents. Given that fact, when humans create "random" distributions, do they tend to fall into (unconscious?) patterns?
posted by grumblebee at 9:27 AM on April 18, 2006

One of the commenters here claims to have modeled it and gotten pretty close by taking the mean and then discounting by a particular percentage at each round.

grumblebee, you're right, the percentage of audience picks for the at-home game always look like a bell curve. Of course, the way they display it makes the differences amoung the picks look greater than they really are, but every single time I've seen it people pick the middle numbers more often. I wonder why people seem to think the middle numbers will be more likely to come up.

I would guess that the third party probably does use a random number generator to assign the values; they would probably get in big trouble if not, for example if some guy was just assigning the values himself and was discovered to have a propensity for putting the million in box 14.
posted by lackutrol at 9:35 AM on April 18, 2006

If you're right, lackutrol, is there ANY reason to avoid picking the cases in sequential order (other than the fact that this might be boring television)?
posted by grumblebee at 9:41 AM on April 18, 2006

Nope, sequential order is just as good as any other order. People just get "feelings" about numbers, or are superstitious, or see patterns that aren't really there (or at least aren't there any more than any other random distribution) that lead them to pick in other ways. I use these tendencies when I enter the at-home game, by weighting my entries heavily toward case 1 and 6 and thus getting a bigger share of these less-picked numbers and greater likelihood of winning should they come up. Strangely I haven't yet won (I wonder how many people enter those).
posted by lackutrol at 9:49 AM on April 18, 2006

It is completely random, just like the roulette wheel at a casino or the luck of getting a straight flush at 3-card poker. It's fun because it's random, but it's also fun because of the superstitions people have about certain numbers.
posted by camworld at 11:16 AM on April 18, 2006

Just while the thread is still open, I noticed on Monday that the at home game had the first non-bell curve I'd ever seen. Case 1 got a very high number of picks. I wonder if other people are using my strategy?
posted by lackutrol at 4:04 PM on May 3, 2006