The sad thing about “Deal or No Deal”

Being a contestant on this show requires no talent whatsoever. You pick suitcases. You decide whether you prefer a riskless offer of money to a risky one. Then you go home with a bunch of money. Along the way, the crowd and your chosen friends scream and cheer like there is great skill in choosing among ex ante identical suitcases. Contestants beam with pride when they pick a good suitcase instead of a bad one. The whole thing has a veneer of skill, when really there is almost no skill at all.

Contrast that with Survivor, Apprentice, Who Wants to be a Millionaire, or Amazing Race. On those shows, winning requires some talent.

Deal or No Deal is essentially a lottery. I find that a little depressing.

You can play it online, as a commenter noted below. It is fun to watch the offers that are made and to try to infer what formula is driving the offers.


Amen...which is why "Jeopardy!" remains the King of the Quiz Shows. Big difference between "game show" and "quiz show."


A fun paper to read is "A Natural Experiment in Jeopardy" (AER 1995)
The author tests how optimal people bet during final jeopardy. People tend to bet rationally when the choices are obvious. But when all three contestants are in contention the bettings is a little suboptimal.

Seems like tv shows are quite popular with economists (Jeopardy, Deal or No Deal, the Weakest Link).


Basically every choice you make has no effect on your predicted winnings. It cn be interesting to see how risk-averse people are but not to the extent that I would bother watching. It is perfect for people who like to second guess because half the time they should thave changed their pick.


One point about Jeopardy: it requires not only knowledge/factual trivia and a great memory, but a bubbly personality and great hand/eye/ear coordination to hit the buzzer at exactly the right time in order to be chosen first. I passed two written Jeopardy tests easily, but couldn't figure out the buzzer system and got so flummoxed, that when I finally did, I was rattled and therefore not very enthusiastic. I was told that I failed the personality screening!

X-Tra Rant » Working for the Weekend

[...] Steven Levitt was unimpressed with Deal or No Deal from an economic study perspective. [...]


Yeah, I'm sucker. It's an interesting study in psychology to me, not only becuase of the risk/reward issues, but the external influences of family members/friends. They even had the kids of one contestant call in. Would these people make different choices if they were in isolation with no camera? What if they knew they were on TV? It's also funny to watch those people that are obviously calculating odds and expected value based on the next successful choice.

Any game show that displays statistics and forces people at home to do some math to understand the choices is pretty good for me. Jeopardy (which I love) is normally "I know this, or I don't". This required thinking through each one!


Wow, so, I was watching the show and thinking about economics... Here's my question, do they change the formula based on any psychological factors? Are they assuming contestants are perfectly rational, or are they adjusting for percieved biases?



Hmm, I'd say they aren't playing the math straight. 1/3 chance of getting a million. The other 2 are minute, 500 and 1000. The offer is 267,000. Now, the value of a 1/3 chance of getting a million is 333,333. So, what gives?


Yeah, it's a lottery. That's why I'm sending a tape in to audition. No skill required, and you can win a fairly large amount of money.

That being said, I'm going to need some advice on what to say I want to do with the million. All I really want to do is pay off my student loans, buy a house, and invest the rest. Somehow I don't think that will sell well with the screeners.

Any ideas?


Say you'll use it to go on an around the world cruise and then go on about how it's your childhood dream to do this.


I'm glad to see that D has such respect for Jeopardy. I was a contestant on the show and won $18,700. Jeopardy has the hardest questions of any game show and pays the least in reward. I guess that irony adds to its appeal in a way. The show seems more serious. As a contestant, the experience was wonderful. The entire production crew was friendly and warm. I was flustered by the buzzer at first (StCheryl has a wonderful point). After figuring out the system, everything cleared up. The show definitely requires, though, more than knowledge. Jeopardy remains my favorite show. Seeing people win so much simply due to luck has become a stereotype on today's television shows. With 500 channels, I would hope that something better would be on. Nevertheless, there is some entertainment in such irrationality.


I checked out the show last night after reading the blog. I think the show will get old real fast. however, sign me up to be a contestant! you're guaranteed to win, they're just giving money away.


I've actually been pretty close at guessing the banker's offer. Looks to me like they are taking an average of the remaining dollar amounts then adjusting the offer downward, and in the early rounds, they are offering about a half of the average of the remaining amounts. The fun in watching the show for me has been announcing the banker's offer to my kids right before Howie Mandel tells the player.


Guessing the banker's offer is fun to do. Interestingly, in the Australian and Dutch version, this task is relatively simple: the offer as a percentage of the average remaining prize increases with every round, starting from about 5% to finally 100%. This rule can explain about 95% of the variation in the offers. I wonder if the US bank uses the same rule.


I watched one tonight, and they were offering pretty much the expected winnings.

The guy had 3 low choices and a 200K. I think they offered him 50K.

He declined and picks a low $ briefcase. Now he has 2 low choices and 200K. They offer him 67K.

He declines and picks another low $ briefcase. He now has 1 low choice and 200K. They offer him 99K. He takes it.

Interesting to watch 1 show, but I can't see it staying interesting for long.


The online game is pretty addictive. Has anyone figured out the algorithm that drives the Bank's offers yet? I would guess about 100 plays or so of the game will give some sharp person out there enough data to reverse-engineer!


The algorithmn is pretty simple. It takes into account the standard deviation of the returns as well as the expected value.

The higher the standard deviation, the lower the bank's offer in percentages of the expected payoff.


I tried to use Econometrics to come up with how the banker comes up with his offer (I used data from the UK version of Deal or No Deal which is very similar, £250k maximum prize, 22 boxes).

I came up with this after two shows:
Bankers Offer = (2.3853 * Average) - (0.86039 * Standard Deviation)

Tried adding things like dummy variables (my theory is to prolong the show, that the offer increases as time goes by:
Bankers Offer = 2.3851*Average -0.88083*SD -10009.6S1 -7268.3SR2 -5629.6SR3 -1463.4SR4 +23086SR5

But at the end of the day, that was two shows worth of data, I do have 25 shows but don't have the analysis with me.

I'll post it later if anyone cares=]

Thierry Post

The banker's offer is no ABC but they basically offer about 5% (round 1) to 100% (round 9) of the expected prize, with a possible markup of 20% or so for the "losers" who opnen the valuable cases and see the expected prize decimated. This rule can explain about 95% of the variation in the offers in the Netherlands, Australia and Belgium.


Responding to something said by rrickner, consider the following:

At the start of the game, there are 26 suitcases and a total of 3,418,416.54 contained in them. Obviously, if one's only goal were to win the million dollar "grand prize" it would make little sense to just opt for the selected suitcase without even "playing the game", as the odds would be less than 4% (i.e., 1:26) that one's case held a million dollars. Imagine, however, that the contestant's dreams of enriching himself are somewhat more modest. He reasons that if there are 26 cases, then the "average" case contains more than $131,000. So he turns the tables on the game show host, and asks Howie Mandel to call the banker and tell the mysterious man in the booth that he (the contestant) will accept $125,000 (i.e., enough to buy himself, after paying applicable taxes, the Lexus he covets) for the briefcase he has selected. The audience is shocked--shocked!--not only that there is gambling in Casablanca, but also that, apparently, there is to be none here tonight. More surprising, perhaps, is the banker's reply.

"NO deal!," intones Howie, who adds, "He says that if you don't want to play, he will give you his MetroCard, and you can take the subway home."

The reason for the banker's refusal to take what seems to many like a "reasonable" deal, is that while the "average" case does indeed contain just over $130,000, there happens not to be any "average" case. You need to bear in mind that more than half of the $3.4 million is contained in only two of the suitcases (i.e., the ones holding the $1 million and $750,000 denominations). And only six of the 26 cases contain denominations of more than $100,000. That's approximately 23%, and the reason why the banker would never give anyone real incentive not to play the game for several rounds. More importantly, though, no game show producer is going to invent a show where there is an actual incentive to do absolutely nothing whatsoever. That isn't drama.

Of course, as the game progresses, the odds of winning a lot of money change for better or for worse. Say what you will about the absurdity of "Deal or No Deal" not requiring any skill besides the ability to calculate (or memorize) probability values, but the very fact that emotion rather than dispassionate rationality factors into it, as well as the realization that none of the contestants seems to be an idiot savant (even if most act quite idiotically) is what makes the show intermittently interesting, if not quite compelling.