There’s a new game show on NBC called “Deal or No Deal.” Here’s how it works: you pick one of 26 briefcases, each of which contains an unknown sum of money somewhere between a penny and a million bucks. One by one, you open the other briefcases, and after every few picks, you are offered a buy-out deal, a known sum of money in exchange for the unknown amount in your own case.
If the cases you open contain large sums, then the chances that your case has a large sum go down and the offer goes down accordingly. If the cases contain small sums, it becomes more likely that yours has a large one and the offer goes up. Let’s say I open six cases, containing $25,000, $10, $200, $400 and $1000. These are relatively low numbers, which is good, so I will probably receive a good offer.
The offers come from a shadowy figure in a control booth high above the stage who telephones the show’s host, who then relays the offer to the contestant. If they decide to take the offer, they lift a glass lid and press a red launch button and the game is over. If not, they must continue to open cases until they accept an offer or reach the last case, their unevaded fate.
The way the game seems to be playing out on episodes I’ve seen, the audience shouts “No Deal, No Deal,” the contestant turns down some good early offers and then, after the larger sums are eliminated from the game, they are forced to settle for a lower offer than they could have had.
There is in fact a very simple formula that can be used to decide if you should take the deal, which is just the average of the sums at stake. Take the sum of all the possibilities on the board, $3,418,416.01, divide by the number of possibilities, 26, and you get $131,477.59. If the offer gets close to $130K, take the deal. Of course, the initial odds change as more information is available, but if you are unable to calculate each time, this can serve as a good rule of thumb. Another strategy would be to open cases until there are six or so left, at which point the math becomes relatively simple again.
“Deal or No Deal” started in the Netherlands in 2002 and has spread around the world. In the American version, the briefcases are accompanied by identically-dressed buxom models who sometimes bend forward slightly as they open them. While the Dutch contestants have to qualify by winning a quiz, the American ones are clearly chosen solely for their emotional demonstrativeness and potential as crowd-pleasers, for their background stories.
Recent contestants have included a high school sports coach, a woman who believed she was psychic, and a Mandy Moore look-alike whose husband was serving in Iraq. There was a man whose ambition was to be a professional sports mascot and whose every gesture screamed let’s-get-fired-up but whose face seemed hurt and sad without a gopher mask to hide it, and a super-manic redheaded waitress with the insane energy of a lady climaxing in a shampoo commercial, who was nevertheless canny enough to raise her arms above her head when she wanted to accentuate her figure. The show pulls stunts, like secretly flying one contestant’s sister out to surprise her or bringing out the exact Harley-Davidson that another hoped to purchase with winnings. It is undoubtedly a little staged if not partly scripted.
As with Idol and Millionaire, the hang-time on the pauses is literally stunning. You sit there, get confused, ask yourself what's going on, and then remember, Oh yeah, they're making me wait. And wait. I think the show's low point to date is abusing the storm warning tone to draw your attention to a message line at the bottom with a show-related announcement.
It may be unfair but it seems to me that the working-class contestants on the show don’t know how to calculate the odds. Is the million still on the board? Then there's still a chance of winning a million. They don't stop to think what that chance is. The contestants don’t seem to make their decisions on a rational basis, even though they have been placed in one of the only situations in which it actually is possible to be rational, a situation involving only numbers subject to calculation. Money presents a perfect opportunity to use math, because the different possible outcomes are also numbers and can therefore be weighted. Choosing between a new car and a vacation in Hawaii is comparing apples and oranges, but comparing two amounts of money is only a matter of degree.
The audience offers boisterous and unvarying support for refusal, as if the point of the game is to be strong and hold out as long as possible against temptation. Towards the end, however, the drama shifts from holding out against temptation to resisting the temptation to hold out too long.
Every contestant seems to be under the illusion that their blind choice of briefcase is meaningful, that they can sense secrets in the air and accurately predict the future. But perhaps they are at the same time aware they are deluding themselves with false and extravagant hopes; they seem to dread actually opening the cases. The ominous music seems to say that any knowledge is dangerous, any contact with the ground will be a hard landing.
A viewer like myself has his own illusion, that he knows better than the contestants. Watching the show I feel the same pity and disgust I do for people who buy lottery tickets or heedlessly feed coins into slot machines, who buy a car for its looks instead of safety and reliability, who never look at the unit prices at the grocery store but instead fall for the voodoo of brand names, and who vote their own worst enemy into power over them as warden and executioner.
There are three explanations of stupidity: manipulation, deficiency and underdevelopment. Which one you adopt may determine whether you become a revolutionary, an elitist or a reformer. It may be impossible to settle on one permanently, as it has been for me, since they are closely related: the deficient are also less developed and more easily manipulated.
As you watch, you are reminded of the basic fact that twenty thousand dollars means different things to different people. To generalize wildly, it probably means more to the people on the show and the people who watch it — the commercials indicate a viewership greatly concerned with getting food stains out of their clothes — than it does to myself or the people who read this. The host fleshes out the numbers a little in the chatty bits, and usually the low end translates to a nice honeymoon or vacation.
My situation, according to Bankrate.com, is that I need to save $400K in the next fifteen years if I want my daughter to have the option of attending a top college. When we decided to have a child, my assessment of our new situation was that all the money we could ever make was already spent. What's more, according to the financial calculator at Vanguard.com, my wife and I will need to save $600K before we can retire. So basically if I won a million dollars on a game show, I probably wouldn’t buy a Lexus or go on a pastry tour of Vienna or even get a new pair of sneakers, I would be back at work the next day brownbagging it in the cafeteria. The result of these weighty numbers is that I have a hard time getting excited about twenty thousand dollars, not because it isn’t a lot of money to me, but because in my terrified state I would be constitutionally or situationally unable to spend any of it, to splurge rather than save.
The game does not test knowledge like Jeopardy or daring like Fear Factor, but it is not fair to consider the game stupid just because it is simple. The real star of the show is the awe and despair of money. When I see a home makeover show, I don’t see a lucky person winning a new house, I see an unlucky person living in a society which has up until then ignored their needs and now considers them potential entertainment, a person who must rely on the media gods to favor them, the NBC peacock and the CBS eye.
Essentially, a contestant on Deal or No Deal has no real choice. You can hold out for a better offer but there is only one bidder. The man in the booth is your adversary and the host is your buddy but really they both work for the show, they are two faces of the system, good cop and bad. In a way, the show is a lesson in making decisions in a world in which you never get to make a real decision.
Watching Deal or No Deal can be like watching Russian Roulette, with a devastating sense of missed opportunity serving as the bullet in the chamber. Why do the people on the show seem to make such bad decisions? Is it human nature, the mentality of the exploited, or is it indicative of some failure in our conception of reason? Is it out of showmanship and bravado that a good deal is turned down? Is refusal the only pride left?
Do I myself make decisions rationally, joylessly hoarding against future calamity? Is it at all possible to do so or does a sliver of chance make everything in the end impossible to truly understand, a shifting foundation of chance ensuring that none of our expectations have any solid basis?
No one in Washington is offering Square Deals, New Deals or Fair Deals anymore. The working class are all suckers now, grateful for scraps and heedless of their birthright. They don’t know why medicine and gasoline cost so much, as shown by the recent e-mail campaign to boycott Exxon until they lower their price to $1.30 a gallon. Or maybe they’re right and the free-market textbooks are wrong; maybe they know exactly why.
In 2004, three Dutch economists and one from Chicago used data from the show as the basis of a study of decision-making. In fact, it is not unusual for economists to study game shows, which they refer to as natural (i.e., naturally occurring) experiments. Andrew Metrick studied the classic game show Jeopardy in 1995, and there has also been a recent study of Who Wants To Be A Millionaire? Limited academic budgets make it hard to create a social experiment with high financial stakes. The authors wryly comment that the show “has such desirable features that it almost appears to be designed to be an economics experiment rather than a TV show (p. 3),” which I take to be an oblique assessment of its entertainment value.
Reading the study, at first I took it to say that “risk-aversion” goes up after a loss, which seemed to me an excellent example of common sense at work. When you're looking for an apartment in New York, the first good one always gets away from you because you aren't sure if it really is good, and then you grab the next one, smarting from and smartened by your loss. Arguably the decision to marry works this way as well: you break up, realize what a good thing you lost, and decide that you'd rather settle down for good than be back out on the market again. House-hunting and dating are examples of decisions which are serial rather than parallel. You rarely choose between two apartments or two relationships, but must rather weigh the present against unknown future prospects. When you shop, you can compare several pairs of shoes in a store, which is a lot easier than weighing a soon-to-expire present offer against whatever may come next. Perhaps the common bait-and-switch sales technique relies on this idea of stinging losses stimulating a purchase. The model you wanted is sold out; doesn't that tell you that you were too picky and should just take whatever is in stock, before that's gone too?
But in fact the study concludes exactly the opposite, that losing makes you less risk-averse, i.e. more reckless. When a gambler is losing, they bet more, hoping to make it back to their break-even point. Losing just makes you more desperate to win. This is the reason bettors start to take long shots at the end of a day at ponies, and traders take bigger risks in the afternoon after a bad morning.
On page 25, the study offers a specific contestant as an example, with unintentional comic effect:
Table VII illustrates our most striking finding -- risk-seeking behavior following large reductions in the expected prize -- using the decisions made by contestant Frank, who appeared in the Dutch episode of January 1, 2005. In round 7, after several unlucky picks, Frank opens the briefcase with the last remaining large prize (€500,000) and he sees the expected prize tumble from €102,006 to €2,508. The banker then offers him €2,400, or 96% of the average remaining prize. Frank rejects this offer and play continues. In the subsequent rounds, Frank deliberately chooses to enter unfair gambles, to finally end up with a briefcase worth only €10. Specifically, in round 8, he rejects an offer of 105% of the expected prize. In round 9, he even rejects a certain €6,000 in favor of a 50-50 gamble of €10 or €10,000. We feel confident to classify this last decision as risk-seeking behavior, because it involves a single, simple, symmetric gamble with relatively large amounts at stake. Also, unless we are willing to assume that Frank would always accept unfair gambles of this magnitude, the only reasonable explanation for his choice behavior seems a reaction to his misfortune experienced earlier in the game.
So much is in that “we feel confident.” How confident? 96%? 105%? Who is Frank, an everyman or a dumbass? Why does he “deliberately” make bad choices? Is he always this way? Can there be a reasonable explanation for unreasoning behavior? Is it the fate of the rational man to study the irrational? Or is reason itself a vain pretension? If he can be so wrong, how can we be sure we are right?
I had assumed the bank offers were a little under value at the beginning. It turns out they are way under, starting at around 10% of the prize value and gradually ramping up to 100%. Thus it is in fact the system, not the individual, that creates the dramatic structure of early refusal. The risk-aversion varies by individual contestant but does not correlate with education. The study also determined that the difference between proper calculation and eyeballing is not great, that a rough guess comes out about right. So three cheers for empirical observation, and three strikes for me.
The study concludes that “’losers’ seem less risk averse than 'winners' (p. 30)“, a statement which needs to be reversed for clarity, i.e. those who take big risks lose and those who are more cautious win. In short, it doesn't pay to gamble.
We are left with the too poignant psychological observation that one’s ”reference point tends to stick to an earlier, more favorable situation (p. 26).“ Being unable to adapt when faced with a change for the worse, people are often ”shattered“ and grow desperate trying to return to their peak position, that irretrievable ”sticky reference point." In this sense, the game is an allegory of experience, watching your possibilities vanish.
Said Shirazi lives in suburban New Jersey. He is writing about music and television on-line for Printculture, where this article first appeared.
Other Articles by Said Shirazi