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Kistaro Windrider, Reptillian Situation Assessor

Unfortunately, I Really Am That Nerdy

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On showmanship and random numbers
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kistaro
Deal or No Deal is a dreadfully dull game. The title of the show is the only meaningful decision the contestant has to make across the entire game; all else is uninformed selection of random numbers. For that matter, "Deal or No Deal" is asked a maximum of seven times per game- and that assumes the contestant says "no" six times, which is frequently a bad idea. Particular random numbers aside, there are only eight meaningfully different games: take deal one, take deal two... take deal seven, take the case. For those not familiar with the game, it involves a person selected by the producers for being excitable and having no grasp of third-grade mathematics coming up on stage, chosing a random number from 1 to 26, and hoping that the briefcase he, she, or it just chose has $1,000,000 in it. Of course, the chance of getting the million is one in twenty-six, which is exactly the same as the chance of getting $.01 instead. The contestant then starts opening the other briefcases- first six at a time, decreasing by one each round to a minmum of one briefcase per round. After each round, one of the producers of the show called "the Banker" sets off a prop telephone on the table in front of the contestant (which has three things: the phone, a red flashing button under a cover, and the briefcase stand where the case selected at the start of the game is placed) and puts an amount of money up on the main screen; the contestant then has to decide whether or not to stop playing the game and take that much money, or keep playing. If the contestant never takes an offer, he, she, or it gets whatever was in the case selected at the start of the game.

This is hardly a gripping concept: N rounds of random numbers, then N bribes to give up. Those bribes are related, of course, to the briefcases that haven't been opened: the possible values that the contestant could walk away with from just taking the briefcase. The banker, of course, almost never offers a fair shake, and why would he? It's to the station's advantage to only give offers below the mathematical average. But it can be to the contestant's advantage to take it, because the station and the contestant are playing very different games. From a statistician's point of view, this actually can be interesting, but most people are not statisticians. The contestant is playing the game one-trial; the Banker is playing the game many times. The Banker can wait for the Law of Averages. The contestant only gets one chance, and is best served by taking an offer above the median, even if it's below the mean.

Deal or No Deal is, however, extremely entertaining television.

The show can be interesting for someone majoring in Psychology, or for that matter just trying to learn about humans (like a lot of the nonhuman sort reading this journal), to watch poorly-planned risk-taking behavior under social pressure; people will make big mistakes when people with no particular vested interest in any particular outcome of the game encourage them to. And it can be amusing to watch how people will be happy with what they get even once they're totally screwed: when a game came down to $1 vs. $5, two of the three lowest values in the game, the woman who decided not to accept the bank's high-stakes offer of $2 was absolutely thrilled when she turned out to be holding the $5. (Enjoy your sandwich, ma'am.) If she had taken the offer one turn before, she would have left the game with $80,000. (Then she opened the 300K and that was that.) She was happy about winning less than one tenth of one percent of what she could have had if she quit the game one turn earlier. And to be honest, I think that's a good thing: there's nothing to be gained by her regretting it and being upset, since she can't play again.

It is not the psychoanalysis aspect that interests most people, however. It is probably due to the fact that there is something inherently interesting about the idea of people being offered "push this button to get a life-changing sum of money" several times in one hour, and then not do it. Consider the idea: someone who makes under $14,000 a year was offered $180,000 for pressing a button and did not do it. (Note that this turned out to be a good call; he left the game when offered $202,000.) Furthermore, his wife, his campaign manager (he is the mayor of Brunswick, Georgia), and his constituents were all rooting for him not to press the button. There was a lot of pro-button support for the $200K, but his campaign manager was telling him "no"- despite him having only one very large value left on the board, with a maximum of $50,000 left if he opened the $500,000 and the possibility of only $300 if he did not quit. Those were the only three values on the board. I don't know about you, but if I was mayor of a city and my campaign manager told me to take a 1 in 3 chance of losing $202,000 for a shot at twice that, I would be looking for a new campaign manager. This was also interesting because it was the first time on Deal or No Deal- in the USA, that is, as it's popular in many countries and this is just the most recent one- in which the Banker actually offered a sum greater than the mathematical average of the amounts left on the board. (Board total was $550,300; the board would have to be $606,000 for the Bank to not expect to lose money on the offer.)

I don't beleive that either of those factors alone, however, are enough to make the show worth watching. It is the antics of the host of the show, Howie Mandell, who actually makes it entertaining.

Consider the situation. This is only the second game show I've seen where switching hosts would destroy the show. (The first is, of course, Win Ben Stein's Money, and it should be immediately obvious why nobody except Ben Stein can reasonably be expected to host it.) The show is, in my opinion, worth spending the time watching, because and primarily because the host is entertaining. It's the host who made this really intrinsically boring idea and made it a lot of fun to watch: his diving catch for the briefcase when the contestant knocked it off the platform, his recovery when the contestant's excited jumping and hooting knocked the telephone off the table and revealed it for the cheaply-made prop it was with the faceplate off and the battery out ("We'll get a telephone repairman, you watch these commercials"), and his willingness to do whatever frequently-inane luck ritual the contestant suggests. It's not all Howie- a lot of it is what the show gives him to work with. The producers don't mind giving out large sums of money if they don't have to do it very often, and a very effective way of doing that is to stretch out the show- which has included Howie running up the stairs to argue with the Banker after a particularly lousy offer for one of the more amusing breaks from the protocol of the show.

There's a lot more to the performance than that, but it's difficult to describe- it's worth spending the hour to watch it at least once. The show is, in and of itself, entirely inane (although probably not as inane as America's Funniest Home Injuries Videos), but the way it is performed and presented makes it entertaining. And really, there's nothing wrong with enjoying stupid entertainment on its own merits as stupid entertainment, y'know?

But the actual conclusion to draw from this is what marketers have known for a very long time: good presentation can make even a really lousy idea really interesting.

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You neglected to mention the scantily clad ladies, which is the main reason that this pervert viewer watches it.

Kalanco here, posting from a school computer.


If you have a 1-3 chance of losing 200,000(I'm rounding), and a chance of winning 400,000, you should take the bet(if all other possibilities mean you break even). Because the best result will double your money, you're at a 2-1 odds, profit wise. You'll have to lose more than 1/2 the time to lose money. because 1/3<1/2, you will, over time, win more than you'll lose.

I play poker too much.

But what about marginal value? The first 200 000 may be much more worth than the next 200 000.

you will, over time, win more than you'll lose

(Emphasis added)

Therein lies the fallacy. The Banker can play as much as he wants. The Contestant only gets to play the game once. The Banker can rely on "win more than you'll lose" and the Law of Averages, but the Contestant only gets one trial.

The distribution of values in the prize list is extremely tilted. The low half- the first thirteen values- are below $1000. This means that the median is almost always much lower than the mean. The thing is, the Contestant has to play the Median, because sure, the Law of Averages says that the Contestant should take the deal, but the Law of Averages never gets a chance to work.

When it's considered from that angle- $202,000 is a lot of money, and with the next prize capped at $50,000 if the 500K doesn't work out, there's a huge fall if those odds don't work out. Being greedy can allow you to multiply those winnings by 2.5, but you can only do that one third of the time, with an equal chance of almost losing everything in the next turn. Not gong "bust" in Deal or No Deal does, at the end, virtually guarantee a drastic increase in winnings, but because the Banker can't offer above the mean and expect to win (I have no idea what posessed him to do so in last night's game), the contestant's views of winning the top prize are inevitably unrealistic.

I now wonder how low the chances of someone actually ever winning the million really are. The only way I'd ever go for it is if due to phenomenally good luck through the rest of the game, my options were $500K-$750K-$1M by the second-to-last possible turn, and the Banker gave me a raw deal. I would take $750,000 at that point; I'd continue the game for anything less than $690K. Don't know about the range between that, though. Then the only way I'd even consider opening the last case is if I was left with $750K and $1M. The Banker's last offer is always a fair deal or better, from my observations. If I had $500K and $1M, I would not gamble the $250K. Consider the same question rephrased: Knowing you could never do it again in your life, would you wager $250,000 on a coin flip?

It's the difference in the Banker's Game and the Contestant's Game that makes the One Cent so much fun. Because whatever the chance of having the best prize is, as long as it's still on the board, the contestant runs the exact same chance of having exactly $.01 instead. And I, for one, would rather have a sure thing than a one-time-only shot at a bonus. If you were on the final two cases, and they were One Million Dollars and One Cent, what's the lowest offer you'd accept?

I don't know the lowest offer I'd accept, but the highest offer I'd consider would be $600. Why? That's the highest amount of money you can win without being taxed for "gambling winnings". Once you hit $601, you're subject to 31% tax on your winnings. If I take the risk and the prize is over $600, there is a 50% chance I'll be taxed, while if I take the bribe at $600 or less, there is a 0% chance of being taxed.

Of course, realistically, I think anyone would be wise to take the risk at $1M, because either way you're coming away ahead of if you had never been on the show in the first place, even if by one cent.

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