No Deal! The Idiocy of Deal or No Deal

Like a lot of people, I enjoy watching the new NBC game show phenomenom, Deal or No Deal. It's very engaging and the tension runs high. The mechanism of the game creates emotional highs and lows that are what good television is about. Gripping drama. The thrill of victory and the agony of defeat. Yet, while I am compelled to watch it, a part of me HATES this show with an irrational passion. I want to unpack those feelings and see if I can understand my visceral reaction.

The first thing that I don't like about the show is that it requires NO SKILL whatsoever. Jeopardy, which is the greatest game show of all time, this is not. The only real skill that contestants use are their latent skills in extra sensory perception. We're not talking mind reading, because with a simple double blind procedure, there would be no mind to read as no one would know what dollar figure is in what briefcase. Just have one person lay out the dollar figures and close the cases, and have a second person who didn't see the first person work put the numbers on the cases. No one knows, so there is no mind to read. We are talking about contestant's ability to either see the future or read the dollar figures through aluminum briefcases. Since I'm a hard core skeptic, I don't think people have ESP. Or at least I don't think they can see the future or read cards through briefcases. So, since that's the only real skill at work here, there is no skill. And that rankles. Why not just play the lottery?

Maybe I'm speaking too fast. There is a science that contestants could use. It's called statistics. Specifically the portion of that science called probability. To date, I have yet to see anyone, aside from the banker, use this science. Let's think about this a little. When you start, you are faced with a choice of 26 briefcases, one of which contains a million dollars. So, you have a 1:26 chance of pulling one million dollars. That's a little worse than 4%. I think this is an obvious statistic, and therefore not particularly interesting.

The key number to work with is the expected value. You may have met this formula before. It was explained pretty clearly by Ed Norton in Fight Club. Chuck Palahniuk and Jim Uhls put it like this:

A new car built by my company leaves somewhere traveling at 60 mph. The rear differential locks up. The car crashes and burns with everyone trapped inside. Now, should we initiate a recall? Take the number of vehicles in the field, A, multiply by the probable rate of failure, B, multiply by the average out-of-court settlement, C. A times B times C equals X. If X is less than the cost of a recall, we don't do one.

What his car company is doing is called a cost-benefit analysis. Part of that, the calculation of X is the calculation of expected value. Simply put, if you look at all possible outcomes and multiply them by the probability of them occuring, you get your EV. Mathematically, it looks like this:

To put that simply again, you multiply each outcome (x) by it's liklihood of happening (p) , add em all up (that's the big greek letter thingy) and you get E(X), which is your expectation. Let's use a simple example. We'll flip a coin. If it's heads, you win a buck. If it's tails, you give me a buck. E(X) is 0. The math for this is like this. p(heads) = .5, x(heads) =$1, p(tails) =.5, x(tails) =-$1. Therefore px(heads) = $.50 and px(tails) =-$.50. I think you can probably take us home from there. Add em up and get zero.

With this tool, you can do all kinds of stuff. You can figure the point at which it makes sense to spend a dollar on a lottery ticket. Or a PowerBall ticket. Or when to place the pair plus bet on carribean stud poker. Or when to initiate a recall on your defective product. It works better for gambling because the odds are pretty explicit. On your defective product, you have to make some assumptions that are prone to error, like how big a jury is gonna punish you in a class action lawsuit. Viewed in this light, it makes perfect sense that large companies (aka likely targets of class action tort litigation) are so in favor of reforming to the tort system. It makes the math easier if you have a hard ceiling on damages. Large margins of error produce very sloppy results. As a consumer, I can say that I want that math to be very sloppy, because I want recalls on pretty much anything that's gonna cause me to sue a major corporation. But I digress.

With Deal or No Deal, your base expected return is about $130,000. This is very skewed by the top dollar figures. You only have 6 outs that result in better returns. So, you expect $130K, but you're probably gonna do worse with about a 23% chance of doing better. Your offer gets better with each small value and worse with each high value you pick out of the remaining briefcases.

Let's think about what happens if you pick off one of the extremes. Your base expectation, as noted already, is a little over 131K. If you pick off the million dolalr case, your expectation drops to a little under $97K. Still not a bad expectation, and your odds of finishing better than that are 4% * 6 outs, or 24%. It's not the end of the world, but it is the end of your chance to win a million dollars.

Alternatively, if you pick off the penny, you have an expected return of just under 137K. You get 6K of upside vs 25K of downside at the extremes. You have improved your odds of beating that expectation to 24%, but you haven't improved your expectation.

I contend that people on Deal or No Deal have no idea what their expectations should be. Not going in and not at any point in the process. They probably have some expectation of being able to pick a million dollars out, or at least $300K. These are bad assumptions. Very bad assumptions. And it pains me to see them make bad decisions like that.

The other thing that kills me is that people don't think of it as real money. And maybe it isn't real money. Afterall, winning a $130K all of a sudden would be like manna from heaven, right? Last night, they had a guy on who claimed to make $13,500 a year. He turned down several offers of a single day paycheck that would increase his annual earnings by 10 fold. 10 fold. He ultimately managed to get out with $202,000 on a briefcase of $50K, but that was after he was offered $198K, no dealed it and picked the million case. The show is all in good fun, but this money could mean a lot to you, your family or the charity of your choice. I dunno about you or Donald Trump, but even $40K for a single day's paycheck would make a good bit of change in my life. Nevermind the really big money on the show.

The perverse incentives of the people who "help" the contestants are kind of interesting. Last night, they had the guy's wife, and then some people who work with him in town government. I assume those people like him. But they might not like him $200K richer. And there is the perverse incentive. Some of your friends may be rooting for you to lose. I dunno that I would, but what do I care if you walk with $5 or $500K. It doesn't change my life, except that you might have pool parties. So, I'm almost never going to tell you to take the deal. Your wife may, since she is involved in your finances, but your friends probably just want to see you go far, not necessarily do well. If you are ever on this show, listen to your wife. Don't pay attention to Howie, your father in law, or your drinking buddy. They don't have anymore sense than you do.

The way people toss NBC's money away bothers me, but not as much as people's belief that they can feel where the money is. Results show that they can't, but even when faced with a good offer, they will return to the fray and pick some more. I guess it's revealing that a mere hour after NBC finishes braocasting the Monday episode of Deal of No Deal, they then air a show, Medium, which promotes belief in extra sensory powers. If you think it's unrelated, you might not be paying attention.