May the Odds Be Ever in Your Favor?: Gambling on Winning the Powerball

November 29, 2012

A shopkeeper waits for customers to buy tickets for the Powerball lottery. (Photo by Chip East/Reuters)

Yesterday, Powerball officials announced that a couple of very lucky folks in Arizona and Missouri will split a mind-boggling $587.5 million prize. The winning numbers were (wait for it): 5, 16, 22, 23, 29, and 6. The odds of winning the prize were a measly one in 175 million. As fantastic as that may sound, the human brain has difficulty comprehending the true meaning of monstrous numbers and odds. Indeed, the study of probability theory is probably the most vexing part of my undergraduate course in statistics—and many haggard students would certainly agree.

If we visualize odds, we actually get a sense of the enormity of winning that Powerball jackpot. For example, let’s start somewhere unexpected: the thickness of the average post card. After digging around a little bit online, I learned that the average post card has a thickness of .007 inches, according to the United States Postal service. Given 1:175,000,000 odds, we can simply multiply .007 by 175,000,000 to calculate the height (in inches) of post cards that corresponds to the total possible combinations in Powerball, only one of which can actually be a winner. Converted to feet, that stack of post cards turns out to be 102,083 feet tall.

Um, that’s in outer space.

At least, I thought that was in outer space. I’m not an astronomer, so again I dug around a little bit and it turns out that there is no clear boundary as to where outer space begins, but the Kármán line is commonly used a as a demarcating point for the purpose of space treaties and that’s 62 miles above sea level. The Powerball odds would place us at a little north of 19 miles up, but not truly into outer space.

Now, the average jetliner on a transcontinental flight cruises around 27,000 to 33,000 feet depending on the airliner, weather, and the sense of humor of the pilot. So, what we’re really saying is that we now have a stack of postcards that is about three times as high as your average cruising jetliner but not quite into outer space, still suborbital. Think about that on your next trip to London.

Really cool things have happened at around 100,000 feet, though. Felix Baumgartner’s “jump from space” in July comes to mind. Here’s a link if you want to see it on YouTube. So, if you really want to visualize the odds of winning Powerball, imagine Felix opening his spacecraft door, peering out over the edge, and jumping. Now, granted his jump was from 128,000 feet – a bit higher than our stack of postcards, but close enough. Let’s give him 26,000 feet to steady himself and stop spinning as he did in the video. As Felix falls at a speed of Mach 1.24 (833.90 miles per hour), imagine Felix reaching out with his right hand and yanking one post card out of our skyward stack.

That post card is your post card. You just won the Powerball lottery. Congratulations.

Once you’ve finished celebrating, let’s contemplate a more interesting question: why do people play? Given the overwhelming odds of failure, one would think that nobody would try. In fact, many observers consider playing the lottery a highly irrational activity. Most professional poker players, who make their living calculating odds, consider the lottery to be nothing more than a “tax on the mathematically challenged.” But, that’s not a particularly sufficient answer simply because most lottery players will acknowledge the great unlikelihood of winning but play anyway. It’s not that they fail to appreciate the odds, they simply ignore them. Images of Jim Carrey in Dumb and Dumber saying “so, you’re telling me I’ve got a chance” come to mind.

People regularly discount odds and pay more attention to rewards. Those of us who have studied pathological gamblers see this phenomenon on a regular basis. Instead of focusing on the great likelihood of not winning, pathological gamblers discount risk while attending to implausible gains no matter how unlikely it is to win. We see the same phenomenon in substance users and individuals with impulsivity problems – failure to appreciate consequences complemented by a single-minded focus on potential reward.

What really drives gambling, whether with cards, the lottery, or the stock market, is the effect the behavior itself has on us. From a physiological perspective, gambling activates the same part of the brain that lights up when we engage in sex. That’s a pretty potent reward system. It is also the same part of the brain that is stimulated with many forms of substance use, so should we be all that surprised to find that a high proportion of pathological gamblers also have alcohol, nicotine, or other drug addictions?

Of course, playing the lottery does not mean that a person is a pathological gambler. There are many different gambling subtypes and the most common is the social or recreational gambler—the person who plops a little money down just to see what happens. A loss has no meaningful effect on his or her life, but a win might. Researchers have found that women tend to prefer the lottery and slot machines whereas men tend to prefer more action-oriented or confrontational games (e.g., blackjack, poker, etc.).

My wife Tere always plops down a little cash whenever the Powerball jackpot surpasses $100 million. Sometime after buying her ticket, we’ll spend about 15 minutes talking about all the good things she will do with the money if she wins. We both know she’s not likely to win but, for a buck or two, we spend some time thinking “what-if” and chuckling about it. Well worth the price of admission. We know the conversation will never really end because there will always be another Powerball and another round of fantasizing. So I never discourage her from playing just because I like what follows. Instead, I nod my support and say, “Good luck, Felix.”

David CS Richard

By David CS Richard

Richard is dean of the Hamilton Holt School, a professor of psychology, and co-editor of the upcoming Wiley-Blackwell Handbook of Disordered Gambling with Alex Blasczcynski (University of Sydney) and Lia Nower (Rutgers University). The handbook is expected to be available by summer of next year. He is also co-editor of the peer-reviewed journal International Gambling Studies.

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