TO GRASP HOW unlikely it was for Gloria C. MacKenzie, an 84-year-old Florida widow, to have won the $590 million Powerball lottery in May, Robert Williams, a professor who studies lotteries, offers this scenario: Head down to your local convenience store, slap $2 on the counter, and fill out a six-numbered Powerball ticket. It will take you about 10 seconds. To get your chance of winning down to a coin toss, or 50 percent, you will need to spend 12 hours a day, every day, filling out tickets for the next 55 years. It's going be expensive. You will have to plunk down your $2 at least 86 million times.

Williams could have simply said the odds of winning the $590 million jackpot were 1 in 175 million. But that wouldn't register. "People just aren't able to grasp 1 in 175 million," Williams says. "It's just beyond our experience — we have nothing in our evolutionary history that prepares us or primes us, no intellectual architecture, to try and grasp the remoteness of those odds." And so we continue to play. And play. People in 43 states bought a total of 232 million Powerball tickets for the lottery won by MacKenzie. In fact, the lottery in the United States is so popular that it was one of the few consumer products where spending held steady and, in some states, increased, during the recent recession. That's still the case. About 57 percent of Americans reported buying tickets in the last 12 months. For the 2012 fiscal year, U.S. lottery sales totaled about $78 billion.

It may seem easy to understand why we keep playing. Somebody has to win. But to really understand why hundreds of millions of people play a game they will never win, a game with serious social consequences, you have to suspend logic and consider it through an alternate set of rules — rules written by neuroscientists, social psychologists, and economists. When the odds are so small that they are difficult to conceptualize, the risk we perceive has less to do with outcomes than with how much fear or hope we are feeling when we make a decision, how we "frame" and organize sets of logical facts, and even how we perceive ourselves in relation to others. The lottery is a game where reason and logic are rendered obsolete, and hope and dreams are on sale. And nobody knows how to sell hope and dreams better than Rebecca Paul Hargrove, president of the Tennessee Education State Lottery Corp.

HARGROVE IS A lottery legend. In the 1980s and '90s she built the state lotteries in Georgia and Florida from scratch. After two years of Hargrove's leadership, Florida was outselling every other lottery in the nation, including California, which had a population twice Florida's size.

One morning in June, I was ushered into Hargrove's office. With a mass of snowy white hair swept back in a loose bun, and a pair of glasses perched precariously on the bridge of her nose, Hargrove came across as a folksy Fairy Godmother, with a gift for schmooze. Within minutes of my arrival, she was spinning out anecdotes about her hairdresser's predilection for cat-themed instant game tickets and the little old lady who lives down the block from her mother and won $56 million.

Hargrove has an intuitive understanding of what drives her customers to play the game. She has a preternatural sense of where their psychological buttons are located and how to push them. She responded in a flash to my comment about the logical futility of playing the lottery. "If you made a logical investment choice, you'd play a different game," she said. "It's not an investment. It's entertainment. For a very small amount of money, you might change your life."

In 1985, when Illinois Gov. James Thompson tapped Hargrove to head the state lottery, she didn't know much about the business. She did what any savvy marketer would do: She sat down and thought about her own motivations. "I played the lotto when I was caught up in the frenzy of a $40 million jackpot," she said. "And I thought, 'What made me play?' What made me play was the thought of what I would do with $40 million. You pay $1 and then for three days you can think about that question."

With that simple insight, Hargrove struck marketing gold. More than 200 ads went up on billboards across the state. "How to Get From Washington Boulevard to Easy Street" read one in a poor Chicago neighborhood. Hargrove also pushed for larger, attention-grabbing jackpots.

From her first days in the lottery business, Hargrove learned to make the lottery fantasy tangible by making sure that winning, on a smaller scale, is something people experience. "If you play a lot and you play for three years and you never win, you're not going to keep playing," Hargrove said.

In Illinois, Hargrove experimented with smaller prizes, which had better odds of winning than the big state lottos. To prevent player burnout, she pioneered games with different prices, designs, and themes. She might trot out a game where you scratch off cute cats for cat lovers, and a game with footballs for Bears fans. She might sell four-leaf clovers on St. Patrick's Day, and reindeer-themed tickets around Christmas. The odds of winning may remain remote, but keeping it "fresh" and "exciting" added a sense of possibility and made it more fun, she said.

While Hargrove's feel-good marketing goes a long way toward explaining why we keep playing the lottery, scientists are increasingly making it clear how lottery marketing taps into our brains and impacts our communities.

SELLING THE LOTTERY dream is possible because, paradoxically, the probabilities of winning are so infinitesimal they become irrelevant. Our brains didn't evolve to calculate complex odds. In our evolutionary past, the ability to distinguish between regions with a 1 percent or a 10 percent chance of being attacked by a predator wouldn't have offered much of an advantage. An intuitive and coarse method of categorization, such as "doesn't happen," "happens sometimes," "happens most of time," "always happens," would have sufficed, explains Jane L. Risen, a behavioral scientist.

In the conceptual vacuum created by incomprehensible odds, people are likely to experience magical thinking or superstition, play a hunch, or simply throw reason out the window altogether, says George Loewenstein, a professor of economics and psychology. "Most of the weird stuff that you see with decision-making and risk happens with small probabilities," he says.

One reason may be that uncertainty activates a network of brain areas that push us reflexively to find a resolution, says Giorgio Coricelli, a professor of economics and psychology. "To make the choice, your brain automatically looks for suggestions, searches for more information, and if there is little information, we can make strange associations, assume something is realistic, even if it is superstitious."

Our proclivity for fantasy makes us an easy target for advertising. Lottery commercials depict winners in stretch limousines, counting stacks of money, dressed in evening gowns and tuxedos, sipping champagne. The commercials hit home because fantasizing about winning the lottery activates the same parts of our brains that would be activated if we actually won, notes Daniel Levine, a professor of psychology: "The motivational areas of the brain can be heavily influenced by vivid daydreaming."

But even fantasy will drop its hold on us if we always lose. Research has shown that positive reinforcement is key in virtually all of the successful lotteries, notes Williams. Lotteries that allow players to choose combinations of four or five numbers from a total of 60 numbers are popular, he says, because many players experience "the near miss," which creates the illusion that they came close to winning the multimillion-dollar jackpot.

IT'S NOT JUST the way we frame the odds in the lottery that can affect how likely we are to play the game. It turns out that the way we frame our own economic status can also play a role in our decision to play the lottery.

"The lottery is a way to raise the ceiling on what can happen to you," says Loewenstein. "So if you are reminded of your poverty, it makes the idea of lifting the poverty a more salient motive. Lottery tickets become that much more attractive at that moment."

For many poor people, he adds, there is "no scenario they can come up with in which they are suddenly going to get very rich." To them, the lottery may be a low- probability event — but so is getting a job that pays six figures.

That point is driven home by a 2006 study that surveyed 1,000 adult Americans about their personal views on wealth. The survey found that 21 percent of Americans — 38 percent of whom had incomes below $25,000 — thought that winning the lottery represented the "most practical" way for them to accumulate several hundred thousand dollars.

"A lot of people say that the lottery is a regressive tax, which is true," Loewenstein says, referring to taxes that aren't pegged to income, and take a larger proportion of income from those who can least afford it. "It is true that poor people spend a substantially higher fraction of their income on lottery tickets" than the affluent, he notes. "But I don't think it is necessarily irrational." When your economic prospects are dim, buying hope makes sense.

How we perceive ourselves in relation to others also shapes our decision to play the lottery — a lever the industry consistently pulls. A salient example is the "Postcode Lottery" in the Netherlands. Weekly it awards a "Street Prize" to one postal code, the Dutch equivalent of a zip code, chosen at random. When a postal code (usually about 25 houses on a street) is drawn, everybody who played the lottery in that code wins about $12,500 or more. Those living there who neglected to buy a ticket win nothing — except the chance to watch their neighbors celebrate.

In a 2003 study, researchers in the Nether-lands noted that fear of regret played a significantly larger role in the Postcode Lottery than in a regular lottery. It was not the chance of winning that drove the players to buy tickets, the researchers found, it was the idea that they might be forced to sit on the sidelines contemplating missed opportunity. "The brain is very sensitive to loss — even low-probability losses," explains Coricelli. "So if you frame something as a loss, biologically there is a compulsion to avoid it. We have an aversion to it."

Fear and regret are the flip sides of hope and dreams — all are powerful emotions that when tapped can cause us to relinquish rationality, to act on instinct, even to make decisions that might not be in our best interest. As I left Hargrove's office, I scanned the highway for the giant Powerball billboards that she had touted as the best marketing tool in her arsenal. She didn't need many words to get her message across, as the billboard that week trumpeted a $100 million jackpot. I couldn't help but think, "What would I do with that much money?"

Excerpted from Nautilus.