Rick Hampson

USA TODAY

Quicken Loans and Warren Buffett are offering up to 15 million people a very, very, very small chance to win a very, very, very big prize — a billion dollars for filling out a perfect NCAA men's basketball tournament bracket.

No one in recorded history has done it. "People realize it's a long shot,'' says Jeff Bergen, a mathematician at DePaul University in Chicago. "They don't realize how long.''

The tournament's field and pairings are announced Sunday. Since the Quicken contest to predict its outcome has no entry fee, many entrants presumably will enter knowing nothing of men's college basketball, other than they'd like to make a billion bucks off it.

Result: A lot of brackets are going to border on random selection, which means winning is going to take a lot of luck.

How much luck? Bergen says the chance of randomly predicting the outcome of the main draw's 63 games is one in 9,223,372,036,854,775,808.

Still, the Billion Dollar Bracket Challenge has an appeal.

"How many ways can you make March Madness fresh?'' asks Brad Carlin, professor of something called biostatistics at the University of Minnesota School of Public Health, and an amateur bracketologist who admits he's intrigued by what amounts to a stunt.

"A billion is a big number,'' he says. "It's a bet the bookies won't take.''

Jason Mandel, a Philadelphia legal recruiter who's run the Mandel Madness tournament pool for the last 21 years, agrees: "It's a great piece of marketing, a great gimmick.''

Don't be totally discouraged by those long odds. With a modicum of knowledge, you can improve them.

For instance, a No. 1 (highest) seed has never lost to a No. 16 (lowest) seed in any of the four regional tournaments into which the big one is divided since 1985.

With information like that, Bergen estimates, you can significantly reduce the odds against you … to 128 billion to 1.

That means you'd still have less chance of winning the billion than of:

Seeing your favorite team win the next seven World Series.

Predicting which political party will win the presidency in every election from 2016 through 2160 (assuming the winner is always a Republican or a Democrat).

Flipping a coin and getting heads 37 times in a row.

"It's highly, highly, highly unlikely anyone will win,'' Bergen says, "but you can still have fun with it.''

The Billion Dollar Bracket Challenge is backed by an insurance policy issued by a company in Buffett's Berkshire Hathaway conglomerate. The contest is limited to 15 million individuals, each of whom can submit one bracket.

In addition to the big prize, Quicken will award $100,000 for each of the contest's 20 most accurate brackets.

Players, who must register online through Yahoo! Sports, have until 1 a.m. ET Thursday to submit their selections. The tournament's first 16 games are played later that day.

The search for the perfect NCAA men's bracket has been long and futile.

ESPN has been running a contest since 1998, and none of the more than 30 million submissions has come close to perfection. Over the past three years, every entry (participants can file more than one) had missed at least one game by the end of the first round of 32 games.

Chris Hamman of SCA Promotions in Dallas, who's tracked bracket competitions for years, says he's never seen a perfect first round, even though each year there are dozens of prize offers for a perfect bracket. An online gambling site once offered $10 million; Fox Sports offered $1 million; Papa John's offered a million pizzas.

Bracket pickers can improve their chances by using statistical analysis to recognize teams' propensities, according to Tim Chartier, who teaches the subject at Davidson College in North Carolina.

He and his students use complex computer applications to pick brackets. Their algorithms place weight on factors such as difficulty of a team's schedule, and downplay others, like scores of games that were blowouts. (Once the score gets out of hand, it's less relevant to teams' true quality.)

He also suggests betting on a team whose numbers show they:

Can win on the road, because all tournament games are played on a neutral court.

Are able to sustain a winning streak, because the team that wins the tournament has to win six or seven games in a row.

Have momentum going into the tournament, because games at the Maui Invitational over Thanksgiving aren't as relevant as what happened in the conference season and tournament.

Last year Jane Gribble, a Chartier student who also happens to be a Davidson cheerleader, submitted a bracket that beat 96% of those in the ESPN contest. In 2010, another Davidson student, Daniel Martin, beat 99.9% of the ESPN contestants.

But to put Martin's achievement in perspective, his bracket still was bested by 5,169 others submitted to ESPN — none of which were close to perfect.

Martin, a math major and class valedictorian, did win a coupon for a free Ben and Jerry's ice cream cone — the annual trophy in Chartier's class.

The experience left him both chastened and jaded. He now works for a real estate investment firm in Columbia, S.C., in an office with other sports-mad young financial analysts, but he won't even fill out a bracket.

"I told the other analysts I've retired. I don't have the math program anymore, so there's not the same allure. What's the point? Now, it'd just be guesswork.''

It remains to be seen how much interest the billion-dollar offer will generate. But Jay Farner, Quicken's president and chief marketing officer, says that so far, "a significant chunk" of people who've signed up to play have never registered to do so before with Yahoo Sports, which is running the competition.

And why not, he asks: "All it requires is a minute of your time and none of your money.''

He rejects complaints that entry is not really free, since entrants not only register (at no charge) with Yahoo but also give Quicken information — birthday, address, mortgage details. They're asked whether they want to get Quicken marketing e-mails, or to speak to someone about "mortgage opportunities."

Farner says Quicken needs to know who the contest "attracts and who it doesn't, if we're going to target our marketing. … We're investing a lot of money.''

That size of that investment is a matter of speculation. Farner refuses to say what Quicken paid Berkshire Hathaway to insure the payoff.

In 2003 Berkshire Hathaway received a reported $10 million premium to insure a billion-dollar sweepstakes for Pepsi. (There was no big winner and some small ones.) The Omaha World-Herald (Buffett's local newspaper, which he also owns) points out that it's unusual for him even to admit to providing such an insurance policy. But in this case, his magic name is part of the contest's appeal.

Carlin, the Minnesota biostatistician, computed what he described as Buffett's "expected loss,'' based on a 1 in 80 billion odds estimate. Given a .000187 probability (about 1 in 5300) of one of the 15 million players getting it right, what actuaries call the "fair premium'' would be $187,000, he says.

This means that if Buffett charged this same premium every year, he'd recoup the loss of $1 billion every 5,300 years.

Carlin's guess: Buffett may have charged Quicken 10 times the so-called fair premium to cover the bet, or about $1.87 million.

That'd be a nice markup. "He's not the second-richest man in America for nothing,'' Carlin says.

But has Buffett reckoned on savvy players like Sarah Klett? She's a Davidson math major who spent last summer on campus working with Professor Chartier on ranking algorithms.

Last Thursday she was at the National Museum of Mathematics in New York, offering tips about how things called linear systems and matrices can help create a successful NCAA bracket.

She called the Quicken-Buffett offer "exciting,'' not because she wants to buy a dozen Ferraris, but because it brings math to bear on a monster pop cultural event: "It's an opportunity to apply what I'm learning to something that's so massive and recognized by so many people everywhere.''

She's registered for the contest and awaits the release of the tournament pairings and seeds Sunday evening. "The next few days,'' she said, "are going to be pretty intense.''