$1 Billion for a Perfect N.C.A.A. Bracket, Courtesy of Warren Buffett

Each March, tens of millions of brackets are filled out in the hopes of predicting the outcome of the N.C.A.A.’s men’s basketball tournament. But the odds that a bracket will be perfect, that is, every game guessed correctly, are long â€" to the tune of 9.2 quintillion to one.

So don’t bet on anyone winning the $1 billion being offered by Quicken Loans, the Detroit-based mortgage lender, with the backing of Warren Buffett’s Berkshire Hathaway, to anyone who fills out a perfect 2014 tournament bracket. The prize money will be paid out in 40 annual payments of $25 million, or a one-time lump sum of $500 million. The first ten million people who enter the contest will be eligible for the grand prize.

“It’s going to be fun,” said Mr. Buffett from Omaha, Neb. “If there’s one left at the end, I plan to go to the game with him or her. I’ll take a check along in my pocket.”

Mr. Buffett was in Detroit on November 26 for Goldman Sachs’s “10,000 Small Businesses” initiative when he met up with Dan Gilbert, the chairman of Quicken Loans. As the two toured Detroit, Mr. Buffett said, they hatched the idea for the billion-dollar payout. The two plan to fill out their own brackets and have a side bet on this year’s tournament.

Indeed, Mr. Buffett seems to have an appetite for insuring unusual events. (A Quicken Loans spokesperson would not disclose the premium it paid to Mr. Buffett.) For example, he said, Berkshire Hathaway insured a $260 million permanent disability policy on the baseball player Alex Rodriguez when he joined the Texas Rangers. The company did not have to pay on the policy.

Still, the odds of filling out a perfect bracket are almost non-existent.

“I don’t think we need to lose any sleep for Mr. Buffett tonight,” said Jeffrey Bergen, a professor of mathematics at DePaul University who is an expert in bracketology. With 64 teams (the four play-in teams are excluded in the contest), the odds are more than the number nine quintillion, or the number nine followed by 18 zeros. The odds go down if you know something about basketball to one in 128 billion, he said.

Limiting the number of brackets to 10 million does not help much. The chances of even one perfect bracket is still only one in 100 billion. That is the same odds as those for picking the winning party in every presidential election through 2164, assuming a two-party system, or having a favorite football team win the Super Bowl seven years in a row.

There has never been a documented perfect bracket, as far as Mr. Bergen is aware.

Despite the long odds, Jay Farner, the president and chief marketing officer of Quicken Loans said he is “super hopeful” there will be a billion-dollar winner. But whether or not there is a winner, Mr. Farner said he is looking forward to the publicity the contest will bring to his company.

As part of the contest, Quicken Loans, the nation’s fourth largest home mortgage lender, will also award the 20 contestants with the most accurate, albeit imperfect, brackets $100,000 to be used toward buying, refinancing or remodeling a home. Quicken Loans also announced on Tuesday that it will donate $1 million to inner-city Detroit and Cleveland nonprofit organizations.

On a Facebook page created in conjunction with the contest announcement, there was some skepticism (“obviously, the grand prize isn’t going to be won”) and a lot of discussion of what people would do with $1 billion: pay their bills, pay off their mortgages, go on vacation and “buy the St. Louis Rams and move them back to LA.”

But while Mr. Buffett said he thinks the odds are against having a billion-dollar winner, he acknowledged there was a slight possibility. “You never know,” he said, “You just never know what’s going to happen.”