Warren Buffett’s Berkshire Hathaway Inc. is backing a $1 billion prize offered by Quicken Loans Inc. if a contestant predicts the winner of each game in the National Collegiate Athletic Association’s men’s basketball tournament.

The prize would be paid in 40 annual installments of $25 million and split among multiple winners if there is more than one perfect entrant, the Detroit-based lender said Tuesday in a statement. The winner has the option of a single payment of $500 million.

Berkshire has specialized in unusual insurance risks for decades, protecting clients against big losses in return for premium payments. The Omaha, Neb.-based company won a bet in 2010 on the World Cup after France was eliminated from the tournament in South Africa. Berkshire has previously guaranteed against the potential payout of $1 billion in an event sponsored by PepsiCo Inc.

“We’ve seen a lot of contests offering a million dollars for putting together a good bracket, which got us thinking, what is the perfect bracket worth?” Quicken Loans Chief Marketing Officer Jay Farner said in the statement. “We decided a billion dollars seems right for such an impressive feat.”

Buffett suggested the $1 billion contest to Quicken Loans founder Dan Gilbert when the Berkshire chairman was in Detroit late last year.

Gilbert has previously worked with Buffett on philanthropy, not on a business venture, Farner said. Ajit Jain, Buffett’s reinsurance lieutenant, was involved in the deal, according to Farner.

The 68-team, single-elimination tournament begins in March. Submissions will be limited to one per household and capped at 10 million entrants, according to the statement.

Aaron Emerson, a spokesman for Quicken Loans, declined to say how much the company paid for the policy. He said the tournament excludes the play-in games, which narrow the field to 64 teams.

The odds of picking every winner correctly in a 64-team bracket are less than 1 in 9 quintillion, according to Jeff Bergen, a math professor at DePaul University in Chicago. Even with some basketball knowledge, that only improves to about 1 in 128 billion, he said.

The odds of Buffett having to pay out reach about 1 in 10,000 in the Quicken Loans contest if all 10 million entrants have basketball knowledge, Bergen said.

Trying to predict the winners of each game has become a fixation in the U.S., where colleagues often bet in office pools and compete against celebrities who post their picks online. President Obama has made a public show of releasing his bracket, including in 2009, when he correctly selected the University of North Carolina to win.

Of the 8.15 million brackets submitted to ESPN last year, none was perfect after the field was narrowed to 32 teams. The best record, shared by 5 brackets, was 30 and 2.

Gilbert owns the National Basketball Association’s Cleveland Cavaliers. The team plays in an arena named for Gilbert’s company. Berkshire owns The Buffalo News, and Buffett is the newspaper’s chairman.