A perfect NCAA tournament bracket comes with its perks: winning your office pool, the undying respect of college-basketball fans and, now, $1 billion from a guy who knows something about cashing in on his picks.

Quicken Loans announced on Tuesday a $1 billion prize paid out over 40 years—insured by Warren Buffett's Berkshire Hathaway —to anyone who pulls off the ultimate forecasting feat in sports: predicting every tournament game's winner. Past contests tied to the tournament have dangled seven- and eight-figure rewards, but this one significantly ups the stakes, even without the extra incentive of investment advice that Buffett promises.

The exact chances of nailing the winner of all 63 games are incalculable. "There are no true odds on something like this," Buffett said in an interview. "Einstein himself could not figure out the odds."

But they are wildly astronomical even by the most generous assessments. A previous Wall Street Journal survey of mathematicians pegged them anywhere between 1 in 150 million and 1 in 9 million trillion. Last season, the odds of pre-tournament favorites winning every game were roughly 1 in 3 billion, said the basketball statistician Ken Pomeroy. Buffett crunched the numbers himself but declined to reveal his own estimate. "I'm not telling you that!" he said.

Buffett said he fills out NCAA tournament brackets and, like most casual basketball fans, isn't always proud of his picks. "I was not notably successful on the basketball court, and I'm not notably successful in selecting winners," said Buffett, who roots for Creighton's basketball team, which is also based in Omaha, Neb.