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# March Madness Bracket Odds: In the Pentillions!

# March Madness Bracket Odds: In the Pentillions!

Ezra Miller calculates the odds of winning Warren Buffett's $1 billion challenge

Durham, NC - If you're a mathematics professor, what's the chance you'll be called by a business reporter for the Los Angeles Times and asked to calculate the odds of Warren Buffett having to pay out $1 billion for the perfect March Madness bracket?

If you're Ezra Miller, who teaches the popular "Math Everywhere" class at Duke, the odds are in your favor.

Miller, who is also an associate director of the National Science Foundation-funded Statistical and Applied Mathematical Sciences Institute in RTP, says Stuart Pfeifer of the LA Times found him on Tuesday by looking for mathematicians who know something about game theory (not an ideal fit, actually, for this question).

"What you want is a good actuary or a sports analyst," Miller said. "But any math professor could probably answer his question."

And since Miller is at Duke, the Times reporter figured Miller must know something about basketball. That was roughly correct. For the past several years he has had Duke basketball players in the "Math Everywhere" class, which is team-taught with professors Ingrid Daubechies and Jonathan Mattingly. The class covers, among other things, voting theory that underlies college sports rankings.

"I have had occasion to learn more about the related mathematical issues," he said.

Miller got Pfeifer's call around 1 p.m. on Tuesday. "He followed my calculations -- which I carried out during our roughly hour-long phone call -- remarkably well," Miller said, "and he demonstrated substantial understanding of what the results of the calculations meant."

The story -- with Miller's conclusion that even a skilled handicapper would have at best about a 1-in-1-billion chance of completing a perfect 67-game bracket -- was posted on the newspaper's website the same afternoon and was quoted on the "CBS Evening News" that night.

Tracking the story after that was easy. "My brother's father-in-law, who is as close as any of my family, lives in Santa Monica and is a big UCLA fan," Miller said. "He was so surprised to see my name. The feedback came quickly."

Miller came up with his 1-in-1-billion probability through a calculation that placed games into categories ranging from close calls that could go either way to near locks. (See accompanying story for the math.)

He says he did pull out a calculator to prevent errors in estimation. "The calculation comes down to multiplying 67 numbers together, and while that isn't so hard to estimate, given a couple of minutes, the penalty for mistakes is rather high if it gets published in a widely read newspaper," he says.

Based on his finding, Buffett would need to charge contest sponsor Quicken Loans Inc. a premium of about $10 million to break even against his expected results, Miller told the Times.

"If I were Warren Buffett, anything over $10 million, I would probably do it," Miller told the Times. "If $1 billion were going to ruin me, I wouldn't. But it's not going to ruin Warren Buffett."

Responding later by e-mail to a fact checker for CBS News, Miller calculated the actual odds for a single person choosing all the game winners randomly to be about one in 148 pentillion (that's 1 in 148,000,000,000,000,000,000)

Miller says his "Math Everywhere" students thought his media walk-on was "amusing and cool." He says they will soon have the know-how to complete the same rough estimate he offered to the newspaper.

Does he plan to submit a bracket of his own when the contest opens on March 3? "My bracket would be terrible," he admits, adding that it wouldn't be worth his time. Still, he has nothing against the bracket craze in general. "It's fun to have a little more of a stake in the games."

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