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What Are the Odds of Predicting a Perfect NCAA Tournament Bracket?

What are the odds of winning Warren Buffet's \$1 billion prize for picking the perfect 2014 NCAA tournament bracket? Should Mr. Buffet be worried about his money? And how are the odds of winning related to the famous rice and chessboard problem? Keep on reading to find out!

By
Jason Marshall, PhD
Episode #189

The Rice and Chessboard Problem

As a quick aside, by some bit of cosmic good fortune, it turns out that chessboards have exactly the same number of squares as there are teams in the NCAA tournament. And I say "good fortune" because this means that the numbers behind the NCAA tournament odds are the same numbers that, as legend has it, the inventor of the game of chess knew about when he made a deal with the emperor of India way, way back in the day.

The story goes that the emperor was so impressed with this new game that he told the inventor he could have whatever reward he wished for. Being a rather ingenious fellow, the inventor did not ask for gold, jewely, or anything obvious like that. Instead, he wished only to receive 1 grain of rice for the first square of his chessboard, 2 for the second, 4 for the third, 8 for the fourth, and so on doubling the number of grains for each square of his board.

The emperor thought this a rather meager request, but happily agreed to what he thought was a pretty sweet deal for himself. Until somebody ran the numbers and realized that the final square of the chessboard would have to contain 263 grains of rice—which, as we know from our NCAA tournament math—is perhaps only about 10 times fewer grains of rice than there are grains of sand on Earth. That's a lot of rice!

Warren Buffet's \$1 Billion Bet

If we didn't know it before, we are all now well aware of the fact that 263 is a HUGE number. Which means that Warren Buffet's \$1 billion is pretty safe, right? Yes, probably. Although the truth is that the odds of winning aren't actually quite as bad as I've led you to believe.

And that's because most people aren't making brackets by randomly guessing about winners and losers. In fact, there are a number of very safe bets that you can make—such as the fact that first round games are almost certain to be won by the higher ranked team—that bring the odds down a fair bit.

How much? Don't get your hopes up because they're still pretty steep. But according to a Business Insider article, DePaul University math professor Jeff Bergen believes that the odds could be reduced to somewhere around 1 in 128 billion by applying this sort of clever thinking. Which is something like 70 million times better than the odds based upon pure random guessing.

So, should Mr. Buffet be worried? Well, you don't become one of the most successful investors in history by making stupid bets. And we've seen that the math is on his side. So I'm guessing he's not too concerned. But there's always a chance, so be sure to get those brackets submitted!

Wrap Up

Okay, that's all the math we have time for today.

Please be sure to check out my book The Math Dude’s Quick and Dirty Guide to Algebra. And remember to become a fan of the Math Dude on Facebook where you’ll find lots of great math posted throughout the week. If you’re on Twitter, please follow me there, too.

Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!

Chessboard and basketball player from Shutterstock.