As basketball fans around the country finalize their NCAA brackets today, **John Pike**, a professor of mathematics at Cornell University who specializes in probability and statistics, offers some advice to increasing your perfect bracket probability.

**Pike says:**

“The 1-in-9.2 quintillion estimate is based on the assumption that each guess of a particular game outcome is like an independent toss of a fair coin. Of course, if you tweak the assumptions, you get different answers.

“For example, if you suppose that someone has a 60 percent chance of correctly guessing the outcome of each game, then the odds of them guessing all games correctly are about 1 in 94 trillion. If their chance of guessing correctly is 70 percent, then this works out to just over 1 in a 5.7 billion.

“In general, one would assess the likelihood of a particular bracket by multiplying together the (conditional) probabilities of the 63 purported wins. There are all sorts of reasonable ways to estimate these individual win probabilities, but assuming that they are consistently around 70 percent is certainly optimistic.

“For the sake of argument, let’s assume that your guess of the winner of each game is based on the flip of a coin that has an 70 percent chance of indicating the true victor. If 10 million people fill out brackets like this, then the chance that no one wins is about 99.8 percent.

“It is perhaps worth noting that given a sequence of head to head win probabilities, the most probable bracket does not necessarily consist of choosing the team that you think is most likely to win at each stage.”

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**Daryl Lovell**

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