Actually, The Odds Of Winning Warren Buffett's Billion Dollar Bracket Challenge Are Way Better Than 1 In 9,223,372,036,854,775,808

Billionaire Warren Buffett and Quicken Loans are sponsoring a bracket challenge for the NCAA Men's Basketball Tournament.

If you can fill out a perfect bracket, you will win a billion dollars.

So, what are your odds of winning?

1 in 9,223,372,036,854,775,808

The probability "one in 9.2 quintillion" has been cited quite a few times in various articles about the bracket challenge.

Before the 2012 tournament, DePaul University math professor Jeff Bergen posted a video on YouTube explaing where this number comes from.

There are 63 total games in a tournament bracket. For each of those games, two teams play, and one team wins. So, filling out a bracket consists of picking 63 winners.

So, you have two options for the first game, two options for the second game, two options for the third game, and so on, for all 63 games. To get the total number of possible ways to fill out a bracket, you multiply together all 63 of these twos, giving us 2⁶³, or about 9.2 quintillion, possible brackets.

Actually, it's more like 1 in 576,460,752,303,423,488

If all of these brackets are equally likely — if each game in the entire tournament is a 50-50 tossup, and picking the winner is basically a coin flip — we then get the odds of a correct bracket at one in 9.2 quintillion.

Of course, flipping a coin 63 times is probably not a very good strategy for deciding how to fill out your bracket. Most of the games are not 50-50 matchups.

Consider the first round (the round of 64) of the NCAA Tournament.  Of the 32 games in the first round, there are four games in which four of the best 64 teams (1^st seeds)  play four of the worst 64 teams (16^th seeds).

Since 1985, when the tournament first expanded to 64 teams, no 16^th seed has ever beaten a 1^st seed in the round of 64.

If we're comfortable assuming that this trend continues, we can safely fill in the four 1^st seed vs. 16^th seed games on our brackets.

Now we have 59 games to pick, and if we flip coins for all those, we have a one in 2⁵⁹, or about one in 576 quadrillion, chance of winning the tournament. Still pretty terrible odds, but by making this one assumption, we have boosted our chances by a factor of 16.

Or maybe it's more like 1 in 128 billion

Professor Bergen suggests that by taking a more nuanced approach to the tournament along these lines, we can improve our odds to around one in 128 billion.

That is still insanely unlikely — you are about 500 times more likely to win the lottery. And Quicken and Mr. Buffett probably have very little to worry about this coming spring.

Watch Bergen's video here:

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