March Billionaire Madness

How is everyone's bracket faring after day 1 of the tournament? Well, for those of you who entered Quicken Loans's Billion Dollar Bracket Challenge, I hope the answer to that question is, "Absolutely perfect!" and not, "North Dakota State has a basketball team?" I'm a big fan of March Madness, both because I like college basketball and because I like all the math that you can whip out while making a bracket. Pretty nerdy I realize, but hey, we like what we like! That being said, something caught my eye when reading the terms and conditions of Quicken Loans's challenge:

Odds: Grand Prize – 1:9,223,372,036,854,775,808, which may vary depending upon the knowledge and skill of entrant

So, that's one in, roughly, nine quintillion. But, how did they arrive at that number? The Motley Fool has an article discussing the reality behind the billion dollar offer with some fairly interesting notes:

A couple years ago, the Associated Press talked to Augsburg College professor Michael Weimerskirch, who explained the odds of filling out a perfect bracket.

If a coin flip is used to pick the winner of each game, the odds of a perfect bracket are one-in-100 quintillion -- that's a one with 20 zeros. Weimerskirch said, "You're just as likely to win Powerball three consecutive times."

There's clearly a difference in opinion as to the odds (also, you're about 50,000 times more likely to get a perfect bracket only using a coin than you are to win Powerball three times consecutively). Looking at the odds given by Quicken Loans, it's clear that they're treating all of the games as coin flips and calculating from there since 1/0.5^63 = 9,223,372,036,854,775,808. So, how does Weimerskirch get to a number over ten times as large? Not surprisingly, by utilizing all 67 games, including the four play-in games. Now, here's where the fun starts, what are the odds if you actually know a little about basketball?

However, most don't flip a coin to pick their NCAA tournament winners and losers. Assuming a semblance of basketball logic is used, DePaul's Jay Bergen puts the odds of a perfect bracket around one-in-128 billion.

That's a pretty substantial drop merely by including a semblance of basketball logic. However, he doesn't mention what that logic would be. How would you monkeys go about calculating the odds of a perfect bracket? Because you see, apparently there's some big money to be made by insuring these prizes:

The holding company was paid $10 million to insure Pepsi's "Play for a Billion" sweepstakes back in 2003.

Now, this wasn't a bracket competition, and the odds of winning were exactly 1 in 1,000 (which, doesn't seem like a good strategy for an insurer). So, given that the secondary prizes will end up costing $2 million with 100% certainty and entries are limited to the first 10 million brackets, how much would you charge to insure a contest like this? Well, if ten million people all have a one in one hundred billion chance (i.e. they all have a semblance of basketball logic) of winning one billion dollars, your expected outlay is a mere $100,000 to insure against the $1 billion loss - seems like an awfully cheap premium. What do you monkeys think? How much is Berkshire bringing in on this deal?