What is the probability that someone could fill out a correct bracket for the ncaa tournament?

Question

With 64 teams in a single elimination bracket, what is the chance that you could pick every single game correctly? I realize it's a very very small chance...I was just curious as to what the actual number was and how you could find it out. On Yahoo they're giving $5 million to anyone who can fill out a correct bracket...i wonder if anyone will even get it. Let me know if you can find it out. Thanks!

Answer 1

You would have to pick the correct outcome to all 63 games (that ignores the "play-in" game, including the play-in game would mean 64 total games).  Assuming that each game has a 50/50 chance of outcome, that means there are 2^63 possible brackets.  That's 9,223,372,036,854,775,808 possible brackets, good luck picking the perfect bracket.  It's never been done, by the way.

Answer 2

there are 32 games in the first round with 2^32 possible outcomes

there are 16 games in the second round with 2^16 possible outcomes

there are 8 games in the third round with 2^8 possible outcomes

and so on for 4, 2, 1 games in the next three rounds

there is a total fo 2^(32 + 16 + 8 + 4 + 2 + 1) = 2^63

= 9.223372e+18 possible brackets.

if you pick at random you have only a 1.084202e-19 probabilty of being correct.