The NCAA estimates the odds of picking a perfect 63-game NCAA bracket are 1 in 9.2 quintillion. Although, that assumes every game is a 50-50 coin flip.
A DePaul professor once said that injecting a little NCAA men's basketball knowledge into the equation drops the odds of picking a perfect bracket down to 1 in 28 billion. He also said if every person on the planet filled out a bracket per minute, it would take more than 2,000 years to get to 9.2 quintillion and the perfect bracket.
Famously, wealthy investor Warren Buffett runs an annual March Madness bracket contest promising to give away $1 million a year for life to any Berkshire Hathaway employee who can pick a perfect Sweet 16 in the tourney.