A couple articles I saw said there's about 9 quintillion ways to fill out a bracket, but if you have "some expertise" you could get it down to around 1 in 128 billion. They didn't define "some expertise," but I'd assume that at least means not picking 16s or 15s (unless vs Mizzou
).
For comparison, the odds of picking the winning number in the MegaMillions lottery is 1:259 million and Powerball is 1:175 million.