I've seen in several places that the odds of filling out a perfect NCAA tournament bracket are roughly 1 in 9.2 quintillion (9,223,372,036,854,775,808). That's just not true.
The math is sound. There are 63 games, each with two possible outcomes. That really big number I already typed out once is equal to 2^63. If you want to know the chances of correctly predicting 63 consecutive coin flips, that's your answer.
The thing is, NCAA tourney games aren't coin flips. The worst-case scenario you have for picking any given game is 50/50, but a lot are much easier. When 34-0 Kentucky plays 17-17 Hampton tomorrow night, I'd guess there's about a 99 percent likelihood (maybe more) that the Wildcats emerge victorious.
If choosing every winner was that simple, a perfect bracket would be too--you'd have a 54 percent chance (.99^63). Obviously most games are harder to get right than that. For the sake of simple math, I'll estimate there's a two-thirds probability of picking each one correctly on average. Under that premise, the calculation becomes 1.5^63, which makes the odds of predicting a perfect bracket "only" 1 in 124 billion or so.
9,223,372,036,854,775,808
vs.
124,093,581,920
Pretty big difference, huh?
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