ncaa math odds itconnexx

Dear ITConnexx,

I am in an NCAA Tournament office pool, and I really want to win.  If I cover all my bases, how many different ways are there to fill out the NCAA Brackets?  

Signed, Interested Nerd

 

Great question Interested Nerd!

Since there are 63 games to be played, and you have two choices at each stage in your bracket, there are 2^63 different ways to fill out the bracket. 2^63 = 9,223,372,036,854,775,808 That’s more than nine Quintilian possibilities.

 

So ITConnexx, what are my chances of a perfect bracket?

 

Wow Interested Nerd, you are full of great questions today!

Even if every person in America filled one out (300 million people), the probability of someone winning is:

300,000,000
----------- = .00000000003253
  2^63

Thinking of it in another way?  

Imagine that you’re going to fill in a bracket by flipping a coin. Each time you get heads, you fill in the first team (the one above, or to the left). If you get tails, you fill in the second team. Each possible sequence of 63 coin flips corresponds to a unique way of filling in a bracket. So the number of ways to fill in a bracket has to be the same as the number of unique sequences of 63 coin flips, which is 2^63.