# Bracket Math

I love March Madness! Not only is it a chance for me to watch 4 basketball games at one time, I get to geek out with some ridiculously large numbers—the odds of producing a perfect bracket prior to the tournament. For this exercise, we will limit ourselves to the round of 64 and beyond (since the NCAA can’t trick us into pretending we care about the First Four unless our team is playing).

**Basic Probability**

**Number of teams- 64**

**Number of games- 63 **

This is way more obvious than most people realize so you can stop counting the blanks on your bracket. If one team is eliminated in every game, it will take exactly 63 eliminations (games) to leave one team victorious.

**Possible outcomes of each game- 2**

One team will win, one team will lose.

**Possible number of brackets- 2^63 = 9,223,372,036,854,775,808 (over nine quintillion)**

If you don’t understand basic probability, here is a crash course. Multiply the number of possible outcomes of an event times the number of possible outcomes of every other event. In this case…

2 (the number of possible outcomes of the first game) x 2 (the number of possible outcomes of the second game) x 2 (the number of possible outcomes of the third game)…x 2 (the number of possible outcomes of the 63rd game) = 2^63 power.

If you don’t trust that math, work it out with a simple 4 team bracket:

There are only four possible winners of the tournament, but there are two different ways for each team to win because there are two possible opponents for each winner in the championship game. To verify the math…

2 (the number of possible outcomes of the first game) x 2 (the number of possible outcomes of the second game) x 2 (the number of possible outcomes of the third game) = 8

2^3=8

**Astronomical Numbers**

**Understanding 9,223,372,036,854,775,808 possible brackets**

If you printed out 1,000 brackets you would have a stack of paper 8 inches tall.

Print 1,000 brackets 999 more times you would have one million brackets.

You now have enough 8 inch stacks to cover ¼ of a basketball court.

Repeat that whole process 999 more times and you will have one billion (1,000,000,000) brackets that are now covering 250 basketball courts in 4 inches of paper.

You would need to repeat this entire process over 9 billion (9,000,000,000) more times in order to have every possible bracket.

**If you printed that many brackets…**

- You would be able to cover over 76.5 billion basketball courts up to the height of the rim.
- You would be able to make 6,261 stacks of paper that reached the sun. and still have one-tenth of a stack left over.
- If you enlisted the help of every person on earth (all 7,000,000,000 of us) to make one unique bracket per minute with no breaks to sleep, eat, or do anything else…we would finish a few months after the tournament ended in the year 4519.
- From the time the bracket is finalized to the time entries are locked in most contests is about 89 hours. In order to have all of the brackets printed in time, you would need to have a computer capable of printing 28,787,054 brackets every nanosecond.

But don’t bother with all of that…

I made out the perfect bracket this year and have already spent Warren Buffet’s $1,000,000,000.

Posted on March 19, 2014, in Math, Sports and tagged astronomical numbers, bracket challenge, odds, one billion dollars, Warren Buffet. Bookmark the permalink. 1 Comment.

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