This vCalc Probability of Picking NCAA Basketball Tournament equation computes the probability that someone could pick all the winning games in the NCAA basketball tournament bracket.  In other words this shows the base probability of picking all 63 tournament games before the tournament begins. This probability calculation does not take into account any applied knowledge that might be employed to make smarter picks.

Usage

You have two selections to change the display of the output probability:

• Tournament Round - you may select to see the probability of picking all the games correctly through each of the 6 rounds of the tournament. To see the probability of correctly picking all 63 games (all six rounds), select "6th round (Chamionship)"

• How to show results - this equation will display the resulting probability in one of three selectable ways:
  1. 1 in N: this displays the result as "1 in 9223372036854775808 chance of picking all correct through the 6th round (Championship)" if you choose the final round probability
  2. decimal percentage: this choice displays the result as a decimal value of probability; e.g., selecting "3rd round(56 games)" will display 1.387778780781445675529539585113525390625E-17.  That is approximately 0.0000000000000000139 -- a VERY small fraction.
  3. number of possible choices:  this displays total number of possible choices you could make in picking winners through the chosen tournament round; e.g., if you select "1st round (32 games)", the result will show 4294967296, which is the total number of possible bracket choices of the first 32 games

Description

The NCAA Division 1 Basketball Championship draws a tremendous amount of attention during March Madness and will again in March and April of 2015.   The tournament has 64 selected teams which play 63 total games. That is

• 32 games in the first round
• 16 games in the second round
• 8 games in the 3rd round
• 4 games in the regional finals
• 2 games in the final four
• the national championship game.

The total number of games is:  32+16+8+4+2+1= 63

In recent years there was a bracket challenge from Warren Buffet offering $1 Billion to the person who could pick the entire bracket correctly.  The odds of correctly picking the entire bracket were so small that Warren decided the the promotional opportunity was well worth the risk of the $1 Billion.  If you wish to try picking the whole  bracket, you can follow along with many of the sports networks and others who have bracket charts posted on-line^{1 2} and many sites will be following the progress of the tournament closely.

Here's how the large probability adds up:

You have two choices for each game at each round of the bracket.  Because there are two choices, there are `2^63` different ways to fill out the bracket with the names of the starting 64 teams.

`2^63` = 9,223,372,036,854,775,808   Try it in the equation. we let you see how improbable it is to pick the bracket at each round of the tournament as well.

This means there are more than nine quintillion different combinations you could choose from to fill out the entire bracket.

To put this in perspective, let's look at this probability compared to the number of people in the United States.  There are presently over 320 million people in the united States.  So, if everyone of those 320 million were to take a shot at picking the winners of each game in the the bracket, the probability that someone in the U.S. would pick the whole bracket correctly is:

`"Probability"_"(US)" = "320,000,000"/"9,223,372,036,854,775,808"` That's a probability of approximately `3.47" X "10^-11`.  That probability expressed as a decimal is 0.00000000003469447.  That is extremely small, even if everyone --every single person in the United States -- were to take a shot at completing the NCAA basketball tournament bracket.

1. ^ http://roundbyround.ncaa.com/
2. ^ https://tournament.fantasysports.yahoo.com/