## Mathematicians Show Randomly Guessing NCAA Outcome Is Extremely Improbable

March 1, 2006

Combinatorics calculates that randomly picking the outcomes of every game in the NCAA tournament stands one chance of success in more than 18 quintillion. If every person on Earth could fill out a bracket every second, then it would take them roughly one century to fill out all possibilities.

## Science Insider

BACKGROUND: It's time again for "March Madness," when U.S. college basketball teams compete to win the NCAA Division I Basketball Tournament, and buddies compete with each other by picking winning teams to guess the ultimate outcome of the tournament. But the realities of mathematical probability dictate that it's almost impossible to get your picks 100 percent right.

CALCULATING THE ODDS: Since there are 64 games in the March Madness tournament and two possible outcomes for each team's game -- a win and a loss -- the number of possible outcomes for the tournament is a staggering 2 to the power of 64: that is, 2 multiplied by itself 64 times, or 18,446,744,073,709,551,616. If one dollar bill represents each of the possibilities, and the six-inch bills are placed lengthwise end-to-end, the line would make two round trips between the Earth and the middle of the Big Dipper -- a distance of about 75 light years. In fact, if you put in a dollar for each of the possible ways to fill out the team bracket chart (see link below), you would be able to pay off the U.S. National Debt (about \$8 trillion as of March 2004) 2.3 million times over.

THE MATH OF FILLING OUT THE POOL FORMS: Combinatorics is a mathematical theory of counting individual objects, particularly units of a finite set, like a collection of marbles stored in a small pouch. Once primarily a mathematical curiosity, it is vital to many areas of modern technology. For example, it is a useful tool in determining probabilities and the number of structures possessing certain properties as applied to telephone (fiber optic) networks and computers. It can also be used to analyze industrial process schedules, electrical networks, and economics. And it's the math that you'd use if you actually filled out every possible form.

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## Did you know?...

If you wrote out all your predictions for one bracket in one second, it would still more than 500 billion years to write down all the possibilities -- longer than the age of the universe. If a billion of your closest friends pitched in, you'd be done in 500 years.