Gotta love March Madness… all the games, the buzzer-beaters, the upsets, the cinderellas. And I’ll admit it, unless it’s a Husky game, I don’t even follow college basketball until Selection Sunday. Then it’s bracketology time!
With some websites offering big prizes for correct brackets, including CNN SI’s $10 million prize, I thought that someone with enough time and programming smarts could brute-force their way to victory. I mean, with a finite number of teams (64) and a finite number of games (63), there must be a definitive, finite number of possible outcomes.
It stands to reason then that someone could feasibly write code to create enough unique userIDs and brackets to systematically guarantee themselves victory. But then I did some math and found out why that will never happen.
Sometimes the best way to tackle a big problem is to start small. What if there were just 4 teams, playing a total of 3 games (2 semi-final games and then the championship)? It is easy to chart the number of potential outcomes:
In this mini-tournament, there are 8 possible outcomes. Two possibilities in each game, raised to the power of 3 games: 2^3 = 8. Alternatively, you could say you have a 1 in 8 chance of picking the perfect bracket. This is the same probability of flipping a coin “heads” three times in a row.
Now imagine the odds of flipping a coin heads 63 times in a row, and begin to grasp the improbability of building the perfect NCAA tournament bracket.
Two possible outcomes in each game, raised to the power of 63 games: 2^63 = 9,223,372,036,854,775,808. Yes, 1 in 9.2 quintillion. Looks like Sports Illustrated’s $10 million is safe.
So even if someone did write the computer program, 9.2 quintillion entries would surely crash the database and get the user banned from the contest. I think it might raise a red flag when the number of entries is more than a billion times the entire population of the planet. But imagine the headline:
GoDawgs230498652304892308@gmail.com Wins Grand Prize!
Given that a No. 1 seed has never lost their first round game to a No. 16 seed, you could effectively remove 4 games from the exponent, bringing your total number of combinations down to a more reasonable 576,460,752,303,423,000. Only 500 quadrillion? Piece of cake!
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Tags: math
Wow! And I thought Bryn was the math nerd in the family.
Did Bryn help with this??
[...] enough. The odds of winning are obviously very small, but it can’t be harder than picking a perfect bracket, [...]