What is the chance of getting a perfect bracket?
The NCAA March Madness tournament is a beloved tradition in the United States, where millions of fans fill out brackets predicting the outcomes of each game. One of the most captivating questions that arise during this event is: What is the chance of getting a perfect bracket? This article delves into the mathematics behind this intriguing question and explores the likelihood of achieving such a feat.
The NCAA March Madness tournament consists of 68 teams, with the winner being crowned as the national champion. To win a perfect bracket, a person must correctly predict the outcome of every single game, including the championship game. This seems like an almost impossible task, but how unlikely is it, mathematically speaking?
The number of possible outcomes for a single game is two, as either team A or team B can win. For a tournament with 68 teams, there are 67 games to be played. Therefore, the total number of possible outcomes for the entire tournament is 2^67, which equals 7.189 billion.
To win a perfect bracket, a person must predict all 67 games correctly. The probability of this happening can be calculated by dividing the number of successful outcomes (1) by the total number of possible outcomes (7.189 billion). This results in a probability of approximately 0.0000000137%, or 1 in 73 million.
This figure highlights just how unlikely it is for an individual to fill out a perfect bracket. Despite the low probability, many people still attempt to do so, driven by the thrill of the challenge and the possibility of winning substantial prizes. In recent years, companies like Quicken Loans have offered massive cash prizes for perfect brackets, adding to the allure of the quest.
While the chance of getting a perfect bracket is incredibly slim, it doesn’t diminish the fun and excitement that the tournament brings. March Madness is a time for friends, family, and colleagues to gather, discuss picks, and share in the collective experience of filling out brackets. And who knows? Maybe one year, someone will achieve the seemingly impossible and win a perfect bracket.
