During the school year when I should be writing papers, catching up on my academic readings, or beginning any number of projects that need to get finished, I am as usual overthinking completely irrelevant and useless pieces of knowledge. In this instance, it has been the Monty Hall problem.

For those that don’t know, the Monty Hall problem is a mathematical brain teaser that proves that up is down, black is white, and chaos is the fundamental nature of the universe. To briefly summarize, there are three doors, and behind one of them is a prize. You pick any door, and without revealing anything, one of the remaining two doors will be opened to unveil the not-prize. You are asked to choose again, and there is now a 2/3 chance the prize will be behind the last, unpicked door. You have a better shot of getting the prize if you switch your answer from the original choice. Like I said, chaos.

From Wikipedia: Maths!

Anyway, this voodoo of probability increases with additional doors. So if you pick between ten doors, and eight of them reveal the not-prize, you have a 9/10 chance of getting the prize if you switch your answer. What if we increase the number of doors to infinite? There are infinite doors, you pick one, and then all but two doors are eliminated: the one you picked, and a second door. Maths say that there is a 100% certainty of the prize being behind the other door. Now, we could use this as a point of contention in the never-ending 0.999… equals 1 debate, or we could just accept that it is literally impossible to not be behind the second door.

What this means in practical terms is that when you are faced with a universe full of opportunity and choices, you will, with mathematical inevitability, make the wrong decision. Thanks Maths!

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