ELI5: What is Monty Hall problem?

Imagine you're at a birthday party, and your friend says: "I have a super cool prize for you! Let's play a game!"

She shows you three boxes:

• Box #1
• Box #2
• Box #3

You pick Box #1. Your friend, who knows where the bike is, says: "Hmm, before we open that, let me show you something." She opens Box #3, and there's a goat!

She then asks: "Okay, so you picked Box #1. Now, do you want to stick with your original choice of Box #1, or do you want to switch to Box #2?"

The Monty Hall Problem is: should you switch?

• Most people think it doesn't matter – it's 50/50, right? Either the bike is behind Box #1 or Box #2.

• But, switching actually doubles your chances of winning the bike!

1. When you first picked a box, you had a 1/3 chance of picking the box with the bike. This also means there was a 2/3 chance the bike was behind one of the other two boxes.

1. When your friend opened a box with a goat, she didn't change the original odds. The 2/3 probability that the bike was behind one of the other two boxes is now concentrated on the one remaining unopened box.

1. By switching, you're essentially betting on that initial 2/3 probability instead of your initial 1/3 guess.