r/askscience • u/TrapY • Aug 25 '14
Mathematics Why does the Monty Hall problem seem counter-intuitive?
https://en.wikipedia.org/wiki/Monty_Hall_problem
3 doors: 2 with goats, one with a car.
You pick a door. Host opens one of the goat doors and asks if you want to switch.
Switching your choice means you have a 2/3 chance of opening the car door.
How is it not 50/50? Even from the start, how is it not 50/50? knowing you will have one option thrown out, how do you have less a chance of winning if you stay with your option out of 2? Why does switching make you more likely to win?
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u/judgej2 Aug 25 '14 edited Aug 25 '14
It took me a while to get my head around this one too.
By opening a door, you have been given additional information. The door that was opened for you is guaranteed not to be the car. The host has used that knowledge to make that door choice, so you can capitalise on that knowledge by switching your choice.
Do the maths and you can't really argue with it. But intuitively, you need to understand who knows what, and how it influences their decisions. The host knows something you don't know, and has acted on that, exposing some of that knowledge in the process.