Why does switching doors in the Monty Hall Problem increase odds: 2 doors, 50-50

Question

I have read through around 10 articles and webpages on this problem, and still don’t understand. I’ve run simulations and yes, switching does get you better odds, but why?

In: Mathematics

Answer 1

Here’s a way of framing the problem that allowed me to understand it. (Let’s use the 100 doors example). Let’s think about it inversely.

Instead of making it so the goal of your first choice is to pick the prize door, make it so the goal of your first choice is to pick the *wrong door.* With that in mind, you have a 99% of making the right decision (aka the wrong door).

Then the host eliminates doors until the only there are only two remaining. Since the door you first picked had a 99% chance of being the wrong door, then odds are, the remaining door has to be the prize door.