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

Well two CHOICES, don’t automatically make both choices of equal probability. If instead we roll a die, and choice A is “roll a 1” and choice B is “roll anything but a 1”. You need to choose A or B before the die is rolled. Do you assign 50/50 chance of success to both choices?

Monty Hall is essentially saying, choose a door. Now we group the other two doors into the other choice. Do you stick to your choice or switch? You are given the option to switch your CHOICE. Because Monty Hall always opens a door (not randomly) that does not have the prize, he is essentially saying stay with your door choice or switch to choose the other two doors.