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
The key piece of info many have a hard time with is that Monty knows which door has the prize at all times.
He will never eliminate the car. That makes it so what Monty does DOESN’T MATTER. He will never remove the car from the equation.
The bit that makes you think it’s a 50:50 is that the swapping confuses people. The entire thing is a 2 step problem. You pick -> other door is revealed to be goat. BUT you initially had 3 choices, so the outcomes branch from the initial 3. The fact that is is 2 steps cause people to see it as your door vs remaining door, thus the 50:50 until you actually map out all possibilities.
I know you pretty much got the gist from the other comments, I wanted to note why I think the 50:50 is so common.
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