I am having a very hard time understanding the Monty Hall Problem, from an intuitive level. I've had a lot of people trying to explain this to me, including my professor and my brother, who is a graduate statistics student. However, I can only understand up to the part that the host's door choice is not random, but cannot wrap my head around the fact that this non-randomness makes the probability to win, if the player switches doors, jumps from 1/3 to 2/3.
Note: I am a maths graduate student who doesn't have much experience with everyday life's statistics situations. Learning statistics/probability to me has always been challenging, not because of the maths, but because of the (intuitive) meaning of the equations. This Monty Hall problem is an example of my inability to comprehend a real-life statistics situation.
While answering the question, please keep in mind that I hope to relate this Monty Hall problem to something intuitive that I can experience in real life.
