My intuition is failing me with the monty hall problem, the one with the three doors. Explain it to me in a way that ACTUALLY makes sense. I can't understand intuitively how it would be a 66% chance to win if you switch, I could see 50% but how is it 66%?
The reason for the 66% chance if you switch can be explained with casework. Because one of the losing doors is always opened after you choose, switching when the initial choice was the winning door will lead to the other losing door, but switching when the initial choice was one of the losing doors will lead to the winning door.

Effectively, the probability of switching leading to the winning door is the probability that the initial choice was wrong, or 66% due to two of the three doors being losing doors.