This is a very good explanation. I hope you won't mind if I say the exact same thing you did in just a slightly different way that might help it click for someo

This is a very good explanation. I hope you won't mind if I say the exact same thing you did in just a slightly different way that might help it click for someone still not getting it. Your initial chances of choosing correctly are 1 in 3. So the car is behind the door you chose 1/3 of the time. After the host reveals which of the 3 doors definitely does not have the car it's still the case that your initial choice will have the car 1/3 of the time [0]. That means the other door must contain the car 2/3 of the time. So you should switch. [0] The haters are correct that the host hasn't changed the odds that your initial choice is correct. They just aren't tracking the implications of that fact.