I wrote my own program and, to my surprise, 66% is the right answer. ( I thought it was 50% chance)
Then I reviewed my own program and I finanlly understand why 66% is the right answer.
The reason is at the door the host opened.
In 2/3 of chance, the door he opened is not a random pick.
In your first guess, you have 2/3 chance to guess wrong, so the door number the host must opened is limited to a certain door. (He can not opened the other door).
By doing the switch, you are saying: “the first door I chose is wrong”, which is 2/3 of chance.
