Probability Riddle

This is a pretty standard question in probability, often referred to as the "Monty Hall question" There are 3 standard arguments:

Argument 1: It does not matter. The probability of finding the car in the remaining two doors was equal in the beginning, and they are still equal now. The fact that you put your hand on one of them cannot increase or decrease its probability of having the car under it.

Argument 2: If we repeated this experiment a million times, you would get the the car only one third of the time by sticking to your first door. People who consistently switch would win the other two thirds. Therefore you should switch.

Argument 3: Think about what you would do if there were a thousand doors, rather than three, and you opened 998 doors with goats behind them.