The answer to the problem is yes; the chance of winning the car is doubled when the player switches to another door rather than sticking with the original choice.

There are three possible scenarios, each with equal probability (1/3):

* The player picks goat number 1. The game host picks the other goat. Switching will win the car.
* The player picks goat number 2. The game host picks the other goat. Switching will win the car.
* The player picks the car. The game host picks either of the two goats. Switching will lose

In the first two scenarios, the player wins by switching. The third scenario is the only one where the player wins by staying. Since two out of three scenarios win by switching, the odds of winning by switching are 2/3.