Yet Another Monty Hall Question - Please advise if alternative scenario proves the same principle

If the host is under no obligations except not to lie, "behind one of the doors is a goat" reveals absolutely nothing. There is no conditional probability here. The chances of winning are 2/3 if the contestant stays, and 1/3 if he switches.

Also, if he wins, the goat should ride shotgun; they're notoriously bad drivers.

Edit: To answer your last comment, this version is more intuitive than the original. In the original, one has to interpret the information provided by the host's big reveal; in your variant, it is easy to see that the information is useless and that we can ignore the host.

Edit 2: I want to express the solution in an absolutely clear way that is not unique to this problem, because I think this mode of thought will be helpful to people who are perennially confused by these kinds of puzzles.

First, let's take the original Monty Hall problem. There are 3 doors, 2 hiding goats and one hiding a car. You choose a door uniformly at random. Now, there is a 1/3 chance that you've chosen the car, and 2/3 chance that you've chosen a goat. The host reveals a goat behind a door other than the one you've chosen. Now what?

2/3 of the time, you will be in this situation:

• you are standing in front of a door with a goat
• the other unopened door has a car
• if you switch, you will win
• if you stay, you will lose

1/3 of the time, you will be in this situation:

• you are standing in front of a door with a car
• the other unopened door has a goat
• if you switch, you will lose
• if you stay, you will win

2/3 of the time, switching is correct. Having no other information, you should switch.

Now, let's look at your problem in exactly the same way. There are 3 doors, 2 hiding goats and one hiding a car. You choose two doors uniformly at random. Now, there is a 2/3 chance that you've chosen the car and a goat, and 1/3 chance that you've chosen two goats. Regardless of what the host does:

2/3 of the time, you will be in this situation:

• you have chosen two doors, one with a car and one with a goat
• the unchosen door has a goat
• if you switch, you will lose
• if you stay, you will win

1/3 of the time, you will be in this situation:

• you have chosen two doors, both with goats
• the unchosen door has a car
• if you switch, you will win
• if you stay, you will lose

2/3 of the time, staying is correct. Having no other information, you should stay.