That's the answer to the original Monty Hall problem. The statement of this problem is slightly different. Are you sure that difference does not change the answer? For instance, do you think that the fact that in the original problem the host had an intent to open a non-car door, and in this problem the intent of the host is unknown can change the ansewr?

The only thing you changed was that one of the goats is the sheep. For the purposes of the problem, you could simply redefine both of these as "animal". Now there are two animals and one car, which is identical to the Monty Hall problem. The intention of the host does not have any impact on the probability of the doors, only opening a door has this impact.

@IanMacDonald, not quite. I also changed the fact that the motives of the host are not known anymore. In particular, we don't know that he intentionally revealed the sheep. For all we know, he just opened a door at random, which might have been a door with a car, but happened not to be one.

+1 because without guessing the host's motives I can't see a difference from Monty Hall.

@CalebBernard, but in the original problem the intent of the host played a very important role. It might not be correct to assume that if the intent of the host is unknown, then the answer remains the same.

@Ishamael Maybe, but if I am forbidden to think about his motives, I see no choice. When the host opens the middle door, maybe he chose a non-car door or maybe he opened any random door... maybe he even had a chance of opening the door I myself picked! But if he played classic Monty Hall then I should switch, and if he chose randomly I think I should still switch, since (as I think of it) the two other choices have been "collapsed" into one doubly-good choice. If he had opened the middle door and it led to a car, I couldn't switch to it, so that hardly even matters as far as I can see.

@CalebBernard: "If he played classic Monty Hall then I should switch" is correct. "If he chose randomly, I should still switch" is wrong; if he chose randomly, then there is no advantage to switching. See the accepted answer. This is a subtlety of the Monty Hall problem that many smart people miss. This subtlety is actually the entire point of the question, and this answer is wrong.

@Nemo In THIS instance, the information gained by knowing where the sheep was automatically means you should switch, even if the host chose it randomly. You HAVE the extra info, regardless of HOW you got it, and switching IS beneficial, right now in this instance.

@JLee, do you think you could explain why it is beneficial to switch mathematically? You're reasoning seems to be based on you not seeing any "essential difference between this problem and the Monty Hall problem", which is incorrect because the rules of the door shown are different.

@jlars62 I could, but it is the exactly the same as switching in the Monty Hall problem. The extra information given (sheep behind another non-chosen door) is extra information, regardless of how it was obtained, whether randomly (this problem) or deliberately (original Monty Hall).

@JLee: I know you think you are right, but you are wrong, and the accepted answer is correct. Just like people who do not believe switching helps in "classic" Monty Hall, it can be very hard to convince people of the right answer for this (completely different) question. What sometimes works is to say "do a simulation and get back to me".

@JLee The fundamental difference between the op's version and the classic problem is the door chosen by the host has a dependency on the door selected. In the ops problem there is no dependency. So, suppose the sequence of events were reversed. You are standing in front of all 3 doors without having made a choice at all, and then out of the blue the middle door opens and you see the sheep. You still have not made your choice... Then, you pick door 1. At this point, you are in the exact same position as the OP's problem and in this scenario the choice to switch is obviously 50/50.

@Nemo I am no stranger to being wrong. I also like to create simulations.

@Jlee: I have written up my own version of the answer. See what you think.

@JLee I think the OP complicates it unnecessarily by saying that you "don't know" the host's motive. But if the host chooses the door randomly, for sure switching doesn't help. It's not that hard to crunch the numbers on this.

@JLee Assuming you can not switch your choice to the door that the host opens, the (1, 2) and (3,2) combinations should be 0% for switching, which makes the percentages on each side even. Granted, the op is unclear on whether or not that assumption is valid.

@jlars62 That's quite an assumption there

@JLee Yes you are right about that, and I edited my comment.

@Ishmael. That is an assumption, since the problem statement never says that we cannot pick a revealed door.

@JLee: Actually it does not matter what your options are when the host opens the prize door, because by assumption that did not happen. I am sorry but your analysis is still wrong. I have updated my answer...

@JLee: I have rewritten (and expanded) my answer once again. See what you think of the "deck of cards" analogy, and compare it to your own analysis.