You are making an assumption on the host behavior, the assumption being that if you repeat the experiment the host will open a door containing a goat. If you th

You are making an assumption on the host behavior, the assumption being that if you repeat the experiment the host will open a door containing a goat. If you think you're not and that the 1/3 - 2/3 probabilities are correct based on the single observation you made, consider this: you have 1 black ball and a 2 white balls in 3 different urns each containing a ball. You select one urn A. Some external agent randomly overturns an urn. That ball it contains is white. What's the probability that the ball in urn A is black? The answer is 1/2. Not 1/3. It's 1/2 because you the assumption you make on the external agent's behavior is that it's random. If you don't make an assumption on its behavior, you can't calculate probabilities. If you make the assumption that the external agent picked up the white ball on purpose and will repeat that behavior when faced with similar circumstances, the probability is 2/3. My point is that if you don't make an assumption on the host's behavior, you can't calculate probabilities.