No, it’s a problem of certainty…
Let’s assume the host knows what is behind every door: then winning the “game” is contingent on both probability and whether the host “approves of” the contestant (for known / unknown factors) for reasons I shall now explain.
The Probability
From the beginning, there are three doors to choose from. A contest may pick the prize at a 33% chance odd compared to the 67% chance of the goats. However, this is rather inconsequential to the “game” at large.
The Certainty
From the beginning, the certainty exists in the host knowing which door has the prize and which two have the goats. Now, factor in this context: the contestant either severely dislikes, dislikes, likes, or severely likes the particular contestant (for any personal reasons). In all likelihood, the game show host is white, because this is a common trend in America. Therefore, if the contestant is non-white, then the host may or may not dislike that person more than if that person were white-skinned. This, among many other factors, contribute to the later suggestion of the host to the contestant…
If the host severely dislikes the contestant, then he (a male) will likely not even give the contestant a chance if that (black) contestant picked the first choice in error (a goat). My conclusion is this: if the (black) contestant picks a goat from the beginning, then the host may expose the goat right then & there, because he (being white) severely dislikes the contestant. Thus, the game is prematurely ended (for seemingly no reason).
If the host severely likes the contestant, then he will likely give the contestant a chance if that (white) contestant picked the first choice in error (a goat). My conclusion is this: if the (white) contestant picks a goat from the beginning, then the host may expose the other goat right then & there, because he (being white) severely likes the contestant. Thus, the game is continued (for seemingly no reason).
Furthermore, if both the host and contestant are white, then the host may or may not go so far as to actually suggest which door the prize is in directly to the contestant on the spot if you know how to look for these suggestive clues, a subtle nod, a wink, a pat on the shoulder, etc.
Thus, the game is rigged by the host knowing beforehand which doors the goats were in and which door the prize was in.
Welcome to the “game” … I wonder if it’s as fun when the host doesn’t know which things are behind which doors???
…I bet not! =D>