You also have to trust the host to behave fairly. For instance, a malicious host might decide to open a door with a goat only when your first choice was correc

You also have to trust the host to behave fairly. For instance, a malicious host might decide to open a door with a goat only when your first choice was correct. If the rules of the game are such that the host must always open a door with a goat regardless of whether your first guess was right or wrong, then it makes sense to switch doors. If not, it might be a trap; probably the best strategy is just to flip a coin.