In the Monty Hall problem if once the player has picked a door another door is randomly opened and happens to reveal a goat should the player switch his choice to the last door?

Answer 1

No, there's no reason to do so, switching in this case will win half of the time, exactly like sticking to the initial choice.

This Monty Hall problem variant is called the "Monty Fall" or "Ignorant Monty" variant. The possible scenarios which made switching win more often in the original Monty Hall problem, correspond in this variant to the scenarios where the randomly opened door revealed the car (and as such are not considered here).