This is a variation of the famous Monty Hall problem.
I assume you know the usual setup. Here, the host behaves a bit different:
The host knows what lies behind the doors, and (before the player's choice) chooses at random which goat to reveal. He offers the option to switch only when the player's choice happens to differ from his.
Am I better off switching, or not?
One third of the time the initial choice the player makes is the prize and Monty offers a change
One third of the time the initial choice is Monty's Goat - no goat is shown
One third of the time the initial choice is the other goat - a goat is shown ad a choice is given
In two cases you are shown a goat - one of these you have picked the prize, the other you have a goat. It's $50:50$ stick or change.
In the third case you are not shown a goat. By this you know you have picked a goat (!) and you should change (if that is on offer) for a fifty percent chance of a win.