Mysha, I explored all three scenarios because they had all been previously mentioned. While each one had been examined, they had not been compared.

Oh dear! I didn't expect or intend anybody to take my rather tongue in cheek comment "unless you're particular about which goat you get" seriously. As it is unlikely that the contestant has met either goat (and possibly doesn't even want a goat) they would be unlikely to be concerned with the which they got. So I'll move away from goats and use loo brushes instead (same make, same colour, same value, no names).

The reality of the first scenario is that your first choice is irrelevant, and is pure showmanship as somebody has already said. Whether you make a choice or no choice at all, you know that Mr Hall will eliminate one loo brush. Therefore your only meaningful choice is in the second stage, and will always be 50/50. Your part in the first stage was meaningless, and did not improve or lessen your ultimate chance of winning. It is always a straight choice, a loo brush or a car, the rest is window dressing.

The second case is very different. If the prizes are a loo brush, a TV, and a car, your first choice influences what Mr Hall eliminates. If you choose the loo brush, then the TV will get eliminated, you are then guaranteed to get the car by changing your choice. If your first choice is either the car or TV, then the loo brush is eliminated. You are then left with a 50/50 chance of getting the car.