Monty Hall

You will have gathered from past posts that I have a keen interest in statistics and probability. I have no qualifications or specialised knowledge - just an interested amateur. The name of Monty Hall cropped up the other day, and his name is associated with a particular probability problem, which might entertain any of you who share my interest. This is a subject which may well take a series of posts to cover properly, so for starters, here's the problem -
You are the contestant in a game show. You have seen off all the other contestants, and are now alone going for the big prize, a top-of-the-range sports car. You are presented with three doors - call them A, B and C, and told the car is behind one of them. You are invited to pick a door. Let's say you choose Door A. The game-show host (Monty Hall) now opens one of the other two doors, say Door B, and shows that to be empty. He now says to you "Well, obviously the car is not behind Door B. It is therefore either behind Door A - the one you chose, or behind Door C. You may now change your mind if you wish. Do you want to open Door A and take whatever is behind there, or do you want to swop to Door C and take whatever is behind there?" You have been watching this game-show for months now, and have come to realise that Monty Hall will never open the door with the car behind it - after all, this would spoil the game. So, knowing all this, what is your best strategy? Should you stick with your original choice of door, swop to the other door, or doesn't it make any difference? More later.