The fact is, you have double the chances of winning the 1 million dollars if you switch doors once you are told one of the doors that has a penny behind it. You have a two out of three chance to win the million dollars if you switch doors every time while only having a one out of three chance if you stick with your first door.

This hasn't been proven to be 100% true. Its just one way of looking at things.

Another way would be:

• Contestant Picks Door two out of the three choices given. This gives a 33% chance at winning $1 Million dollars. The other two doors each also have a 33% chance at containing 1 Million Dollars or Nothing.

• The person making the offer then reveals Door number 3 has nothing in it and offers the contestant to switch doors.

• There's now two doors to choose from not three making odds of winning 50/50. The contestant doesn't gain any advantage via switching doors.

This debate was a hot topic and debated frequently at one point. The game show Lets Make A Deal hightened the debate as they offered prices in the same fashion as your example. That being said, if I was every given such an offer I would change doors because ........ why the hell not.