You are a contestant on a game show.

There are three closed doors.

Behind one door is the star prize, which is a brand new car.

The other two doors have a booby prize behind them.

The game show host knows which prize is behind each door.

You are asked to pick one of the doors.

Instead of opening the door you have chosen, the host then opens one of the other doors. And behind this door is a booby prize.

So that leaves two remaining closed doors. Behind one of these doors is the second booby prize. And behind the other door is the car.

You are then asked whether you want to stay with your original choice of door. Or whether you want to switch to the other remaining door.

And the question is, whether you have the better chance of winning the car if you stay with your original choice? - or if you switch to the other door? - or whether each door actually has exactly the same chance of winning the car?