The chance of the car being somewhere behind the other two doors is two out of three . So to improve his chance of winning a car , the player if given the choice , should swap his one door for the other two doors right away .
The player therefore has the choice of either sticking with the original choice of door , or choosing the sum of the contents of the two other doors , as the 2\/3 chance of hiding the car has not been changed by the opening of one of these doors .