You're a contestant in a game show and win your way to the final prize...

The host presents you with three doors concealing prizes. Behind one is the grand prize - a brand new Ferrari. The other two conceal scraggly old goats as booby prizes. You are invited to choose a door. After you've chosen a door and before it is opened the host explains that "Because you scored so high in the contests I'm going to show you where one goat is, behind a door you didn't pick" and then opens a door you didn't choose to reveal one of the goats. The host then asks if you're comfortable with your chosen door because if you want to you may change your choice. When you settle on a choice you get the prize behind the door.

What is your best chance to win the Ferrari?
(Check one option - of the odds you expect in the column representing your best choice).

Keeping my first choice, my odds are: No matter what I chose my odds are: Changing my choice my odds are:
1/4 1/4 1/4
1/3 1/3 1/3
1/2 1/2 1/2
2/3 2/3 2/3
3/4 3/4 3/4
1/1 1/1 1/1