Suppose you're on a game show with the following rules:

- There are three doors. Behind one of the doors is a prize; which door has the prize behind it is chosen completely at random. You must pick one of these doors.
- Once you pick a door, the host chooses one door and shows you that there is nothing behind it. The host will never choose the door that has a prize behind it, nor will the host choose the door that you chose.
- You are then given the option to use the door you originally picked or to switch to the door you know nothing about.
- If the door you chose in step 3 contains a prize, you win. If it does not, you lose.

What strategy (if any) will give you the highest chance of receiving the prize, and what is your chance of winning the prize with this strategy? (Hint: it's not 1/2.)