You have N doors. Behind 1 door is a prize. Behind the other N-1 doors there is nothing. You pick a door. One of the remaining N-1 doors with nothing in it is revealed.

Now you're given an option: declare your chosen door as your final choice, or select a new door. If you select a new door, one of the remaining N-2 doors is revealed to you to have nothing.

Now you have an option to keep this new door as your final choice, or pick a new door. You may continue picking doors until N-2 doors have been opened, revealing nothing.

What's the optimal strategy? When should you declare a door as your final pick to maximize your odds of receiving the prize?