Monty Hall and the 1000 Doors

Monty Hall decides to perform his final episode of theLet's Make a Dealseries with a little twist, and Calvin is elated when he is the first contestant to be called to the stage. Everyone eagerly watches as Calvin approaches the stage, waiting to see the surprise Mr. Hall will present.

Mr. Hall then hollers into his microphone, "AND THE SURPRISE IS...... CALVIN WILL BE PLAYING WITH 1000 DOORS INSTEAD OF JUST 3." The audience gasps, but Mr. Hall keeps talking, explaining the rules:

• 999 of the 1000 doors covers a pig, while the last coversthe most amazing super special magnificent supercar of your dreams.
• Calvin will pick 1 of the 1000 doors, after which I will open 998 doors which cover a pig, leaving two doors for Calvin to choose from.
• Calvin will then have to choose whether to open the door he originally chose or the door I left closed.

Should Calvin open the door which he originally chose, or switch to the door which Mr. Hall did not open?