Google Monty Hall Problem. Answer: switch. It improves your chance of success from 1/3 to 2/3.

The best way to think of this problem is imagine a group of 1,000,000 doors. You are asked to pick a door behind which you imagine there is a prize. The host then opens 999,998 of the doors, leaving only your door and another door. He then asks you whether you'd like to switch or to stay with your original pick, as behind only one of the doors is a prize. Here, it seems obvious that switching is correct, improving your original 999,999 to 1 against shot to a 999,999 to 1 shot in your favor.

Similarly, you are 2 to 1 against picking the right door in the Monty Hall problem before the host opens the door, but the odds are 2 to 1 in your favor if you switch after being shown an empty door.