Problem, btw, because some guy named Monty Hall had a game show where he actually did this very thing--except I don't think it was $1 million behind the one door).

/interactivate/activities/SimpleMontyHall/

There are many other simulators of this as well.

Anyone who doubts the people who say you should switch, go ahead and play it a bunch of times. You can either switch or not (this particular simulator keep track of the stats for both cases). You would have to play MANY times to get your win/loss percentages to match the actual probablilities to within a decimal point, but you don't have to play very long to get reasonably close. If switching didn't matter, you would quickly get your winning percentage close to 50% for both strategies, but since it does matter, instead you will soon see that you win somewhere close to 66% of the time if you switch and 33% of the time if you don't.

Statistics can be pretty abstract, and for some people, seeing is believing.

(You could even do this experiment yourself with three face cards--say the two jokers and an ace. Have someone else place them in a random order, you pick a card, they show you one of the two remaining cards (that isn't the ace), and you either switch or not. That way you could be sure there wasn't some mathematician conspiracy behind all the Monty Hall simulators on the internet.)