Yes, you should choose the other door. The reason why is because you are
statistically more likely to win than by sticking to your current choice. I
know that's very hard to believe at first but the maths is relatively simple.
Do you trust maths? It put men on the moon and makes possible the technology
that you're using right now. I'm terrible with maths but I saw this very
quickly:

When you made your initial choice you had a 1 in 3 chance of being correct. That
is, you had a 66% chance of being INCORRECT. So the chances are you're wrong,
sorry. When the host opened the other door he gave you additional information.

When you make your first choice you have a 33% chance of winning. There is a 66%
chance that the money is behind one of the two other doors; the odds are stacked
against you. It's far more likely that one of the two OTHER doors is the winning
door. When the host shows you an empty door, that 66% chance doesn't just
vanish, that 66% chance is now on the other closed door. Therefore your greatest
chance of winning is on the other closed door, so you should switch.

Try it 100 times and you'll see it for yourself :)

Put another way:

You make your choice. 33% of the time you will be correct. 66% of the time you
will be incorrect and, when this happens, there are two remaining options: One
good and one bad. If you KNEW you were incorrect in your initial choice then
you would know that there is a 50/50 chance of winning behind each of the two
other doors, and if the host then opens one of those other doors then you know
you have a 100% chance of being correct. But you don't KNOW that you're
incorrect, however there is a 66% chance that you are incorrect and therefore,
if you are indeed incorrect with your initial choice, you will then have a 100%
chance of being correct by switching. So therefore, 66% of the time it will be
better to switch.