Game show . . .?

Yes, I would switch. Since there are three doors to start with, I have a probability of 1/3 to have the prize behind the door I pick; and each of the other doors has the prize behind them with a probability of 1/3.

Once a "wrong door" is selected by the host, the probability of the prize behind my door remains 1/3 (no change has been made to the contents behind it). However, since the total probability has to be 1, the probability of having the prize behind the other door goes up to 2/3.

I would therefore, switch and pick the other door.

Switch or don't switch; go with your gut. It is a coin flip either way.

ASIDE TO loki: After one of the doors is open the probability for your door DOES change. in the beginning there were 3 equally probable places where the prize might be hidden. At that point there is a one-in-three chance that the prize is behind the door that you pick. *NOW* after one of the empty doors is open, there are two equally probable places where the prize might be hidden. Thus, there is a one-in-two chance that the prize is behind your first pick. However, there is also a one-in-two chance that the prize is behind the remaining door that you didn't pick.

ASIDE TO moose: Before one of the doors was open you did have a 2/3 chance that you picked wrong. HOWEVER, after one of the empty doors is open, the probabilities change. There is now only a 1/2 chance that you picked the wrong door. If you switch doors THAT door has a 1/2 chance of being the wrong door too.

There is no way to improve your odds at this unless the host knows which is the right door and has a lousy poker face.

You should switch doors.

I think the key is that whichever door you choose, the host can always open a door which has nothing behind it.

This means that the probability of having picked the right door originally is the same as the probability, given that the host opens an empty door, of having picked the right door originally.

This probability is namely 1/3

Clearly if the probability of the prize being behind your door is 1/3, the probability of it being behind the other open door is 2/3 (as probabilities must add to 1), so by switching you double your chance of winning from 1/3 to 2/3

you probably chose wrong the first time. there was a 2/3 chance of it. when one of the doors is opened, and there is no prize in it, the third door is the most likely to have the prize.

I would switch doors.

No I always go with my gut instinct. I can't be sure if he is asking me to switch to the empty door or the one he is about to open.

I would stick to my first instinct for two reasons. Naturally, someone's first guess is the correct one. Even if someone weren't so sure what to do, you have a 50-50 chance, so it's worth taking it. According to your description, there's nothing to lose.

I would follow my first mind on this one because that is the most famous quote especially when you do and theirs nothing behind your second choice.

no, you have to stick with the first choice you had or if you switch and you end up being wrong it is not nearly as worse as if you had gone with your originally pick and didn't get it.

ok by my expierence in guessing [I am about to be a freshmen] I have learned that my first choice most of the time is right

Personally, I believe it would be best to ask advice from someone else (a best friend or neighbor?) if you cannot make the decision yourself.