Trust me, I realize that this sounds like "fuzzy" math, but it's not. This is in fact a case of fuzzy reality.

Try it like this (this was basically my methodology, except I didn't have a pal around):

Get a pal.
Get three cards, of which two are black, and one is red.
Your pal holds the cards.
Choose a card.
Your pal flips over a black card that you did NOT pick.
Stick with the card you picked.
Record whether you won or lost.
Repeat 30+ times.

Now repeat, but this time switch cards.

By your logic (which I understand), sticking with your initial pick should give you approximately a 50% success rate. After all, it's the same as choosing from two cards, right? But it's not. It's a continuation of the original probabilities. I guarantee that in this case you'll win more times when you switch than when you stick.

Better yet, write a computer simulation to do the above a million, jillion times (I expect Enron will have to do this).

If you still don't believe me, answer this:
Why should sticking with your first pick give you any better odds than your initial 1/3 odds?