Since this question comes up regularly, I somehow expect my last message won't be convincing to some people.
Here's a (hopefully) better way to explain it:
OK, we're drawing marbles out of a bag. In the bag, there are two green marbles and one red marble. Green is good. You and I get to draw one marble each. If I get to go first, does that mean I'm more likely to draw a green marble than you are? (This is what the first-base advocates claim happens with the 'good' cards in the shoe.)
No.
2/3 of the time I will draw a green marble, leaving you a 50/50 shot.
1/3 of the time I will draw a red marble, and you're 100% certain to get a green one.
Let's add the probabilities... (2/3) * 50% + (1/3) * 100%
Well, imagine that.

The probability that you'll draw a green marble after I've drawn whatever, is the same 2/3 shot that I had when I drew first.
Order doesn't matter.