What were your testing parameters?

It's fairly simple, I would think. You set up two cards (perhaps one red, one black), face down.. with the assumption that your "third" (nonexistant) card has already been revealed as a "death" card. So, you can either stick with your card, or switch cards between the two remaining cards. Because you don't know what the two cards are that remain face down, the fact that previous cards were "wrong" cards is totally irrelevant. You could remove the two remaining cards, shuffle them randomly and lay them back down on the table and your odds would not change if you still selected the card on the "left" or the "right" as you had originally decided.

Your odds do not increase from switching cards when you must pick between the two.

The compound odds of flipping over two consecutive "wrong" cards are really what the math guys are talking about.. not the odds of selecting the "right" card in the second situation. It's the presentation that screws with your head.

Try flipping a quarter sixty times and see how many heads/tails you get. You're not likely to get 30 heads and 30 tails due to statistical deviation from a small data sample.