Beating the Casino Edge with a Solid Betting Strategy?

[DoomSlice]

I havn't thought the math out on this one, and I really just want to get it down on "paper" while it is fresh in my mind. So feel free to tear me apart if this is totally wrong. Ok here goes.

Let's say you are playing a Casino game where the House has an inherent edge, like a roulette table. I start by placing a $1 bet on Black. If I win, I take my profit and on the next hand I bet $1 again. Now let's say I lose this time. Instead of betting $1 on Black, this time I double my bet and place $2 on black. Now if I win this time, I start at $1 again. If I lose again, the next time I bet $4, and so on and so on.

Now it would seem that if you found a game that had a small enough House edge, you'd be able to play this as a winning strategy since EVENTUALLY you'd be gauranteed to win your exponentially expanding bet and net a profit of $1 per "series". No?

This seems to go against all common sense, so someone prove me wrong with some math!