Assuming a fair table, with just the inherrant mathematical edge to the house.
I walk in with £2,000.
I bet £100 Red. approx 49% that red comes up. It comes up black.I lose £100.
I bet £250 on Red. It comes up Green. I'm now down £350.
I bet £500 on Red. It eventually comes up Red. I'm up £150.
The above is 2 losses to my 1 win. A dangerous game to play, but even with more losses, I should still win, as long as I have the capital to keep playing and I know when to quit.
That only works if you bet more when you know you're going to win and less when you're going to lose. If you had bet $100 on each spin in your scenario you would be down $100. Like you said, the odds favor the house, so you'll lose in the long run. If you happen to bet big and manage to win that spin, walk away a winner.