I am sure that someone in here can give you mathematical probabilities regarding your chances of breaking even doubling after a loss. However, I do know it will lead to your ruin. Theoritically speaking, (assuming there is no table limit and a bottomless bankroll) doubling after a loss will not only make you break even, it will put you ahead due to the DD, splits, bj, etc. Doubling after every loss, in theory, you will always at least recover all your losses and turn them into wins.
The problem, however, is that 1) you need testicles as huge as an elephant, 2) you need a very large bankroll, 3) if you get a losing streak you will eventually hit the table betting max . . . . . and that point . . . you're screwed BIG TIME!
In the scenario you presented of a $500 table limit and $10 bet observe the following losing streak and results of doubling after a loss:
These losing streaks WILL happen. Even if the table limit was $1000, that would only allow you to double down one more time.
If your playing BS, 6 deck shoe, I seem to remember some math whiz in here stating that the odds turn in your favor (+1%) after 5 straight losses, if this is true then perhaps it is a good time to start increasing your bets in moderation, not doubling, as losing streaks longer than 5 are not uncommon. And remember, the more decks played with, the odds are increased of having longer losing streaks. So, suffice it to say that doubling are a loss is a real bad, bad, bad thing to do! :-) It will lead to the poor house!
I wrote a simple Java program that simulates Martingaling to see how bad it is. Let's just say that it is not a good idea..
Bad streams occur. I was playing at the Las Vegas Club today, and lost 12 hands straight. Yes. You read it right, 12 straight. This was a five min table and I started out with 10, and stayed 5 every time afterwards. If I had doubled every time...