The Martingale betting system works well in theory. You double your bet each time you lose, so that when you finally win, you net a profit. Once you win, you reset your betting so that you are back to your original bet size. This allows you to make a profit slowly since the amount you will win is always just a shade over what you have previously lost. This method of betting works only when there is a fifty-fifty outcome.
In practice, this does not work. For one, no bankroll is big enough to weather out the variance that can occur in a game like blackjack. Suppose you lose ten hands in a row. The amount that you would lose with a $1 base bet is $1,023. It is possible to lose even more hands in a row than this. If you lost fifteen hands in a row, your total loss would be over $32,000. This is uncommon, but very much a possibility. There are table limits in place that would prevent a game from getting this out of control. When the system dictates that you would need to bet this much, a common table has a limit of $500—your bet would be impossible to place and the system would fail you.
The Martingale system might work on paper, but this is something that the casinos know of, and have measures in place to prevent from occurring. Having a set table limit is a concrete and easy way for them to protect against the losses that a system like this would cause them.