Do online casinos allow martingale system?

YES, and they LOVE it when you use it! It is a surefire win for the casino! Too much risk for little reward for the player, and little risk with great reward for the casino!

Up to your credit limit or rather the amount you've deposited to your account which means that the Martingale system won't work as it assumes you have infinite resources.

The Martingale system is the exact opposite of a rational bet sizing system. With every loss, the Martingale system has you doubling your bets, resetting to the minimum bet after a win. This can be mathematically proven to ensure ultimate ruin as the number of iterations go to infinity.

You're far better off with proportional betting such as Kelly or Fractional Kelly. Keep in mind that not all payout odds and probabilities warrant a bet under Kelly, indeed you'd be hard press to find one that is positive Kelly in a Casino.

Note that with log utility systems like Kelly, you reduce your bet size with each loss.

The mathematical basis of Kelly is the same equations used to determine if those are 1's or 0's that's being read off your hard drive and Kelly can be proven to always result in exponential growth of wealth provided that betsize can be infinitely divisible however since there are minimum bet sizes, it's possible but unlikely to be bankrupt by Kelly as well, hence the use of fractional Kelly. If you want to minimize the risk of bankruptcy with Kelly, be sure that your wallet >> minimum bet size.

Of course, Kelly requires you to have a reasonable estimate of probabilities.

They would probably send you a fruit cake as a "thank you" if they knew you'd be using the Martingale System.

In case you're not following, the Martingale System is a fast way to make you broke and the casinos rich.

Lol. Of course not. If you tell them you're going to do it, they might comp you extra.

Casinos love martingale players because they know eventually, they're going to make a killing off of them.

EDIT: John W needs to go back and re-read about the Kelly criterion, or read it somewhere from somebody who actually knows what they're talking about. Kelly criterion is only helpful in POSITIVE expectation games, like for card counters at blackjack. It will do nothing but make you lose slower in negative expectation games.

Yes. They allow you to use it, but they won't allow you to make a bet greater than their table maximum.