I keep hearing about this on gambling forums over and over so it's time to put an end to this once and for all (at least on Bitcointalk, I'm aware this system has existed for centuries and is not going away any time soon unfortunately)
There are even many people selling bots here that use the martingale system on several sites.
The martingale system entails doubling down your stake upon every loss. So, if your initial stake was, say, $1, then you'd bet $2 if you lost a game, and $4 if you lost another one, and so on until you go broke.
The expectation is that you'll never lose with this method, which I'll debunk mathematically.
The saying "The house always wins" exists because there is always the 'house edge', we'll be generous and assume the house edge is a small 1% (when it usually is 2% or higher).
This means that the probability of you losing a game is 51%. Let's assume your bankroll is $100, and your initial stake is 1% of that, or $1.
After six consecutive losses, you would have lost $63 dollars using the martingale method, and will have a remaining balance of $37, after which you would be unable to double down any further.
Many would say that the probability of losing six in a row is very low. That is indeed correct, however, this is exponentially more likely with more games played.
So, assuming a loss rate of 51%, your chances of losing six in a row are: 1 in [ 1/(0.51^6) ] games, or 1 in 57 games.
So, based on this math, after you have played 56 games, statistically speaking, you have a less than 1% chance that you will not have gone nearly bankrupt.
And this is using calculations which don't even assume a minimum or maximum betting limit. Every single game I know has had a maximum stake limit. You may or may not hit that maximum stake limit before you hit the six losses in a row, in which case, you would have a permanent negative ROI a lot faster than calculated above.
There are also many conspiracy theories that games implement various anti-martingale methods, like deliberately giving people long losing streaks at certain intervals. However, I believe this is largely a hoax. The martingale system is, for the most part, self defeating, and casinos would actually love someone who plays like that, because it means the casino is basically guaranteed a win.
Also, if they did implement anti martingale techniques, then one could simply play with an algorithm that defeats such a pattern. For example, you could play the anti martingale technique which entails doubling down when you win, and halving your stake when you lose. It would be every mathematician's dream come true if casinos did make their games follow a fixed/rigged anti-martingale losses pattern like that. Instead, games scatter wins and losses at a random pattern, combining that with the house edge is effectively a guarantee that the casinos will make money. If you truly want to win in gambling, you have to learn creative ways to defeat the house edge. The martingale method does not reduce the house edge, it merely satisfies you psychologically by changing how you perceive your losses.
martingale only sucks to gamblers who has a small amount to gamble and also most gambling site has a maximum stake limit (just like you said) the reason they put this "limit" is because martingale does work and the house can lose continuously if they didn't implement the maximum stake limit.