The arithmetic
What is a gambling system?
A gambling system is a rule for what to bet and how much, usually derived from recent results. Martingale, Labouchère, Paroli, D'Alembert and every named variation are the same idea in different clothing.
None of them change the price of the bets they place, so none of them change what the session is worth.
The two families
Negative progressions increase the stake after a loss. They win small and often and lose catastrophically and rarely. Martingale is the pure form.
Positive progressions increase the stake after a win, which caps the damage and also caps the upside. Paroli is the common version.
Pattern systems bet on runs, alternations or overdue numbers. They rely on a machine having a memory, and no machine in a casino has one.
What would actually be needed
To beat a house edge you need a bet priced better than its true odds. In a casino the rules prevent that except in a couple of famous historical cases involving physical tables and, briefly, a card count.
Online, the shuffle is a certified random number generator and there is nothing to count. A system cannot manufacture value that the game does not contain.
Why they keep selling
Because they work most of the time. A negative progression produces a long string of small wins, which is exactly what a convincing testimonial looks like.
The losses arrive rarely and take everything, which is exactly what nobody posts. Anything sold with a guaranteed win rate is selling the good half of that distribution.