Martingale (negative progression). Double after every loss, revert to base after a win. Recovers the whole losing run with one win. Fails on table limits or bankroll exhaustion during a run of seven to ten losses. Highest risk of ruin of any common system.
D'Alembert. Increase the stake by one unit after a loss, decrease by one after a win. Linear rather than exponential, so drawdowns are far shallower than Martingale. Still cannot overcome the edge.
Fibonacci. Stake according to 1, 1, 2, 3, 5, 8, 13, 21 and so on, moving forward on a loss and back two steps on a win. Used only on even-money bets. Gentler than Martingale, slower to recover, identical expectation.
Labouchère (cancellation). Write a sequence whose sum is your target profit, bet the first plus last numbers, cancel them on a win, append the loss on a loss. The list, and the required stake, grows during bad runs.
Paroli (positive progression, sometimes called anti-Martingale). Double after each win, usually resetting after three consecutive wins. Risks only recent winnings rather than reserves, which caps the downside, but converts many small wins into occasional larger ones without changing the average.
James Bond. A fixed coverage bet: the bulk on 19 to 36, a smaller portion on the six line 13 to 18, and an insurance chip on zero, covering 25 of 37 numbers in one spin. Wins often. The eleven uncovered numbers, 1 to 12, produce a large single-round loss. The blended edge stays at 2.70%.
Flat betting. The same stake on every round. Not glamorous, I know. Empirically the cheapest way to play for a fixed number of spins, and the only approach whose worst case you can calculate before you sit down.
Independent simulation work reaches the same conclusion about "improved" rule sets: