The Martingale is the king of the so called Progression Systems in roulette. Actually, this system is most popular in roulette, but in can also be used in blackjack and craps.

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Martingale Theory
The idea behind the theory, is that you cover your losses when you play roulette by doubling up on your bet if you lose. This way, you always cover your loss, as a subsequent win will pay back at double, giving you the funds to soak up a run of bad luck. Any winning streaks will accelerate your profits.
The theory is that you will never hit an infinite sequence of losses.
When to use the Martingale
This roulette system is best employed on the even money bets (eg black/red, even odd, 1-18/19-36). Why? Well, these have the best odds on the table anyway, and you don´t want a long progression of losses.
2 Key Banana Skins in Martingale
We did say that there was no such thing a sure bet in roulette!
The first thing to realise, is that even money bets may give even money payouts but they don´t offer 50-50 odds, as there is a nasty 0 pocket in the wheel. This actually gives the house edge. So in European Roulette, in any case, your odds aren´t 1:2, they are 1:2.06. So every now and then the ball is going to pop into the 0 and you´ll lose the bet.
(Top TIP): the only way to increase your odds in roulette is to play European Roulette and not American Roulette. This is because American Roulette has 2 zero pockets (greedy, eh?), meaning your odds are now 1:2.11 on even money bets.
The other issue with this strategy, is that there is no such thing as an infinite betting limit. All tables have a maximum betting limit (some more than others). Anyway, the upshot is, is that you may hit a losing streak that takes you beyond it, which means that you are unable to cover your losses from the next round.
In order to minimise this effect, go for small initial starting bets (say £1) and look for roulette casino sites that have a high table limit. But be careful! It´s easy to rack up losses on Martingale if you are not methodical and you stop at your loss limit. On the other hand, set yourself a win target and if you hit it walk away!