Winning Roulette Systems
Since casinos have existed, players have been coming up with systems to beat them. Roulette is one of the most successful and common casino games due to the small - but existent - house edge. Though it is not possible to win in the long-term, here are several systems designed to minimise losses and maximise returns:
Martingale is one of the most famous systems for gambling. Essentially, one doubles their bet after each loss (generally in an even money bet such as odd/even on roulette). In theory, you will always win enough to cover your losses plus one extra bet.
For example, if you lose $10 you will then bet $20; lose this and you bet $40. If you win, you will now have $80. You then bet $10 again and continue. In practice, this system isn't foolproof as it is quite easy to lose a number of bets in a row and have to wager large amounts to get your losses back. If you have a large bankroll, though, it's a good way to enjoy a lengthy roulette session.
"Roulette systems have been touted as ways players can overcome the casino's house edge, and while in the long term you simply can't increase your odds, betting patterns and strategies can payoff in the short term."
The Cancellation System/Labouchere
This system has a goal of winning a certain amount of units in roulette with odd/even or red/black bets. It is up to you how much a unit is and what you will be risking.
Assuming a ten-unit goal, you would note down ten 1s on a piece of paper. When all the numbers have been crossed off, you have won ten units and can quit for the day.
For each bet, you will be wagering the sum of the number on the left and the number on the right (unless you have just one number left, in which case you bet that). If you win, cross off both numbers; if you lose then place the sum at the end.
For example, you have a ten-unit goal and ten 1s written down like so: 1 1 1 1 1 1 1 1 1 1.
To start, you wager 2 units (1+1) and win. Cross off both numbers, leaving 1 1 1 1 1 1 1. The next stage is another 2-unit wager. This time you lose, so you add a 2 to the right (1 1 1 1 1 1 1 1 2). This means your next bet will be 3 (1+2). If you were to lose, your paper would read 1 1 1 1 1 1 1 2 3.
There is still a risk of losing the bankroll you have assigned if you have an unlucky streak - if you don't have enough left to bet the sum of the left and right number, you bet only the left number. Continue until you have replenished your bankroll to bet normally, or you have bust.
Human beings habitually recognise and find patterns, even when none exist - this is why people see faces in inanimate objects, for example. Many online roulette players like to view the previous spins and try to spot a pattern - for example, if there have been an abundance of results of red, they might decide black is overdue and bet it heavily. Of course, another player might feel red is "on a streak" and bet red. Of course, roulette games are completely random and you cannot predict future spins with past results on a fair wheel.
Gambling systems, especially for games with a clear house edge, are far from fool-proof. However, playing them responsibly with disciplined practice will minimise losses and maximise your time at the tables.
If you are interested in a deeper understanding of the math behind the systems, it's worth reading up about optimal strategy. The numbers and calculations behind it can be rather complex, but this paper (PDF) is a good read on the subject.