Just to make this crystal clear, there are no roulette systems that you can use to beat the roulette table in the long run.
There are some systems that show a positive result in the short run but when the law of large numbers kicks in, all systems will eventually lose. This is not to say you can not get rich quick off a roulette table.
Imagine if I offered you a million pounds to play Russian Roulette. A single bullet and all you had to do was pull the trigger next to your head. Five times out of six you would be able to walk away a million pounds richer but one in six times, you will die. The people that walk away, assume they have found a great way to get rich but the reality is much different.
I like to think of the use of roulette systems, like playing Russian Roulette. You can win but when you lose, you lose big and it can wipe you out.
Martingale Strategy
The martingale strategy is probably the best-known roulette system. Its a double your bet system. The idea is to bet, say a pound. If it wins, pocket the pound and start again. If it loses, then “double-up”, ie bet £2. If that wins, then it will wipe out your £1 loss and make you £1 profit. If it loses, then “double-up” again and so on pocketing a pound every time you win.
The theory is that eventually you will win and it will clear your losses. The system slowly generates cash 1 pound at a time. For simplicity's sake, assume the probability of getting a red is 1/2. The chances of losing 3 bets in a row are 1/8 (12.5%). The chances of losing 10 bets in a row is 1/1024, less than one-tenth of a percent. If you keep doubling up, your win will eventually cancel out losses.
Theoretically, this is sound. On an infinite bet roulette table, the martingale strategy will make money. Unfortunately, we live in the real world where there are no infinite stake roulette tables. Sooner or later you will hit the house limit. After 13 “double-ups”, you would be betting £8192 just to try to win a pound.
You might think that 13 reds or 13 blacks would never come out but they do. Over a long period, you'd be surprised if 13 reds never came out. By then, you would have hit the table limit. You'd have lost £16383. Unless you have been extremely lucky beforehand, this will have wiped out any profit from the previous games and much more.
Labouchere System
The Labouchere System is another progressive betting system where you increase your bets after each loss. You start with a sequence of numbers, for example, 1,2,2,4,5,5. It doesn't matter what they are. The first bet is the sum of the first and last number, in our example, this would be 6.
If you win, your cross out these numbers, leaving you with 2,3,4,5. The next bet is 2+5=7. If you lose, you add the last bet to the sequence. For example, it would be 1,2,2,4,5,5,6. The next bet would then bet 7 units.
This has more appeal to some people as it looks like it provides stable returns. Every line you clear will win you the total of the line. In our example, this is 19 units. It suffers from long streaks of losing bets in the same way as the martingale does. You can make short terms gains using this but one losing sequence can wipe you out.
Reverse Labouchere System
This is a famous system that was used by Norman Leigh to break a casino in France. This system actually worked for him. The basic idea is to increase stakes after every win. You start with small stakes and every time you win, you increase your bet. The small losses will be inconsequential and a long sequence will have you hitting the table limit and winning.
So for example, if you had the sequence, 1,2,2,2,2. The first bet would be 3 units. If you won then you would add the win to the line, eg, 1,2,2,2,2,3. The bet after that would be 4 units. If the bet has lost, the end numbers would simply get removed, eg, 2,2,2.
This keeps going until the table maximum is hit or the line is wiped out. As the line is relatively small, the losses will be inconsequential. That's the theory anyway.
I suspect that there was something else going on when Norman Leigh broke the bank. First, this was done on a wheel which could have been slightly biased. This could have just tipped the balance in favour of a certain set of numbers. Secondly, there could be some survivor bias. Only the winner write about their exploits – the losers simply disappear.
I don't think this would work on an online casino with its near-perfect random number generators (RNGs). If you want to try though, the best place is Bet365 Roulette where you can bet for just 1p all the way up £5000 on red or black. For any system to work, you really do need a big variation between the minimum and maximum bet. The bigger the better.
Other Systems
There are many other systems that are essentially the same as the ones described above. They involve, increasing, decreasing stakes in a systematic manner. These include, D'Almbert and Fibonacci sequences.
They all suffer from the same problem that a long sequence will wipe you out. If, on the off chance, you do find a foolproof roulette system, keep it to yourself. Do not write an Ebook about it!! Most people will assume you are a scammer so will not buy. You may as well live off the roulette earnings rather than selling your idea.
Conclusion
Roulette is a negative expectation game. You can win in the short term but in the long run, you cannot beat the casino. Think of systems as playing Russian Roulette or picking up pounds in front of a steamroller. You can win in the short term but when the losses come, they will be painful.
Roulette is a fun game and should be only played with money you can afford to lose. If you are tempted to try out any systems, try playing at bet365, the 1 penny roulette table will limit your losses.