Albert Einstein supposedly once said: “No one can win at roulette unless he steals money from the table while the croupier isn’t looking.”

There are systems that beat roulette. A few years ago on Victors forum they had a contest. Out of 6 players, I think 4 of them were still ahead after a month or 6 weeks. Not saying they would stay ahead forever, but if your understanding of the game is that good, you're not far off from figuring a way to stay ahead. The simplest roulette computer I offer is called the 'Basic roulette computer'. It is just a basic roulette computer using the basic design described above. It is FREE to my roulette system players because it realistically can beat only perhaps 5% of wheels, and still the accuracy is nowhere what could be achieved.

Although I wouldn’t normally question Einstein, this statement isn’t true. In fact, you can use Einstein’s specialist subject, physics, to help you win. Or you can find a biased wheel that makes some numbers more likely to come up.

What Einstein actually meant was that there is no mathematical trick that can help you win at roulette. Each spin is an independent trial and, in the long run, the casino will win. This is different to a game such as Blackjack where the probabilities change as cards are dealt.

But some believe that it is possible to exploit the way the roulette wheel, and the betting cloth, is laid out to give themselves an advantage. The idea is that you can make bets on the layout in a way that you are guaranteed to win. But is this really possible?

Roulette wheel layout

Like a dartboard, the layout of a roulette wheel did not come about by accident. It was carefully planned and exhibits certain properties. In fact, there are two different layouts. An American wheel and a European wheel. The two layouts are shown below.

Notice that the American wheel has two zeroes. This is important as it doubles the advantage for the casino. On a European wheel you would expect to lose, in the long run, 2.7% of any money you bet with. On an American wheel you can expect to lose 5.26% (if you are interested in the mathematics of roulette, the video at the end will show you how these odds are calculated).

The numbers are arranged in a different order on each wheel but there are some similarities in the patterns. On both wheels, the red and black numbers alternate around the wheel, although if you removed the zeroes, the American wheel would have consecutive reds and blacks. The wheels are also structured so that the low numbers (1-18) and the high numbers (19-36) should alternate as much as possible.

On a European wheel, this is only violated where the 5 sits next to the 10 (both low numbers). On the American wheel, there are many examples where this rule is violated. It is for this reason that the American wheel is considered not as balanced as the European wheel. Both wheels also try to distribute odd and even numbers as evenly as possible. But again there are a number of violations of this rule on both wheels.

On the European wheel there are two other interesting symmetries. First, all the low red numbers and black high numbers are on one side of the zero, and the high red numbers and low black numbers are on the other side. Second, the sequence 29-7-28-12-35-3-26-0-32 contains no numbers between 13 and 24 (the second dozen). You can place a bet on the whole of the second dozen, with odds of 2-1.

So, can we beat the maths?

A simple search on Google will return many (possibly millions) of systems for playing (and supposedly winning) roulette. Some easy, some complicated, some well described, some not so.

A system should really be a combination of a playing strategy and a money management strategy. Perhaps the best known money management strategy is the Martingale system. This system is guaranteed to win money as long as you have enough of a bankroll to double your bet after every loss and you do not hit the table limit, which you will quickly do so. The Martingale system is probably the quickest way to bankruptcy known to man.

Whatever betting strategy, and money management strategy, you choose, they all suffer from the same fate. Assuming that each number on the wheel has the same probability of being selected – meaning the wheel is not biased – the maths means the casino will always win. The system may look good, and may work in the short term, but when one of the numbers comes up that you have not bet on you will lose and the casino will move towards its win expectation (2.7% or 5.26%).

Beat Roulette With Math Games

Some systems involve betting on many numbers, perhaps 20. In this case, you will win quite often as you are covering more than half of the numbers. But when one of the numbers does not turn up (and it will almost half the time) you lose all of the 20 bets you have made. This will often wipe out any wins to date.

Any system, so far devised, can be analysed to show that there is a win expectation for the casino. The following video shows the maths.

You might as well place a single chip on the same number every time and hope that it appears more than it should during the short time that you are playing.

We can dress up the layout of the wheel, the layout of the betting cloth, our number selection and our money management system however we like, but the maths is always there, quietly working against us. You might as well just have fun, pick random numbers and trust to Lady Luck. Either that, or do as Einstein suggested and steal chips (not that we’d recommend it).

By Ion Saliu, Founder of Roulette Mathematical Strategies

I. Mathematics of Winning Roulette Strategy, Systems
II. Glamour and Attraction of Roulette on Gamblers
III. Statistical Analysis of Roulette Spins (Double- Zero)
IV. Free Winning Roulette Systems #1
• Ion Saliu's Paradox and the game of roulette
• Relation of Birthday Paradox to roulette strategies
V. Free Winning Roulette Systems #2
VI. Ion Saliu's Roulette, Gambling Theory, Software Compared to Other Roulette Systems, Strategies
VII. Roulette Links, Resources, Software, Systems

1. The Mathematical Foundation of Winning Roulette Strategy and Systems

First captured by the WayBack Machine

Beat Roulette With Math Playground

(web.archive.org) on March 11, 2000.

The true book of roulette is founded on mathematics, probability theory and statistical analysis of casino roulette spins and random roulette spins. The winning roulette systems, strategies are totally free at this website; the software is free to run with a reasonable membership fee to download.

The common belief in the gambling world is related to the roulette wheel bias. Many kokodrilos (big–time gamblers) swear by the wheel in the sky that they make millions by exploiting the roulette wheel bias. There are plenty of legends. The wheels must have been terribly worn out.

I do have some problems and some remarks regarding the bias of the roulette wheel. I have done the most thorough research in this field. My tool of choice is computer software. My roulette software is not only unique, but founded on solid mathematics. I have analyzed both real–life casino roulette spins and random–generated spins. The reports are very much the same.

Nobody will ever be able to tell which one is the real spin report and which one is the report on computer–generated roulette spins. The number frequencies are the same. I apply a key parameter in my analysis: the SKIP. The skip represents the number of spins between two hits of the same roulette numbers. Again, the skips are the same for both real–life spins and randomly generated roulette spins. The statistical parameters are in accordance to theory of probability. You will see a statistical report on this page, and another one on a different page.

Wheel bias might occur sometimes. It's hard and costly to check very often every roulette wheel in a casino. Later on this page you will see an event of possible wheel bias I witnessed in a real casino. The data sample was not very large, however.

• The second roulette pairing statistical report I told you about is very interesting. If there is roulette wheel bias, then each roulette number must be followed preponderantly by certain numbers. I call this feature number pairing. It is a common feature that occurs in lottery as well. The pairing is also a feature in computer-generated roulette spins. The roulette pairing is not the result of mechanical bias. It is the result of prob