The Mathematics

You may think roulette computers are always sophisticated pieces of hardware. In actual fact, most are very simplistic, although people that sell them want to you believe it is space-age technology. Here I will explain the simplest possible roulette computer algorithm, and it is used by almost every roulette computer.

Understanding What Makes Roulette Beatable

First we’ll need to identify various parts of the wheel so you know what I’m talking about:

Ball track: where the ball rolls

Rotor: the spinning part of the wheel where the numbers are

Pockets: where the ball comes to rest

Clocking: simply another word for “take timings of”. ie if you “clock” the rotor or ball, you are simply clicking buttons to take timings of revolutions.

What happens during a spin:

When the ball is released, it gradually slows down, loses momentum and falls from the ball track. Sometimes the ball hits a metal deflector (diamond) and falls without much bounce. Sometimes it bounces everywhere. Sometimes there is still a fair bit of ball bounce. And while you can never predict exactly where the ball will fall, YOU DONT NEED TO. You need only to predict roughly where the ball will fall with enough accuracy to overcome the casino’s slight edge against you (house edge). For some wheels, this is very easily done. For other wheels, it is much more difficult.

Here are some of the principles that are typically used to predict where the ball will land with professional roulette prediction techniques:

Dominant Diamonds

Dominant Diamonds
Ball hitting specific diamonds more

On most wheels, the ball will tend to hit a specific diamond more frequently than others. You can check this for yourself at your local casino by creating a chart like the one shown left. At the very least, you will find there are some diamonds that the ball almost never hits, or perhaps some areas where the ball almost never falls from the ball track. This is not random, and inevitably leads to more predictable spin results.

Now that we know WHERE the ball will fall at least an inordinate amount of times, what if we knew what number was under this area WHEN the ball fell? This is easy to determine, and I’ll explain how later.

Consistent Ball Timings

Consistent ball revolution timings
Consistent ball revolution timings

You may think that when the ball is released, the timings of each revolution is random. The reality is especially the last few ball revolutions of the ball occur with much the same ball timings. The right chart shows the revolution timings for the last few revolutions of the ball on three different spins. You can see they are all very similar. The very bottom row shows the sum of all timings from these last seven ball revolutions. The greatest deviation in timings is no less than 300ms (0.3 seconds).

This means that if we knew when the ball timing (speed) was about 1350ms per revolution (about 1.3s per revolution), then we’d know the ball has about 12,500ms (12.5s) before it likely hits the dominant diamond and falls. Again of course this wont happen every time. It only needs to happen enough of the time.

Do you need to know the precise ball speed to know when there are 7 ball revolutions remaining? NO, you can virtually guess when there are roughly 7 revolutions remaining. Do you need to know exactly how many milliseconds are remaining? NO, because the ball revolution timings for the last few revolutions are much the same. This means finding which number will be under the diamond when the ball hits it is very easy to determine. This is a critical to understand.

Ball Scatter

Ball scatter is basically ball bounce. Sometimes the ball will miss all diamonds. Sometimes it hits a different diamond to usual. But a lot of the time, the ball will hit the dominant diamond, then bounce roughly 9 pockets along before coming to rest. There is a lot more to it in reality, but from a simplistic perspective, this is scatter.

If you check your local casino’s wheels and compare where the ball first touches the rotor to its final restring place, you will see the ball bounce is usually still quite predictable over 15-30 or so spins. How we apply this knowledge is explained later.

Visual Ballistics

Adjusting for ball bounce
Adjusting for ball bounce

So far we know that on many wheels, the ball will mostly fall in the same region (dominant diamond), then mostly bounce 9 or so pockets. On many wheels we can actually skip the step where we consider how far the ball bounces after it hits the dominant diamond. This is because there is a more direct approach as explained below:

If you had a method to determine when the ball is about 1300ms (1.3s) per revolution, at that precise moment, you could look at the number under the reference diamond and write it down. Then wait for the ball to fall and come to rest. This will leave you with a first and second number like “A,B”. For example say you got 0,21. This will tell you that the ball landed 5 pockets clockwise of your initial “reference” number. See the left image for reference.

This tells us that starting from our REFERENCE NUMBER (A), the ball has about 12.5 seconds left before it hits the dominant diamond and bounces about 9 pockets, and ends up about +5 pockets from the reference number. Where the ball comes to rest is the WINNING NUMBER (B).

You may need to read this a few times, but the concept is very simple. Also see the video below which explains the concept too.

What I’ve explained above is a very simple method of beating roulette, or more like the science behind a method called “visual ballistics”. The key component of any visual ballistics method is how you determine when the ball is at the targeted speed. Because when you have identified that target speed, you will know the ball has the same ball revolutions left before it falls and bounces however many pockets.

Can you virtually GUESS when the ball has 1 revolution remaining? How about 2 or 3 revolutions remaining? How about 5 or 6? It really is not at all difficult. If you can be accurate to within 1 ball revolution, then you can achieve exactly the same accuracy as most roulette computers without needing any device. Remember, you don’t need to measure accuracy to within 5ms, 20ms or even 100ms because you are only determining how ball ball revolutions are remaining, and this automatically tells you the remaining ball travel time. You can be very sloppy and still be correct most of the time. And that’s as accurate as you need to be to equal the accuracy as most roulette computers.

In a follow-up video I’ll release soon, I’ll teach you a method that can accurately tell you how many ball revolutions are remaining. And you will achieve the same accuracy as almost every roulette computer.

The Basic Roulette Computer Algorithm

This is what most roulette computer sellers don’t want you to know. If you understand all of the above, you’d see how incredibly simple it all is. You’d also understand how you can afford to be very sloppy, and can just about guess how many revolutions are remaining and you’ll still very accurately determine how many milliseconds are left before the ball falls. It is essential to note that ALL roulette computers use the above principles. You can look at the demonstration videos of basic roulette computers, and use basic visual ballistics to achieve almost exactly the same accuracy – without even using any electronic device. But because sellers want to make their products seem more competitive and exclusive, they’ll tell you their devices are highly sophisticated with unparalleled accuracy.

Essentially the differences between the basic visual ballistic method I’ve explained and a simplistic computer are explained in the below chart:

Visual Ballistics BASIC Roulette Computer
How the remaining number of ball revolutions is determined Countless different methods. Some are perfectly accurate but complex to use, while others are just as accurate but very easy to use.Some methods use rotor movement to calculate ball speed, but such methods are ultimately impractical and inaccurate because rotor speeds usually vary too much between spins.Ultimately there are many very simple methods to accurately determine when there are ‘X’ number of revolutions remaining, whatever the value of ‘X’ is (typically about 4 or 5 ball revolutions).

The average visual ballistics method is no more accurate than a basic roulette computer, because whether you use visual ballistics or a basic computer, you still get the same initial reference number, and the same winning number (A,B).

The user keeps clicking a hidden button each time the ball passes a particular diamond. The computer calculates the time interval between clicks like a stopwatch, until the ball speed is in the set range.Let’s assume the computer is constantly waiting for the timing interval to be between 1300-1400ms (1.3-1.4s). When this time interval (ball speed) is reached, the computer vibrates to let the player know the target ball speed is reached. The player then observes which number is under the reference diamond. The ball then has the same number of revolutions remaining before it falls.The player then charts the distance between the reference number (A), and the actual winning number (B) as is done in the visual ballistics example on this page.

NOTE: The main difference is the rotor’s orientation is more precisely calculated, although there are many simple visual ballistics methods that calculate rotor orientation with high accuracy.

How the position of the rotor is determined for when the ball is predicted to fall Again there are many different methods, but this is where visual ballistics gets a bit more difficult. The methods that determine rotor position without electronic timing devices are still simple to learn, but they require practise. Realistically you can accurately calculate the correct number under the dominant diamond when the ball falls, within about 3 pockets of accuracy. This is about the same accuracy as the average roulette computer. A basic computer does not clock the rotor. You may have read of roulette computer sellers boasting that their computer doesn’t need to clock the rotor. It may sound great, but the cost is severely reduced accuracy. It’s like a car salesman boasting that a car doesn’t need wheels. But see how far you can drive without them.A slightly better than very basic computer will allow rotor clocking, and it will more accurately calculate which number will be under the dominant diamond when the ball falls.
How adjustments are made for ball bounce For about 30 spins, you check the distance between the initial reference number (A), and the actual winning number (B). This will give you a chart like the one below:

Adjusting for ball bounce
Adjusting for ball bounce

It will tell you something like the winning number is about +9 pockets from your initial reference number. Then when you know there are the 7 revolutions remaining, instead of taking your reference number from directly under the reference number, just look at 9 pockets clockwise from where you’d normally look. There you will see the 5 or so numbers you need to bet on.

Exactly the same as is done with visual ballistics. Some computers still use the basic algorithm, but allow you to set the computer to make the adjustment to all predictions for you. This is easier, but does not increase accuracy.

Visual ballistics vs a Basic Roulette Computer

The main difference between typical visual ballistics and a basic roulette computer is that roulette computers are EASIER to use. There is no difference in accuracy between a skilled visual ballistic and computer player. Why? Because they both do exactly the same thing. They both just estimate when there are 7 or so ball revolutions remaining. They both “tune” by looking at how far the actual winning number is from the reference number, then making a simple adjustment.

How a basic roulette computer works (almost identical to visual ballistics)

Dominant Diamonds
Dominant Diamonds

First the player finds a wheel where the ball mostly hits a particular diamond. Most wheels are like this. There are a few other basic procedures to evaluate a wheel, but this is just a simplified example. The player can create a small diagram l.ike the one shown left.

To use the computer, the player waits for the ball to be released then clicks a hidden button each time the ball passes a particular reference point (such as a diamond / metal deflector). This determines the timing of ball revolutions.

Adjusting for 9 pocket ball jump
Adjusting for 9 pocket ball jump

The player keeps clicking the hidden button until the time interval between clicks passes a certain threshold – this is when the ball is at a specific speed. When this threshold is passsed, the computer will vibrate at which time the player notes which number is under the reference diamond. Let’s say it was number 32 (number A). This is an un-tuned prediction so we call it the RAW prediction. Then the player waits for the ball to fall and come to rest in a pocket. Let’s say the winning number is 6 (number B). If we look at the distance between each number (A and B) in the chart left, we see this is +9 pockets (9 pockets clockwise) from the first to the second number.

It is important to understand that when the computer vibrates, this is telling the player that the ball has reached a target speed. And from this point, even on different spins, the ball will complete mostly the same number of revolutions before it likely hits the dominant diamond then falls.

Basic ball bounce chart
Basic ball bounce chart

The player repeat this process for 30-60 spins and add each jump value to a chart like the one shown left. After enough spins, we will find that certain areas of this chart have groupings of high bars (called ‘peaks’).

In the chart shown left, the peak is at about +10 pockets. This means for the player to win, they need to place bets around +10 pockets from the “raw prediction” (Number ‘A’).

To simplify:

The player just keeps clicking a button until the interval between clicks is the say greater than 1,000ms (1 second). When this happens, the computer vibrates to inform the player the target ball speed is reached. From that point, the ball will mostly complete 5 or so revolutions before it hits the dominant diamond then bounces much the same distance.

To know where to bet each spin, the player notes the number under the reference diamond when the vibration is felt, then compares how far the ball actually lands from this original number. Then to know where to bet, the player just makes the adjustment on each spin.

Sounds simple enough? Almost every roulette computer you will find for sale will do only the very basics as explained above. It was all you needed 50 years ago, but beating modern wheels in modern casinos is far more complex.

Common Visual Ballistics Deception

Some sellers of visual ballistic methods will charge you thousands of dollars to learn visual ballistics methods you have learned here for free. Before you paid them, they would have told you that the method they teach is the best. But the truth is visual ballistic methods are all very similar. They all use exactly the same principles. Certainly some visual ballistic methods are overall better than others, but the differences are not often significant. One exception is if the method relies on a consistent rotor speed for accuracy to be achieved. For example, one individual claims his visual ballistics method is best because it enables you to obtain a visual ballistics prediction when the ball is at any speed. This may sound great, and he lures in uninformed people. But the reality is the method relies on the player having an unrealistic top-view of the wheel, god-like skill, and a rotor speed that is almost identical on all spins. The reality is such a methods cannot be applied in real casino conditions. Even slight variations in rotor speeds alone eliminate accuracy. On the other hand, one of his competitors who he unjustly attacks teaches a far better method that doesn’t require consistent rotor speeds. So you need to be very careful about who you believe, or rather understand the principles for yourself, so you understand what is feasible.

NASA’s roulette computer, or snake oil?

Roulette computers that you can buy typically range from $500 – $5000, yet most do exactly the same thing. How is the price difference justified? IT ISN’T. Don’t just take my word for it. So you know this for yourself, try using visual ballistics on their demonstration videos, and you’ll achieve the same accuracy without even using a roulette computer. Remember that no matter what a vendor tells you, you can easily expose nonsense with careful testing and research of your own. If you prefer to just take other people’s word for it, don’t expect to know the truth.

Of course every merchant is expected to promote their product, and it is common for merchants to stretch the truth about their products. However, the gambling industry has far more deception and false advertising in it than any other area of business I’ve ever known. It seems every roulette computer seller wants you to believe their device is space-age technology that cannot be obtained anywhere else. But the reality is almost every roulette computer uses the same basic algorithm explained on this page, and the accuracy differences between them are virtually negligible. Don’t let technical talk and fancy charts fool you. When you break it all down, you are left with a salesman trying to sell a basic computer that is no better than visual ballistics.

The simplest roulette computer I offer is called the “Basic roulette computer”. No fancy names. 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. Other device sellers sell comparable devices with exactly the same accuracy for between $500 – $5,000. Again, the price differences are not justified. I distribute this device for FREE. You can achieve exactly the same accuracy with basic visual ballistics methods. Alternatively you could buy a device for $2000 that does exactly the same thing, except the vendor blatantly lies and claims it does much more, and is the most accurate device available anywhere.

The various roulette computers I offer are compared to devices from other vendors at the roulette computer comparison page. There you can better understand the difference between a simplistic device that can only beat easily beaten wheels, and a device that squeezes every last bit of predictability from a roulette wheel while making application practical, covert and easy.

NEXT PAGE > Ball deceleration rate changes

4 Responses to The Mathematics

  1. Aaron, I added the file as an attachment. The document is more a study into the physics of the wheel, in particularly with relation to “tilted wheels”. To answer your question, the algorithms presented are the equivalent of the Lite Version Roulette Computer. The algorithms are about 30 years old. Almost every roulette computer uses them as a foundation, including those from other vendors. In fact, most computers use a much more simplistic algorithm, but they still rely on the same physics. The exceptions to the algorithm are my most advanced computers (the Uber and Hybrid versions), which use a much more suitable algorithm for compensating for ball deceleration rate changes. For a comparison of all roulette computers, see http://www.roulettecomputers.com/comparison.htm

  2. Ok Thanks.

    Article deals with tilted and level wheels see section 3 and is referenced “The above formulas are the roulette equations for the fall-position and fall-time of the
    ball which are valid on wheels with or without tilt.”

    I see that Uber and Hybrid models deal with varying ball deceleration methods, based on variable factors affecting ball distance traveled, drag, air resistance equations as mentioned in this article.

    “Ability to determine where ball will actually fall from the ball track, even when the ball gradually changes the distance it travels (air pressure variations) –
    “The variation of the ball’s deceleration rate is automatically learned. ”

    Can the uber and hybrid allow averages or “line of best fit” after multiple ball deceleration samples are taken or do they derive ball deceleration sample after only one spin ?

    If so which is more accurate ?

    If there is a large variance in air pressure or some other factors that significantly affects this ball deceleration single sample or “line of best fit” how is the impact and accuracy of results affected, I would think that you could be getting inaccurate results and would need more spins to adjust/learn and I’m assuming based on your reading that the Uber/Hybrid learn’s the new deceleration pattern but if the baseline sample is significantly different causing an anomaly in equations reference calculations, how is this scenario overcome with Uber/Hybrid and as a player at a table how would you know when this occurred and what todo to mitigate using Uber/Hyrbid ?

    Ultimately I would think you would need a new ball deceleration sample/samples and “line of best fit”, but then if it keeps changing and variables changing an infinite learning adjustment of ball deceleration model is created with little to no advantage.

    The concern I have is how would you know apart form losing or getting inaccurate/invalid results, which is not an ideal model situation to be in, especially in a casino environment.

    Thanks for your time.

  3. Aaron, your questions are very good. Most people don’t ask them, so it’s good to see you are thinking and investigating. Answers below:

    1. The document you provided is more theoretical and does not accurately represent real roulette wheel physics. For example, if you incorrectly assume a wheel is level, then you are assuming the ball will “scatter” in a uniformed way regardless of where the ball falls. If this were the case, then you may still have peaks in the scatter chart in many cases, although largely diluted because of different scatter for each of the diamond types (vertical and horizontal). In reality though, the scatter is different for every diamond whether it is the same type or not. This is for a few reasons, most notably that the ball’s trajectory and speed at impact is different, in addition to dominant hit points on specific parts of individual diamonds. In simpler terms, you can’t assume a wheel is perfectly level. On top of this, different rotor speeds can enormously affect scatter too, but this is another matter.

    2. The uber and hybrid versions do use line of best fit (polynomials), with the order being automatically set internally by the computer. The uber allows you to see the actual data points and curve on a chart. The sample is adjusted to compensate for ball deceleration changes. The uber and hybrid versions have the capability to either use one “static” sample, or to do the automatic adjustments using multiple samples. You asked which is more accurate. Without a doubt, adjusting for ball deceleration rate changes is most accurate. If the computer doesn’t adjust, then small changes in ball deceleration rates means the predictions can from from hitting the right area, to avoiding the right area. And if you are avoiding the right area, you will lose quicker than random accuracy. The uber beeps after each spin when it has significantly adjusted the ball deceleration curve. The only computers anywhere that do the adjustments are the uber and hybrid versions.

    3. If there was a huge difference in ball deceleration rate from the initial sample to any amount of spins later, the computer still adjusts. Exactly HOW it adjusts is confidential information. Not even the users of the computers are taught the algorithms behind it. They are only taught how to operate the computer.

    4. Your last question is how would you know if you were getting inaccurate results, besides actually losing. The computers (uber and hybrid versions only) have the option of announcing the “raw prediction” last. What the raw prediction is depends on the settings you use. But a common example is the number under the diamond that is hit by the ball, when that diamond is hit (when you hear the “beep”). It can also announce the diamond that is predicted to be hit. So say for example the raw prediction was “15, diamond 2” (the computer says exactly this kind of thing after you hear all predicted numbers). This means the ball is predicted to hit diamond 2 when number 15 is beneath diamond 2. So to answer your question, you only need to monitor the accuracy of raw predictions, then you will know the accuracy is being maintained.

    There is a lot about the computers I dont reveal on this site, but if you are purchasing you can see all the features and capabilities in-person if you visit me. You don’t need to visit me to purchase but it is worthwhile to do so if you can. On this note, be aware that some computer sellers blatantly lie about what their computers can do. For example, one claims his computers do the ball deceleration adjustments automatically, without any noticeable signs, but in reality he uses only the static sample algorithm which can beat very few wheels. I have every computer available from other vendors and every one of them relies on a static sample. Anyway if you keep asking all the right questions and think, you will easily know what is likely truth or nonsense, without needing to buy any computer.

    PS – you may have come across a study from a UK Government Lab (http://www.bis.gov.uk/nmo) in which they tested computers supplied by a man named “Barnett”. They found his computer definitely worked when the wheel had only a slight tilt, but the edge evaporated when the ball deceleration rate changed. Barnett’s computer is about the equivalent of somewhere between my Basic and Lite computer versions. also about the equivalent of a skilled visual ballistics player. You will get the same results with these types of computers, including foresters, howes etc because they all rely on the same assumptions and approaches. You can be impressed with the results of visual ballistics and simple computers, at home in front of your tv and dvd player, but not when you play against modern wheels in realistic conditions.