# Contemporaneous: Transcendental Geometry

On most wheels, the ball will tend to hit a specific diamond more frequently than others. If you want to know what is the probability that the coin will come up heads, then that would be: We now have an equation for the velocity of the ball. This does not mean that only chance is involved. In other languages Add links. With regard to the landing place of the ball, there is perhaps not a strictly forbidden zone. If you place a bet on one of the three options, then you are obviously playing against probability:

## Understanding What Makes Roulette Beatable

In other words, if For a single level we know that the formula is the probability of a win times the net result and the probability of a loss times the net result. To check the second level, the probability of a loss followed by the probability of a win times the net result is compared to two losses and the net result.

Any system can be analyzed like this for any game. Of course, if I had I'd be in a casino right now. This is a well presented maths explanation of the odds against the player when betting at roulette. But it confuses probability with certainty. Probability Theory deals with uncertainty not certainty. Roulette, like all gambling, is a game of chance so , obviously, chance is involved. This does not mean that only chance is involved. If the roulette wheel is random then no one can predict with certainty that we will win or lose.

That certainty belongs to astrology not maths. There is no reason why the wheel should not give the same number continuously for a hundred, a thousand or even a million spins if it is truly random; incidentally, unless we are going to live till eternity then "The Long Run" is irrelevant in real time betting. The writer errs when dealing with betting the First and Second dozens together.

Using the bet we can lower the odds against us. Placing three chips on and one chip on the six-line benefits us should zero occur whereas betting the two dozens does not. To my mind, there is an all too casual attitude to discussing roulette and this is exemplified in this article. Also- but not here -there is usually a knee-jerk reaction to anyone who rejects the notion that you are certain to lose.

A bias in the location of the departure point will lead to a bias in the results of the wheel. Leaving out the gritty details of the math - which can be found in Eichberger's paper - this function is found to be:. We now have an equation for the velocity of the ball. The next step is to find the critical velocity at which the ball will fall from the rim. We can find this using the equation for the normal force against the rim, illustrated in Figure 2. When the normal force N 1 goes to zero, the ball will leave the rim.

From Eichberger, we find the equation for this normal force. It is easy to find the following expression for w f. These new functions are defined to be:. This will add to the clarity of the graph. These new functions also contain the experimental values of the constants such as a, b, and c, which can be found in Eichberger's paper. To find the crossing points of the two functions, we plot them in Fig.

For this graph, we use the reasonable initial angular velocity of 4. We show the results for two angles of tilt, centering the graph around the first crossing-point. Looking at the graphs, we find that the initial crossings both occur near the peaks of the sinusoidal wave.

By changing the initial velocity of the system slightly, we can imagine changing the exponential curve. However, wherever we move those curves and however we manipulate the initial conditions, we see the lines can only cross in a relatively narrow section of the wheel. The regions of the roulette wheel just beyond a peak will never be the location for the first intersection. A shadow is effectively created over part of the wheel, in which the ball will never be found to leave the rim.

This is known as the forbidden zone in the departure point, and its bias is extreme both for cases of large tilt and small tilt.

The motion of the ball after it leaves the rim, as it hits bumpers and scatters, will tend to diminish any bias. However, a strong bias in the departure point of the ball should lead to a remaining bias in the landing location of the ball. We turn to the experimental evidence of such a forbidden zone in the landing location of the ball in the next section.

We now have an understanding of how the tilt of a roulette wheel leads to a bias in the departure point of the ball from the rim. However, the motion of the ball as it bounces off the bumpers before landing in a slot is seemingly chaotic. Will this be enough to outweigh the bias of a tilt? Since this clearly depends on the amount the wheel is tilted, perhaps the proper question is: In this section, we will examine their results.

The wheel was then spun times, and the results were recorded of where the ball landed. For the purposes of recording the results, the wheel was split into eight equal sections - in the stationary reference frame of the table, and the ball was always started in section 5.

It is much easier to detect a tilt-based bias by looking at these stationary sections, ignoring the details of predicting how the wheel itself spins and which numbered slots will be where in the final state. The results of a large number of spins were binned and analyzed for statistical bias. The results of this experiment for several amounts of tilt are shown in Table 1 and also plotted in Fig. Looking at the results in the graph, it is easy to qualitatively see bias in the case of extreme tilt.

For an ideal, level roulette wheel, it would be expected that each of the eight sections of the wheel would be as likely a landing place as any. We would expect only minor differences in the number of balls landing in each section. In the level case, we see that this is approximately true. However, looking at the case of 1. The quantitative bias of the results can be found using chi-square analysis.

This is simply a statistical method of determining the chance that results came about through the hypothesized probability distribution in our case, an even chance for each eight sections. These results are given by Dixon, and they are shown at the bottom of Table 1.

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 ms 0. This means that if we knew when the ball timing speed was about ms per revolution about 1. 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 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. 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 or so spins.

How we apply this knowledge is explained later. 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 ms 1.

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, This will tell you that the ball landed 5 pockets clockwise of your initial "reference" number.

See the left image for reference. 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. 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 ms 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. 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.