Lets talk about the math needed to predict the roulette ball, given measurements. Some people here have of course already developed a well proven formula, and I would be delighted to see what they have found out! What is really the algorithm in those roulette computers?
My first idea is simply the following:
Consider only two variables, S and V:
[ul]S is the distance which the ball will roll until it hits the wheel.
V is the speed of the ball at any given point in time, relative to the wheel. Actually, it is the speed at the point in time between the two times when its position is clocked.[/ul]
Units for both variables are suitably given in terms of “pockets” (i.e. the 37 numbered landing pockets) on the wheel. Position is defined as the pocket which the ball is closest to. Distance as the number of pockets between two positions. Speed as the number of pockets passed by per second.
Measure V and observe the S that follows at many occasions for any specific roulette wheel. Then correlate V and S, i.e. fit a function which minimizes the sum of squered differences from the observed points in the S and V plot. Estimate k in: S = k*V.
Then when the speed is measured, multiply it with the konstant k and viola there is an estimation of S!
It can be a very good idea to extimate k-values for root of V and for V squared too and see which gives the best fit, since there probably is a non-linear acceleration involved. Do the regression S = kV + csquareroot[V] + q*V^2 and see which of k, c and q are significant.
Now, do you think that this simple approach is the best? Or how could it be improved? Note that I do not really care about the physics and mecanichs of a ball rolling and jumping. I just do the statistics an let everything between input and output remain a black box.
Mathematical predition may be done using least squares solution of second order (or higher) equations. But as Forester has pointed out, getting accurate, early timings of the ball is nearly impossible without employing some sort of electronic timing devices, such as lasers.
As you point out, anam, good measurements are necessary. Without it one only gets garbage-in garbage-out models.
But what interests me is whether it would be useful to model the physics involved. For example to estimate the (negative) acceleration and use parameters such as the weight of the ball.
I think that that would over complicate things. We still would have the issue of accurate ball timings. I have a web site reference dealing with the physics of roulette prediction. When I find it I will pass it along.
I think that that would over complicate things.
I think that too. But whenever I Google about roulette, I find statements made by this guy who as a student in the 1970s engineered a roulette computer which, he claims, beat the game. (Incidently, he and his team didn’t continue long enough to make much money…) Anyway, he is everywhere quoted to say things lik this:
[...]equations comprise only a handful of parameters, including the [b]mass and size of the ball[/b], the [b]shape and roughness of the track[/b], and the [b]tilt of the wheel[/b].
He implies that he used a physical model of what actually happened to the ball, not just predictions based on regressions between samples of (the angular location of) the winning number versus (different functional forms of) the measured speed of the ball.
Is he lying?
Was his approach 30 years ago faulted?
Or is there reason to the madness?
Btw, I still have not read that seemingly great physics article on the subject which anem posted above! It may hold the answers.
Having read this article as well as I can, I have catched up on a couple of wisdoms. Note, I have not the command of math or physics to say [i]"that is wrong"[/i], I can only try to make some practical interpretations from what is stated in the article.
First, note equation 18 on page 6.
It seems as if that is the theoretically derived functunal form of the circular (angular) distance until the ball falls off from its track down towards the wheel, as a function of the speed of the ball. So, if we at any time can measure the speed of the ball reliably, just pu that value where that greek letter omega is, and viola, the equation gives the expected distance to where the ball will drop down.
This requires values of a, b and c. These however can be estimated statistically with non-linear regression. The potentially valuable lesson is that the regression should have that functional form: Distance = a ln(b/(speed-c)). Normally, one would just try linear regression with distance to speed, root(speed), speed squared and such. The specific functional form stated in the article could be quite helpful in optimizing the regression.
That is the case of a non-tilted wheel. For the tiltet case, things seems to get a bit too complicated for me in my first reading of the article, although a til is a very good news for a gambler.
Second, note the figure 2 on page 8.
As I interpret it, that zigzag curve illustrates the acceleration of the ball when on the half of the table leaning down, versus the retardation of the ball when on the half of the same table which leans upwards. The falling straight line represents the friction and general retardation of the ball. Of course the ball will fall from its track only when it is on the upward side of the wheel, since it is only then that its speed is falling towards that critical limit of “letting the hug go”. On the other side of the wheel, the ball i accelerating and thus can impossibly let go of its centrifugal force.
I know that description is not exactly what the figure shows, but that was the first idea I got when seeing it anyway, and it lit some light for me anyway. Tilt is a very good friend!
Why to keep things simple if they can be complicated.
Too much is too much and really there is no need for all of that if it can be done more simple. ]
What is the point of ball size, weight and other parameters if you do not know many other factors needed for that kind of calculation? Can you know friction or can you exactly know the angle of wheel base. Even it looks the same it is not the same. What is fraction over there etc?
It is complicated way of calculation and it is wrong way.
But it is most common way that people will chose to use to predict roulette.
That site is very similar to Mark Howe.
Think this way.
Pedal the bike until you are at speed at 20 km per hour.
You stop pedaling and bike continues to travel for 100 meters until it stops.
Now do the same but 10 meters earlier. Of course that bike will stop 10 meters before then previous time. Now what is easier to calculate?
Bike speed, friction of tires, resistance of air, friction on bearings, mass of bike etc. and apply that formula every time, where the smallest mistake will create huge error on 100 meters or simply calculate difference from previous example. Where even if you are wrong by 10% final result will be wrong by 1 meter.
Yes, agree that it is too sensitive for estimation of all the parameters to be quantitatively useful. But it is nice to get an understanding of the physics behind what one observes, and it can be used qualitatively.
It seems as if the article authors agree with the idea that the ball starts falling of its track at the same speed everytime. It is also most encouraging to see that the physics says that the ball should decelerate in a similar way every time, regardless how hard the initial speed of the ball was (it follows the same deceleration curve, it only starts further up on that same curve) or even if the ball is spun around its own axis in different ways everytime, because the spin should be normalized after a few rotations anyway.
I cannot see any other factors which could substantially affect the prediciton. Roulette naivley seems to be a perfect random number generator, and that must’ve been the inventor and great mathematician Pascals intention. But the physics of it is surprisingly regular, allowing for predictions. The randomization comes from the diamonds and the scatter pattern which they cause. But that scatter does not preclude predictions which improve the odds to far better than the 1/36 payout.
As to quantifying things, I as you prefer to measure the inputs and the outputs. Statistics take care of everything in the complicated black box inbetween!