# I Using physics to predict the outcome of a roulette wheel

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1. Jul 15, 2017

### borson

Hey guys!
I have been working on this project during some time.
First off, do you all think that this is possible? Of course, as we all may know, the roulette is a chaotic system, very sensitive to initial conditions, although deterministic.
This means that small errors in the eye-hand-estimations of the parameters would lead to large errors in the final outcomes. So.. so you think it would be feaseble?
whether it is or not, I've developped an algorithm/app with the equations stated here:https://www.google.es/url?sa=t&sour...ggvMAA&usg=AFQjCNGnxAijuBrt3PYkg5_YAMcLhPVESg

(Pay special attention to pages 12-14, in which all is summed up)

The problem is that I cannot get a good fit for the parameters "a" and "b". (With equation 40).
As said in the pdf, I measure the 4-6 last revolutions (from a video, so no human error is present there), with them, I obtain estimations for the parameters (Let's call them Sparameters) which are useless.Although their residual is quite low and significative, I test them then with the equation of the final time, and they work only for predicting the final time behind roughly 10 turns. Beyond 10, their error starts to increase quite a lot, so predictions become useless. Why is this happening?

Thank you all !

<< Mentor Note -- solicitation deleted from post >>

Last edited by a moderator: Jul 15, 2017
2. Jul 15, 2017

### rootone

I think what's happening is that in a real life situation there will be many random variations on top of the ideal mathematical result.
This could be due to slight imperfections of the apparatus, small air currents, tiny bits of dust. .. and so on.
The more spins you do the more the randomness accumulates until the results don't look anything like what the ideal model predicts.

3. Jul 15, 2017

### borson

I thought about it. There may be other variables which are not regarded by the model.. It is unlikely though, as the roulette I took the data from is covered by a kind of glass ceiling (thus less sensitive to the environmental conditions), and it is automated.

I think there must be any mathematical or physical reason for this that I do not understand

4. Jul 15, 2017

### Staff: Mentor

I only skimmed your PDF, but do you have lots of data from the automated test roulette wheel? If so, what are the mean and standard deviation for the fall time of the ball? What are the mean and standard deviation for the position of the wheel at the fall time? How many sample runs do you have data for?

Is the ball rim made of wood or finely polished steel? Does the ball roll with slipping, or just roll without slipping? Or, does it slip at launch and gradually begin to roll in the groove in the first couple rotations?

I would guess that the biggest variable that causes the standard deviation in the fall tome would be the roughness of the wood rim. That will generate some small random variations in the behavior of the ball during the course of many rotations, and will keep you from being able to accurately predict the fall time.

5. Jul 15, 2017

### A.T.

6. Jul 16, 2017

### cosmik debris

7. Jul 18, 2017

### borson

First off thanks for your interest and sorry for delaying in responding, I was on a vacation.

The rim is made of steel or plastic. I do not have any standard deviations nor mean for the fall times, I do have for the falling position though (Which tends to be always at the same part of the track, as the roulette I take the information from is biased, due to the existance of some degree of tilt).
I have been thinking it over, and I have my own hypothesis of why my predictions were, supposedly, mistaken. To start with, I want to bring out that:

-Measuring the 4-6 revolutions gives us "the curve of deceleration" (as literally said in the pdf, in the part of the estimation of the parameters). The space-time function does not have the same degree of nonlinearity in all of its domain/parts. At the beginning, as the ball rotates faster, the time spent to complete a turn is less, thus it is much less deaccelerated each spin, therefore, the relation among the first turns is almost linear.

On the other hand, in the final turns, the ball spends more time to give complete revolutions, thus it is more deaccelerated in each, and the difference stands out more and is more blatant than before, hence more nonlinear.

Here the image of the function to ilustrate this: http://es.tinypic.com/r/1zz3zww/9
the purple and red dots are points of the same spin, the red dots represent the part that is more nonlinear, and viceversa with the purple ones.
(all of them are real measurements). The X axis is the number of the turn (the space), and the Y the time.
The red line is the function to predict the time with the initial time of the first turn (that is, the time that giving the first time took).

As everyone can see the predictions are crap. However, if the initial time is that of the 13 or 14 turn(where the curve begins), the predictions are quite accurate.
However, I want to be able to predict from the 1st revolution.

Trying to get a fit of the entire spit does not work very well either, as when I set the initial time to some in which the curve begins, predictions start to have some error (0,6 seconds. which is in general good, but for predicting the last one, the 21 in this case, the error is of 2 seconds, thus not appropiate).
I have also thought about dividing the function in 2 parts, the curve and the "almost-linear" part, and get a fit for each.

I do not know what is the best option, nor if the reasons for the bad predictions are the ones I have stated.

Thank you all!

8. Jul 20, 2017

### Khashishi

Good luck with that! I don't think you will succeed. You'll never model the exact bumps in the surface of the roulette wheel, the air currents, the vibrations in the ground, temperature gradients in the table, etc.

9. Jul 20, 2017

### NTL2009

Not a slight bias! A bias high enough to overcome the house advantage. From wiki:

A 2.7% or 5.26% strikes me as a very steep wall to climb with this kind of system.I'd be impressed with 1% from an expected 50/50. I'm not sure I can accept the info in your linked article as a rigorous enough study. I'm skeptical, but that's OK.

10. Jul 24, 2017

### nasu

Assuming your model is highly accurate, you need the initial conditions in order to predict the outcome. But you only know these conditions after the ball was launched and the bets are closed. How would you use all this?

11. Jul 24, 2017

### Dr. Courtney

We've analyzed lots of video data to determine object kinematics, and even getting an accuracy of 1% for things like velocity requires both high quality video and attention to the analysis detail.

Keep in mind, at best video most closely measures position vs. time. Velocity is a first derivative, and acceleration and force require two derivatives. When differentiating video data, the limit of the delta t going to zero is only approximate, because of the finite time between frames.

The other big challenge with video is it is uncommon to be able to determine the position of an object to better than one pixel. Pixels are usually converted to distances, but when one uses a faster camera to reduce the error from finite time slices, one also reduces the number of pixels the object moves between frames. But if you are only determining the position to the nearest pixel, you are limited in accuracy of each (frame to frame) velocity measurement by the integer number of pixels the object moved. You will determine it moved 11 or 12 pixels, not 11.5357 pixels.

So if an object moves between 11 and 12 pixels per frame, for some frame to frame gaps it will be recorded as moving 11 pixels and for some it will be recorded as moving 12 pixels. Of course, most interesting dynamics also have the object speeding up or slowing down, so you don't know how to interpret a change from 11 to 12 pixels.

We usually use additional physical insight regarding the dynamics to resolve these issues. Still, we feel that we have done an outstanding job of video analysis if we manage to determine velocities to 1%. This is nowhere near good enough to predict chaotic dynamics accurately for long times in the future on something like a Roulette wheel. From my experience simulating chaotic dynamics by integrating the differential equations, you need initial conditions good to 1 part in 10,000 to 1 part in 1,000,000 depending on the other details.

Then you also need models for friction and air resistance that are sufficiently accurate. Measuring drag coefficients to better than 1% is also a significant challenge, especially when you need to do it over a broad velocity range. Boundary effects with a rolling ball are also going to be a challenge, as will wind currents in any real room.

12. Jul 24, 2017

### CWatters

13. Jul 24, 2017

### Dr. Courtney

"Beating roulette" just means tipping the odds from slightly in favor of the house to slightly in favor of the betting patron. That's a much simpler task than accurately predicting "the outcome of a roulette wheel." Your predictions can still be wrong a lot of the time and shift the odds. I tend to understand "predicting the outcome" of a physical system more in a scientific sense, that the predictions need to be right > 90-95% of the time to be interesting.

Shifting the odds doesn't require a real physical model (Newton's laws, free body diagrams, etc.), it can be done with various extrapolation algorithms that couldn't care less about the laws of physics, they just extrapolate the outcome of one specific system correctly enough of the time so the betting odds shift slightly. It may be interesting to a gambler, but it's more math than physics. (I'd argue that if you don't use established laws of physics, you are not "using physics to predict the outcome.")