Good question and good answer from rollo
I must again point out that I am new to the idea to predict roulette and that I do not have observations to confirm my reasonings. So I'm happy to see that it seems to agree with what very experienced players like Forrester have observed in real life. I welcome all critisism!
Slight tilt on wheel or imperfections on track can change it.
Yes, but of course rather to further advantage of the player, given that this tilt is accounted for. As I understand it, a sufficently large tilt makes the ball accelerate on one half of the ball track (when actually moving downwards), and decelerate the more harder on the other half where the tilt makes the ball track lean upwards. That means that the ball NEVER CAN fall down on the downward leaning half of the table. It can only start falling when deceleration makes it slow down so that the centrifugal force caused by the balls speed falls below the gravitational force.
In this golden situation it is basically sufficient to predict the number of rotations the ball will make (fractions of rotations are not necessary) and how the wheel will stand at that final rotation. This I believe is possible to do without the aid of contraptions, although they would help. By betting on the half of the wheel which is going to be turned towards the upwards leaning half of the ball track during the final rotation of the ball, the odds should theoretically be improved to 1/18 (plus error in prediction of wheel position) which is enourmous, in the long run DOUBLING all the bets!
If the tilt is less than enough to actually make the ball accelerate, there will only be a tendency to the effects above, but still, not much is needed to get ahead of the 1/36 odds.
One should first make enough observations of the wheel to see whether it is tilted or not. If it is tilted, use a separate method for prediction. If it is not tilted, use a method for prediction adapted to that case.
Do either of you think a more accurate (in terms of percentage error) ball timing could be obtained by clocking multiple revolutions rather than single ball revolutions? For example, we would time a group of 5 ball revolutions and plug that into our previously established prediction equation made from video studies of a similar wheel and ball.
I think that you will get better precision when measuring the ball speed over a higher number of revolutions, yes. The measuring error can be assumed to be constant in terms of centimeter (of angular degrees or pockets or whatever unit used). The more rotations this error can be spread out on, the lower it gets as a fraction. 5 rotations as compared to 1 rotation should reduce the measuring error by 80%! In principle.
However, one must consider that to measure the speed one must make measurements at two points in time and space. BUT, the speed measured is valid for the ball at only one point in time and space! One can never measure what speed the ball has NOW. One can only measure the speed which the ball HAD in between the clicks. If deceleration is at a constant rate, then the speed measured was the speed which the ball had exactly in the middle of the two measuring points. At your first click, the ball had higher speed. At your second click it had a lower speed. Half TIME in between (which is NOT exactly the same as half WAY, 2.5 rotations), the ball had the speed which you measured.
To complicate things further, the deceleration is certainly not constant, but friction and air resistance has greater effect earlier when the ball travels faster, than later when the ball is slower. Assuming a constant deceleration gives a smaller error if measuring over one single rotation, than if measuring over multiple rotations. So there is a trade off between the two errors: error of timing the clicks exactly, and the error of non-constant deceleration. Maybe 2 rotation is a good trade off? This reduces the error of timing the click with a wapping 50% and still the ball has not decelerated too much, given that it is already pretty slow so that the deceleration rate has decreased which makes deceleration more constant. Also, the speed measured would be the speed which the ball had when passing (close to) that same reference point on the rotation between the two clicks, which might simplify things (measuring over odd number of rotations, including 1 rotation, would measure the speed of the ball when it was about 180 degrees from the reference point).
The same applies to measuring the wheel speed, however, I THINK that it is practical to ignore deceleration in that case, because it is pretty small, and assume constant wheel speed from time of measurement to time of ball drop.