Predicting the outcome of roulette
Michael Small
1, 2, a)
and Chi Kong Tse
2
1)
School of Mathematics and Statistics, The University of Western Australia
2)
Department of Electronic and Information Engineering
Hong Kong Polytechnic University, Hong Kong.

(Dated: 16 July 2012)

There have been several popular reports of various groups exploiting the deterministic nature of the game of roulette for prot.

Moreover, through its history the inherent determinism in the game of roulette has attracted the attention of many luminaries of chaos theory.

In this paper we provide a short review of that history and then set out to determine to what extent that determinism can
really be exploited for prot.

To do this, we provide a very simple model for the motion of a roulette wheel and ball and demonstrate that knowledge of initial position, velocity and acceleration
is sufficient to predict the outcome with adequate certainty to achieve a positive expected return.

We describe two physically realisable systems to obtain this knowledge both incognito and in situ.

The rst system relies only on a mechanical count of rotation of the ball and the wheel to measure the relevant parameters.

By applying this techniques to a standard casino-grade European roulette wheel we demonstrate an expected return of at least 18%, well above the 2:7% expected of a
random bet.

With a more sophisticated, albeit more intrusive, system (mounting a digital camera above the wheel) we demonstrate a range of systematic and statistically significant biases which can be exploited to provide an improved guess of the outcome.

Finally, our analysis demonstrates that even a very slight slant in the roulette table leads to a very pronounced bias which could be further
exploited to substantially enhance returns.

PACS numbers: 05.45.Tb, 01`.65.+g, 01.80.+b
Keywords: roulette, mathematical modeling, chaos

http://cktse.eie.polyu.edu.hk/pdf-paper/Chaos-1209.pdf




[Moderator's Edit:  I've spaced this out to avoid a solid block of text, thereby making it easier to read on a screen.]

Interesting read, but I'm sure there will be plenty of people to shoot this down, I like to keep an open mind and think anything is possible.