Chaos Theory and a Little Physics Predict the Outcome at the Roulette Table

But with a better understanding of physics and some general knowledge of the starting conditions, it may be possible to shift the odds of winning a little in your favor. According to new research published in the American Institute of Physics' journal Chaos, by knowing some of the starting conditions – such as the speed of the spin and the rotation of the ball – this game of chance starts to look a little less random.

Under normal conditions, according to the researchers, the anticipated return on a random roulette bet is -2.7 percent. By applying their calculations to a casino-grade roulette wheel and using a simple clicker device, the researchers were able to achieve an average return of 18 percent, well above what would be expected from a random bet.

With more complete information, such as monitoring by an overhead camera, the researchers were able to improve their accuracy even further. This highly intrusive scheme, however, could not be deployed under normal gambling conditions. The researchers also observed that even a slight tilt in the wheel would produce a very pronounced bias, which could be exploited to substantially improve the accuracy of their predictions.

This model, however, does not take into account the minor changes of the friction of the surfaces, the level of the wheel, or the manner in which the croupier plays the ball — any of which would thwart the advantage of the physicist/gambler. The gambler, the researchers conclude, can rest assured that the game is on some level predictable, and therefore inherently honest.

Article: “Predicting the outcome of roulette” is published in the journal Chaos.

http://chaos.aip.org/resource/1/chaoeh/v22/i3/p033150_s1?isAuthorized=no

Authors: Michael Small (1, 2) 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