Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/6241
Title: Predicting the outcome of roulette
Authors: Small, M
Tse, CKM 
Keywords: Chaos
Random processes
Issue Date: Sep-2012
Publisher: American Institute of Physics
Source: Chaos, Sept. 2012, v. 22, 033150, p. 1-9 How to cite?
Journal: Chaos 
Abstract: There have been several popular reports of various groups exploiting the deterministic nature of the game of roulette for profit. 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 profit. 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 realizable systems to obtain this knowledge both incognito and in situ. The first system relies only on a mechanical count of rotation of the ball and the wheel to measure the relevant parameters. By applying these 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 significant 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.
URI: http://hdl.handle.net/10397/6241
ISSN: 1054-1500
EISSN: 1089-7682
DOI: 10.1063/1.4753920
Rights: © 2012 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in M. Small & C. K. Tse, Chaos: an interdisciplinary journal of nonlinear science 22, 033150 (2012) and may be found at http://link.aip.org/link/?cha/22/033150
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