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- Article] Predicting the outcome of roulette
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DocNo of ILP: 1144
Doc. Type: Article
Title: Predicting the outcome of roulette
Authors: Small, M; Tse, CK
Full Name of Authors: Small, Michael; Tse, Chi Kong
Keywords by Author:
Keywords Plus: TIME-SERIES; GAMES
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. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4753920]
Cate of OECD: Mathematics
Year of Publication: 2012
Business Area: game
Detail Business: roulette
Country: USA
Study Area:
Name of Journal: CHAOS
Language: English
Country of Authors: [Small, Michael] Univ Western Australia, Sch Math & Stat, Perth, WA 6009, Australia; [Small, Michael; Tse, Chi Kong] Hong Kong Polytech Univ, Dept Elect & Informat Engn, Hong Kong, Hong Kong, Peoples R China
Press Adress: Small, M (reprint author), Univ Western Australia, Sch Math & Stat, Perth, WA 6009, Australia.
Email Address: michael.small@uwa.edu.au
Citaion: Small, Michael/0000-0001-5378-1582
Funding: Hong Kong Polytechnic University; Australian Research Council [FT110100896]
Lists of Citation: Bass T. A., 1990, NEWTONIAN CASINO; Bass Thomas A., 1999, PREDICTORS; BBC, 2004, BBC NEWS; Bell E. T., 1937, MEN MATH; Chung K. S., 2010, PREDICTING ROULETTE; CRUTCHFIELD JP, 1986, SCI AM, V255, P46; DOWNTON F, 1972, J R STAT SOC SER A-G, V135, P336, DOI 10.2307/2344612; Epstein Richard A., 1967, THEORY GAMBLING STAT; ETHIER SN, 1982, J AM STAT ASSOC, V77, P660, DOI 10.2307/2287733; FARMER JD, 1987, PHYS REV LETT, V59, P845, DOI 10.1103/PhysRevLett.59.845; Kingston C., 1925, ROMANCE MONTE CARLO; Life Magazine Publication, 1947, LIFE, P46; Okuley B., 1979, GAMBLERS GUIDE MACAO; PACKARD NH, 1980, PHYS REV LETT, V45, P712, DOI 10.1103/PhysRevLett.45.712; Poincare Henri, 1914, SCI METHOD; SHANNON CE, 1948, AT&T TECH J, V27, P379; Small M., 2008, AS PAC C CIRC SYST; Strzalko J, 2009, LECT NOTES PHYS, V792, P1, DOI 10.1007/978-3-642-03960-7; THORP EO, 1969, REV INST INT STAT, V37, P273, DOI 10.2307/1402118; Thorp Edward O., 1985, MATH GAMBLING; Time Magazine Publication, 1951, TIME, V135, P34; Yung C. T., 2011, PREDICTING ROULETTE
Number of Citaion: 22
Publication: AMER INST PHYSICS
City of Publication: MELVILLE
Address of Publication: CIRCULATION & FULFILLMENT DIV, 2 HUNTINGTON QUADRANGLE, STE 1 N O 1, MELVILLE, NY 11747-4501 USA
ISSN: 1054-1500
29-Character Source Abbreviation: CHAOS
ISO Source Abbreviation: Chaos
Volume: 22
Version: 3
Start of File:
End of File:
DOI: 10.1063/1.4753920
Number of Pages: 9
Web of Science Category: Mathematics, Applied; Physics, Mathematical
Subject Category: Mathematics; Physics
Document Delivery Number: 015EE
Unique Article Identifier: WOS:000309427500050
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