How to beat the roulette-Yaknivek

Published online: 26 September 2012
By Michael Small and Chi Kong Tse

This article was originally posed on chaos.aip.org showing how physics and mathematics could predict the out come of a roulette wheel.

Article outline
1. A HISTORY OF ROULETTE
2. A MODEL FOR ROULETTE
A. Level table
1. Ball rotates in the rim
2. Ball leaves the rim
3. Ball rotates freely on the stator
4. Ball reaches the deflectors
B. The crooked table
3. EXPERIMENTAL RESULTS
A. A manual implementation
B. Automated digital image capture
C. Parameter uncertainty and measurement noise
4. EXPLOITS AND COUNTER-MEASURES

Lead Paragraph
Among the various gaming systems, both current and historical, roulette is uniquely deterministic. Relatively simple laws of motion allow one, in principle, to forecast the path of the ball on the roulette wheel and to its final destination. Perhaps because of this appealing deterministic nature, many notable figures from the early development of chaos theory have leant their hand to exploiting this determinism and undermining the presumed randomness of the outcome. In this paper, we aim only to establish whether the determinism in this system really can be profitably exploited. We find that this is definitely possible and propose several systems which could be used to gain an edge over the house in a game of roulette. While none of these systems are optimal, they all demonstrate positive expected return.