Title: Gambling with Chaos -- How to use nonlinear dynamics to beat the casino
Abstract:Abstract: The casino game of roulette consists of a large spinning disk with many numbered pockets situated in a static frame. A small ball is sent spinning around the rim of the circular static frame and will eventually come to rest in one of the numbered pockets. Wagers are made on which. Essentially, this game is deterministic and bets can (usually) be made after the entire system is set into motion. Several attempts have been made to exploit this determinism to predict the path taken by the ball and hence improve ones’ odds of winning. In his 1896 treatise Science and Method, Poincaré cited roulette as an example of the effect of sensitivity to initial conditions. During the twentieth century, several physicists, statisticians and mathematicians have made attempts to put such schemes in to practise. Notable figures in this endeavour include (in addition to ruminations on the subject by both Einstein and Poincaré): Pascal;Pearson; Thorp and Shannon; and, the Chaos cabal – Farmer, Packard, Sidorowich and colleagues. Indeed, Farmer and Sidorowich acknowledge their attempts to find profit at the casinos of Las Vegas as the inspiration for their work in the 1980’s on predicting chaotic time series (see Physical Review Letters, (1987) 59: 845-848). In this talk I will explain exactly how this can be done and demonstrate our own system applied to a standard casino grade roulette wheel.
This is joint work with Michael C.K. Tse, Electronic and Information Engineering, Hong Kong Polytechnic University.