2,480 research outputs found
Predicting the outcome of roulette
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 realisable systems to obtain this knowledge
both incognito and {\em 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 this 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.Comment: Revise
Optimal embedding parameters: A modelling paradigm
Reconstruction of a dynamical system from a time series requires the
selection of two parameters, the embedding dimension and the embedding
lag . Many competing criteria to select these parameters exist, and all
are heuristic. Within the context of modeling the evolution operator of the
underlying dynamical system, we show that one only need be concerned with the
product . We introduce an information theoretic criteria for the
optimal selection of the embedding window . For infinitely long
time series this method is equivalent to selecting the embedding lag that
minimises the nonlinear model prediction error. For short and noisy time series
we find that the results of this new algorithm are data dependent and superior
to estimation of embedding parameters with the standard techniques
Surrogate Test to Distinguish between Chaotic and Pseudoperiodic Time Series
In this communication a new algorithm is proposed to produce surrogates for
pseudoperiodic time series. By imposing a few constraints on the noise
components of pseudoperiodic data sets, we devise an effective method to
generate surrogates. Unlike other algorithms, this method properly copes with
pseudoperiodic orbits contaminated with linear colored observational noise. We
will demonstrate the ability of this algorithm to distinguish chaotic orbits
from pseudoperiodic orbits through simulation data sets from theR\"{o}ssler
system. As an example of application of this algorithm, we will also employ it
to investigate a human electrocardiogram (ECG) record.Comment: Accepted version, to appear in Phys. Rev.
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