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Predicting the outcome of roulette

Overview of attention for article published in Chaos, September 2012
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About this Attention Score

  • In the top 5% of all research outputs scored by Altmetric
  • High Attention Score compared to outputs of the same age (98th percentile)
  • High Attention Score compared to outputs of the same age and source (90th percentile)

Mentioned by

news
4 news outlets
twitter
28 tweeters
facebook
5 Facebook pages
googleplus
5 Google+ users
reddit
1 Redditor

Citations

dimensions_citation
11 Dimensions

Readers on

mendeley
86 Mendeley
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Title
Predicting the outcome of roulette
Published in
Chaos, September 2012
DOI 10.1063/1.4753920
Pubmed ID
Authors

Michael Small, Chi Kong Tse

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.

Twitter Demographics

The data shown below were collected from the profiles of 28 tweeters who shared this research output. Click here to find out more about how the information was compiled.

Mendeley readers

The data shown below were compiled from readership statistics for 86 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
United States 7 8%
Japan 2 2%
Germany 1 1%
Australia 1 1%
Brazil 1 1%
United Kingdom 1 1%
Malaysia 1 1%
Spain 1 1%
France 1 1%
Other 2 2%
Unknown 68 79%

Demographic breakdown

Readers by professional status Count As %
Student > Ph. D. Student 18 21%
Researcher 13 15%
Other 9 10%
Professor 8 9%
Student > Bachelor 7 8%
Other 19 22%
Unknown 12 14%
Readers by discipline Count As %
Physics and Astronomy 26 30%
Mathematics 10 12%
Agricultural and Biological Sciences 9 10%
Computer Science 5 6%
Engineering 4 5%
Other 20 23%
Unknown 12 14%

Attention Score in Context

This research output has an Altmetric Attention Score of 64. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 01 December 2022.
All research outputs
#563,979
of 22,873,031 outputs
Outputs from Chaos
#58
of 2,499 outputs
Outputs of similar age
#3,024
of 170,536 outputs
Outputs of similar age from Chaos
#2
of 10 outputs
Altmetric has tracked 22,873,031 research outputs across all sources so far. Compared to these this one has done particularly well and is in the 97th percentile: it's in the top 5% of all research outputs ever tracked by Altmetric.
So far Altmetric has tracked 2,499 research outputs from this source. They typically receive a little more attention than average, with a mean Attention Score of 6.6. This one has done particularly well, scoring higher than 97% of its peers.
Older research outputs will score higher simply because they've had more time to accumulate mentions. To account for age we can compare this Altmetric Attention Score to the 170,536 tracked outputs that were published within six weeks on either side of this one in any source. This one has done particularly well, scoring higher than 98% of its contemporaries.
We're also able to compare this research output to 10 others from the same source and published within six weeks on either side of this one. This one has scored higher than 8 of them.