Techniques for Computing the Probability of a Gambler’s Ruin with Applications to Playing Roulette

William Henry Laverty; Ivan William Kelly

doi:doi:10.11648/j.ajtas.20231202.12

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Techniques for Computing the Probability of a Gambler’s Ruin with Applications to Playing Roulette

William Henry Laverty, Ivan William Kelly

Published in American Journal of Theoretical and Applied Statistics (Volume 12, Issue 2)

Received: 14 April 2023 Accepted: 8 May 2023 Published: 18 May 2023

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Abstract

An interest in gambling has greatly increased over the last few decades with the more common use of slot machines and online gambling, especially sports betting. A concern that has been publically raised is addiction and eventual gambler’s ruin (loss of all money). In this paper we provide a solution to the Gambler’s Ruin problem in regards to roulette. We compute the probability of a gamblers ruin with applications to the various betting opportunities playing roulette by determining the W+1 roots of the relevant polynomials and from there determine the probability of a gamblers ruin. We find situations where the payoff becomes higher, the probability of ruin becomes lower. Lower goals of gain are associated with a lower probability of ruin and larger bets and larger odds payoff also increase the probability of ruin.

Published in	American Journal of Theoretical and Applied Statistics (Volume 12, Issue 2)
DOI	10.11648/j.ajtas.20231202.12
Page(s)	32-36
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Odds, Probability, Gamblers Ruin, Roulette

References

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[2]	Hing, N., Russell, A. M., Vitartas, P., Lamont, M. Demographic, behavioural, and normative risk factors from gambling problems among sports bettors. Journal of Gambling Studies. 2016, 625-641.
[3]	Hing, N., Russell, A. M., Browne, M. Risk factors for gambling problems on online electronic gaming machines, race betting and sports betting. Frontiers in Psychology, 2017; 8, 779.
[4]	Maniaci, G., Picone, F., Von Holst, R. J., Bolloni, C., Scardina, S., Cannizzaro, C. Alterations in the emotional regulation process in gambling addiction: the role of anger and alexithymia. Journal of Gambling Studies. 2017, 633-647.
[5]	Aloi, M., Riccelli, C., Piterà, F. et al. Impaired Metacognitive Differentiation, High Difficulty in Controlling Impulses and Non-acceptance of Emotions are Associated With the Severity of Gambling Disorder. Journal of Gambling Studies 2023, 39, 1–11.
[6]	Williams, R. J., Leonard, C. A., Belanger, Y. D. et al. Predictors of gambling and problem gambling in Canada. Canadian Journal of Public Health 2021, 521–52.
[7]	Rose, S Online gambling addiction: a growing problem. http://steverosephd.com/online-gambling-addiction
[8]	Coolidge, J. L. The Gambler's Ruin. Annals of Mathematics. 1909; 10, 181–192. doi: 10.2307/1967408.
[9]	Edwards, J. W. F. Pascal's Problem: The 'Gambler's Ruin. Revue Internationale de Statistique. 1983; 51, 73–79. doi: 10.2307/1402732. JSTOR1402732.
[10]	Kaigh, W. D. An attrition problem of gambler's ruin. Mathematics Magazine. 1979; 52: 22–25. doi: 10.1080/0025570X.1979.11976744.
[11]	LavertyW and Kelly I W. Computational techniques for Gambling and Effects on Disordered Gambling. Computational techniques for Gambling and Effects on Disordered Gambling. 2022 DOI: 10.13140/RG.2.2.32730.41925.
[12]	Laverty, W and Kelly I W. "Gamblers Ruin": A recursive analysis. 2022. https://www.researchgate.net.publication/356760229_Gamblers_Ruin-A-recursive_analysis
[13]	Katriel, G. Gamblers ruin probability—a general formula. Statistics & Probability Letters. 2013; 83. 2205-2210.
[14]	Skala, H. L. An aspect of the gambler’s ruin problem. International Journal of Mathematics Education in Science and Technology. 2006; 51-56.
[15]	Roulette Bets - All Betting Options Explained - Which One Works Best? (rouletteonline.net) https://www.rouletteonline.net/roulette-bets

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APA Style

William Henry Laverty, Ivan William Kelly. (2023). Techniques for Computing the Probability of a Gambler’s Ruin with Applications to Playing Roulette. American Journal of Theoretical and Applied Statistics, 12(2), 32-36. https://doi.org/10.11648/j.ajtas.20231202.12

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ACS Style

William Henry Laverty; Ivan William Kelly. Techniques for Computing the Probability of a Gambler’s Ruin with Applications to Playing Roulette. Am. J. Theor. Appl. Stat. 2023, 12(2), 32-36. doi: 10.11648/j.ajtas.20231202.12

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AMA Style

William Henry Laverty, Ivan William Kelly. Techniques for Computing the Probability of a Gambler’s Ruin with Applications to Playing Roulette. Am J Theor Appl Stat. 2023;12(2):32-36. doi: 10.11648/j.ajtas.20231202.12

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@article{10.11648/j.ajtas.20231202.12,
  author = {William Henry Laverty and Ivan William Kelly},
  title = {Techniques for Computing the Probability of a Gambler’s Ruin with Applications to Playing Roulette},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {12},
  number = {2},
  pages = {32-36},
  doi = {10.11648/j.ajtas.20231202.12},
  url = {https://doi.org/10.11648/j.ajtas.20231202.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20231202.12},
  abstract = {An interest in gambling has greatly increased over the last few decades with the more common use of slot machines and online gambling, especially sports betting. A concern that has been publically raised is addiction and eventual gambler’s ruin (loss of all money). In this paper we provide a solution to the Gambler’s Ruin problem in regards to roulette. We compute the probability of a gamblers ruin with applications to the various betting opportunities playing roulette by determining the W+1 roots of the relevant polynomials and from there determine the probability of a gamblers ruin. We find situations where the payoff becomes higher, the probability of ruin becomes lower. Lower goals of gain are associated with a lower probability of ruin and larger bets and larger odds payoff also increase the probability of ruin.},
 year = {2023}
}

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TY  - JOUR
T1  - Techniques for Computing the Probability of a Gambler’s Ruin with Applications to Playing Roulette
AU  - William Henry Laverty
AU  - Ivan William Kelly
Y1  - 2023/05/18
PY  - 2023
N1  - https://doi.org/10.11648/j.ajtas.20231202.12
DO  - 10.11648/j.ajtas.20231202.12
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 32
EP  - 36
PB  - Science Publishing Group
SN  - 2326-9006
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AB  - An interest in gambling has greatly increased over the last few decades with the more common use of slot machines and online gambling, especially sports betting. A concern that has been publically raised is addiction and eventual gambler’s ruin (loss of all money). In this paper we provide a solution to the Gambler’s Ruin problem in regards to roulette. We compute the probability of a gamblers ruin with applications to the various betting opportunities playing roulette by determining the W+1 roots of the relevant polynomials and from there determine the probability of a gamblers ruin. We find situations where the payoff becomes higher, the probability of ruin becomes lower. Lower goals of gain are associated with a lower probability of ruin and larger bets and larger odds payoff also increase the probability of ruin.
VL  - 12
IS  - 2
ER  -

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Author Information

William Henry Laverty

Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, Canada
Ivan William Kelly

Retired from Department of Educational Psychology & Special Education, University of Saskatchewan, Saskatoon, Canada

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APA Style

William Henry Laverty, Ivan William Kelly. (2023). Techniques for Computing the Probability of a Gambler’s Ruin with Applications to Playing Roulette. American Journal of Theoretical and Applied Statistics, 12(2), 32-36. https://doi.org/10.11648/j.ajtas.20231202.12

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ACS Style

William Henry Laverty; Ivan William Kelly. Techniques for Computing the Probability of a Gambler’s Ruin with Applications to Playing Roulette. Am. J. Theor. Appl. Stat. 2023, 12(2), 32-36. doi: 10.11648/j.ajtas.20231202.12

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AMA Style

William Henry Laverty, Ivan William Kelly. Techniques for Computing the Probability of a Gambler’s Ruin with Applications to Playing Roulette. Am J Theor Appl Stat. 2023;12(2):32-36. doi: 10.11648/j.ajtas.20231202.12

Copy | Download

@article{10.11648/j.ajtas.20231202.12,
  author = {William Henry Laverty and Ivan William Kelly},
  title = {Techniques for Computing the Probability of a Gambler’s Ruin with Applications to Playing Roulette},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {12},
  number = {2},
  pages = {32-36},
  doi = {10.11648/j.ajtas.20231202.12},
  url = {https://doi.org/10.11648/j.ajtas.20231202.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20231202.12},
  abstract = {An interest in gambling has greatly increased over the last few decades with the more common use of slot machines and online gambling, especially sports betting. A concern that has been publically raised is addiction and eventual gambler’s ruin (loss of all money). In this paper we provide a solution to the Gambler’s Ruin problem in regards to roulette. We compute the probability of a gamblers ruin with applications to the various betting opportunities playing roulette by determining the W+1 roots of the relevant polynomials and from there determine the probability of a gamblers ruin. We find situations where the payoff becomes higher, the probability of ruin becomes lower. Lower goals of gain are associated with a lower probability of ruin and larger bets and larger odds payoff also increase the probability of ruin.},
 year = {2023}
}

Copy | Download

TY  - JOUR
T1  - Techniques for Computing the Probability of a Gambler’s Ruin with Applications to Playing Roulette
AU  - William Henry Laverty
AU  - Ivan William Kelly
Y1  - 2023/05/18
PY  - 2023
N1  - https://doi.org/10.11648/j.ajtas.20231202.12
DO  - 10.11648/j.ajtas.20231202.12
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 32
EP  - 36
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20231202.12
AB  - An interest in gambling has greatly increased over the last few decades with the more common use of slot machines and online gambling, especially sports betting. A concern that has been publically raised is addiction and eventual gambler’s ruin (loss of all money). In this paper we provide a solution to the Gambler’s Ruin problem in regards to roulette. We compute the probability of a gamblers ruin with applications to the various betting opportunities playing roulette by determining the W+1 roots of the relevant polynomials and from there determine the probability of a gamblers ruin. We find situations where the payoff becomes higher, the probability of ruin becomes lower. Lower goals of gain are associated with a lower probability of ruin and larger bets and larger odds payoff also increase the probability of ruin.
VL  - 12
IS  - 2
ER  -

Copy | Download