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Efficient Monte Carlo Methods for Multidimensional Modeling of Slot Machines Jackpot

Author

Listed:
  • Slavi Georgiev

    (Department of Informational Modeling, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 8, 1113 Sofia, Bulgaria
    Department of Applied Mathematics and Statistics, Faculty of Natural Sciences and Education, University of Ruse, POB 7004 Ruse, Bulgaria)

  • Venelin Todorov

    (Department of Informational Modeling, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 8, 1113 Sofia, Bulgaria
    Department of Parallel Algorithms, Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 25A, 1113 Sofia, Bulgaria)

Abstract

Nowadays, entertainment is one of the biggest industries, which continues to expand. In this study, the problem of estimating the consolation prize as a fraction of the jackpot is dealt with, which is an important issue for each casino and gambling club. Solving the problem leads to the computation of multidimensional integrals. For that purpose, modifications of the most powerful stochastic quasi-Monte Carlo approaches are employed, in particular lattice and digital sequences, Halton and Sobol sequences, and Latin hypercube sampling. They show significant improvements to the classical Monte Carlo methods. After accurate computation of the arisen integrals, it is shown how to calculate the expectation of the real consolation prize, taking into account the distribution of time, when different numbers of players are betting. Moreover, a solution to the problem with higher dimensions is also proposed. All the suggestions are verified by computational experiments with real data. Besides gambling, the results obtained in this study have various applications in numerous areas, including finance, ecology and many others.

Suggested Citation

  • Slavi Georgiev & Venelin Todorov, 2023. "Efficient Monte Carlo Methods for Multidimensional Modeling of Slot Machines Jackpot," Mathematics, MDPI, vol. 11(2), pages 1-18, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:266-:d:1024789
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    References listed on IDEAS

    as
    1. Graham D. I. Barr & Ian N. Durbach, 2008. "A Monte Carlo Analysis of Hypothetical Multi-Line Slot Machine Play," International Gambling Studies, Taylor & Francis Journals, vol. 8(3), pages 265-280, December.
    2. Pantelis-Arsenios Kamanas & Angelo Sifaleras & Nikolaos Samaras, 2021. "Slot Machine RTP Optimization Using Variable Neighborhood Search," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-8, May.
    3. Ryan A. Fitch & Julie M. Mueller & Rebecca Ruiz & Wade Rousse, 2022. "Recreation Matters: Estimating Millennials’ Preferences for Native American Cultural Tourism," Sustainability, MDPI, vol. 14(18), pages 1-11, September.
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    Cited by:

    1. Snezhana Gocheva-Ilieva & Atanas Ivanov & Hristina Kulina, 2023. "Special Issue “Statistical Data Modeling and Machine Learning with Applications II”," Mathematics, MDPI, vol. 11(12), pages 1-4, June.

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