Efficient Monte Carlo Methods for Multidimensional Modeling of Slot Machines Jackpot

Slavi Georgiev and Venelin Todorov ()
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Slavi Georgiev: Department of Informational Modeling, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 8, 1113 Sofia, 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

Mathematics, 2023, vol. 11, issue 2, 1-18

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.

Keywords: gambling; jackpot; multidimensional integrals; Monte Carlo methods; lattice sequences; digital sequences (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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