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The symmetric 4-Player gambler’s problem with unequal initial stakes

  • Abid Hussain EMAIL logo und Salman A. Cheema
Veröffentlicht/Copyright: 4. Dezember 2022
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Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 72 Heft 6

Abstract

This research advances the 4-player gambler’s ruin problem for the case of arbitrary initial stakes. The aim of the research is attained by offering simple expressions using the difference equation approach and thus providing closed form solution to the problem. Moreover, the existing technique of Chang [A game with four players, Statist. Probab. Lett. 23(2) (1995), 111–115] dealing with equal initial stakes is demonstrated as a sub-case of the newly devised scheme. The legitimacy of the proposed formulation is further verified by considering various parametric settings.

Keywords: 4-player game; arbitrary initial stakes; expected ruin time
MSC 2010: Primary 60-03

  1. (Communicated by Gejza Wimmer)

References

[1] CHANG, D. K.: A game with four players, Statist. Probab. Lett. 23(2) (1995), 111–115.10.1016/0167-7152(94)00101-DSuche in Google Scholar

[2] CHO, D.: A game with N players, J. Korean Statist. Soc. 25(2) (1996), 185–193.Suche in Google Scholar

[3] EDWARDS, A.: Pascal’s problem – the gambler’s ruin’, Int. Stat. Rev. 51 (1983), 73–79.10.2307/1402732Suche in Google Scholar

[4] El-SHEHAWEY, M. A. — AL-MATRAF, B. N.: On a gambler’s ruin problem, Math. Slovaca 47(4) (1997), 483–488.Suche in Google Scholar

[5] FELLER, W.: An Introduction to Probability Theory and its Applications, vol. I., John Wiley & Sons, New York, 1968.Suche in Google Scholar

[6] HUSSAIN, A. — CHEEMA, S. A. — HANIF, M.: A game based on successive events, Stat. 9(1) (2020), Art. ID e274.10.1002/sta4.274Suche in Google Scholar

[7] HUSSAIN, A. — CHEEMA, S. A. — HAROON, S. — KIFAYAT, T.: The ruin time for 3-player gambler’s problem: an approximate formula, Comm. Statist. Simulation Comput. (2021); https://doi.org/10.1080/03610918.2021.1888996doi:10.1080/03610918.2021.1888996.10.1080/03610918.2021.1888996.Suche in Google Scholar

[8] JAYASEKERA, R.: Prediction of company failure: Past, present and promising directions for the future, Int. Rev. Financial Anal. 55 (2018), 196–208.10.1016/j.irfa.2017.08.009Suche in Google Scholar

[9] LARDIZABAL, C. F. — SOUZA, R. R.: Open quantum random walks: ergodicity, hitting times, gamblers ruin and potential theory, J. Stat. Phys. 164(5) (2016), 1122–1156.10.1007/s10955-016-1578-9Suche in Google Scholar

[10] OGILVY, C. S.: Tomorrow’s Math: Unsolved Problems for the Amateur, New York: Oxford University Press, 1962.Suche in Google Scholar

[11] PEROTTO, F. S. — TRABELSI, I. — COMBETTES, S. — CAMPS, V. — VERSTAEVEL, N.: Deciding when to quit the gambler’s ruin game with unknown probabilities, Internat. J. Approx. Reason 137 (2021), 16–33.10.1016/j.ijar.2021.06.013Suche in Google Scholar

[12] PETTERUTI, S.: Fast Simulation of Random Walks on the Endoplasmic Reticulum by Reduction to the Gamblers Ruin Problem, Ph.D. thesis, Harvard University, Cambridge, MA, 2017.Suche in Google Scholar

[13] ROCHA, A. L. — STERN, F.: The gambler’s ruin problem with n players and asymmetric play, Statist. Probab. Lett. 44(1) (1999), 87–95.10.1016/S0167-7152(98)00295-8Suche in Google Scholar

[14] ROCHA, A. L. — STERN, F.: The asymmetric n-player gambler’s ruin problem with equal initial fortunes, Adv. Appl. Math. 33(3) (2004), 512–530.10.1016/j.aam.2003.07.005Suche in Google Scholar

[15] SANDELL, D.: A game with three players, Statist. Probab. Lett. 7(1) (1989), 61–63.10.1016/0167-7152(88)90089-2Suche in Google Scholar

[16] SOBEL, M. — FRANKOWSKI, K.: Extensions of gambler’s ruin with even odds: multinomial and other models, J. Statist. Plann. Inference 101(1–2) (2002), 291–310.10.1016/S0378-3758(01)00191-4Suche in Google Scholar

[17] TSAI, C. W. — HSU, Y. — LAI, K. — WU, N.: Application of gambler’s ruin model to sediment transport problems, J. Hydrology, 510 (2014), 197–207.10.1016/j.jhydrol.2013.11.038Suche in Google Scholar
Received: 2021-06-12
Accepted: 2021-09-20
Published Online: 2022-12-04
Published in Print: 2022-12-16

© 2022 Mathematical Institute Slovak Academy of Sciences

Artikel in diesem Heft

  1. Prof. RNDr. Július korbaš, CSC. passed away
  2. Kalmbach measurability In d0-algebras
  3. Quantifiers on L-algebras
  4. Ideals of functions with compact support in the integer-valued case
  5. An algebraic study of the logic S5’(BL)
  6. Triangular numbers and generalized fibonacci polynomial
  7. A general matrix series inversion pair and associated polynomials
  8. Quantum ostrowski type inequalities for pre-invex functions
  9. Hermite-Hadamard type inequalities for interval-valued fractional integrals with respect to another function
  10. Approximating families for lattice outer measures on unsharp quantum logics
  11. On a generalized Lamé-Navier system in ℝ3
  12. Coercive and noncoercive elliptic problems with variable exponent Laplacian under Robin boundary conditions
  13. On some classical properties of normed spaces via generalized vector valued almost convergence
  14. Fan-Hemicontinuity for the gradient of the norm in Hilbert space
  15. Solvability of mixed problems for heat equations with two nonlocal conditions
  16. The global harnack estimates for a nonlinear heat equation with potential under finsler-geometric flow
  17. A note on set-star-K-Menger spaces
  18. A bivariate extension of the Omega distribution for two-dimensional proportional data
  19. Bernstein polynomials based iterative method for solving fractional integral equations
  20. The symmetric 4-Player gambler’s problem with unequal initial stakes
  21. Enveloping action: Convergence spaces
https://doi.org/10.1515/ms-2022-0113
Schlagwörter für diesen Artikel
4-player game; arbitrary initial stakes; expected ruin time

Artikel in diesem Heft

  1. Prof. RNDr. Július korbaš, CSC. passed away
  2. Kalmbach measurability In d0-algebras
  3. Quantifiers on L-algebras
  4. Ideals of functions with compact support in the integer-valued case
  5. An algebraic study of the logic S5’(BL)
  6. Triangular numbers and generalized fibonacci polynomial
  7. A general matrix series inversion pair and associated polynomials
  8. Quantum ostrowski type inequalities for pre-invex functions
  9. Hermite-Hadamard type inequalities for interval-valued fractional integrals with respect to another function
  10. Approximating families for lattice outer measures on unsharp quantum logics
  11. On a generalized Lamé-Navier system in ℝ3
  12. Coercive and noncoercive elliptic problems with variable exponent Laplacian under Robin boundary conditions
  13. On some classical properties of normed spaces via generalized vector valued almost convergence
  14. Fan-Hemicontinuity for the gradient of the norm in Hilbert space
  15. Solvability of mixed problems for heat equations with two nonlocal conditions
  16. The global harnack estimates for a nonlinear heat equation with potential under finsler-geometric flow
  17. A note on set-star-K-Menger spaces
  18. A bivariate extension of the Omega distribution for two-dimensional proportional data
  19. Bernstein polynomials based iterative method for solving fractional integral equations
  20. The symmetric 4-Player gambler’s problem with unequal initial stakes
  21. Enveloping action: Convergence spaces
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