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The one-dimensional minesweeper game: What are your chances of winning?

Author

Listed:
  • M. Rodríguez-Achach

    (Facultad de Física, Universidad Veracruzana, Circuito G. Aguirre Beltrán s/n, Zona Universitaria, Xalapa, Veracruz 91000, México)

  • H. F. Coronel-Brizio

    (Facultad de Física, Universidad Veracruzana, Circuito G. Aguirre Beltrán s/n, Zona Universitaria, Xalapa, Veracruz 91000, México)

  • A. R. Hernández-Montoya

    (Centro de Investigación en Inteligencia Artificial, Universidad Veracruzana, Sebastián Camacho No. 5, Col. Centro, C.P. 91000, Xalapa, Ver., México3Centro de Investigación y de Estudios, Avanzados del IPN (Cinvestav), Av. Instituto Politécnico Nacional 2508, Col. San Pedro Zacatenco, Delegación Gustavo A. Madero, Código Postal 07360 Apartado Postal)

  • R. Huerta-Quintanilla

    (Departamento de Física Aplicada, Centro de Investigación y de Estudios, Avanzados del Instituto Politécnico Nacional, Unidad Mérida. Km. 6 Carretera Antigua a Progreso, Mérida, Yucatán 97310, México)

  • E. Canto-Lugo

    (Departamento de Física Aplicada, Centro de Investigación y de Estudios, Avanzados del Instituto Politécnico Nacional, Unidad Mérida. Km. 6 Carretera Antigua a Progreso, Mérida, Yucatán 97310, México)

Abstract

Minesweeper is a famous computer game consisting usually in a two-dimensional lattice, where cells can be empty or mined and gamers are required to locate the mines without dying. Even if minesweeper seems to be a very simple system, it has some complex and interesting properties as NP-completeness. In this paper and for the one-dimensional case, given a lattice of n cells and m mines, we calculate the winning probability. By numerical simulations this probability is also estimated. We also find out by mean of these simulations that there exists a critical density of mines that minimize the probability of winning the game. Analytical results and simulations are compared showing a very good agreement.

Suggested Citation

  • M. Rodríguez-Achach & H. F. Coronel-Brizio & A. R. Hernández-Montoya & R. Huerta-Quintanilla & E. Canto-Lugo, 2016. "The one-dimensional minesweeper game: What are your chances of winning?," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 27(11), pages 1-7, November.
    • Handle: RePEc:wsi:ijmpcx:v:27:y:2016:i:11:n:s0129183116501278
    DOI: 10.1142/S0129183116501278
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