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

M. Rodríguez-Achach, H. F. Coronel-Brizio, A. R. Hernández-Montoya, R. Huerta-Quintanilla and E. Canto-Lugo
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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

International Journal of Modern Physics C (IJMPC), 2016, vol. 27, issue 11, 1-7

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.

Keywords: Game theory; Fermi–Dirac statistics; Bose–Einstein statistics; Monte Carlo methods (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1142/S0129183116501278

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