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

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

E-mail Address: achachm@gmail.com

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H. F. Coronel-Brizio

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

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A. R. Hernández-Montoya

Centro de Investigación en Inteligencia Artificial, Universidad Veracruzana, Sebastián Camacho No. 5, Col. Centro, C.P. 91000, Xalapa, Ver., México

Centro 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: 14-740 07000 México, D.F., México

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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

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, and

E. Canto-Lugo

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https://doi.org/10.1142/S0129183116501278Cited by:1 (Source: Crossref)

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:

PACS: 02.50.Le, 05.30.−d, 02.10.Ox, 02.50.Ng

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