Exploring Efficient Strategies for Minesweeper

Abstract

Minesweeper is a famous single-player computer game, in which the grid of blocks contains some mines and the player is to uncover (probe) all blocks that do not contain any mines. Many heuristic strategies have been prompted to play the game, but the rate of success is not high. In this paper, we explore efficient strategies for the Minesweeper game. First, we show a counterintuitive result that probing the corner blocks could increase the rate of success. Then, we present a series of heuristic strategies, and the combination of them could lead to better results. We also transplant the optimal procedure on the basis of our proposed methods, and it achieves the highest rate of success. Through extensive simulations, a combination of heuristic strategies, 'PSEQ', yields a success rate of 81.627(8)%, 78.122(8)%, and 39.616(5)% for beginner, intermediate, and expert levels respectively, outperforming the state-of-the-art strategies. Moreover, the developed quasi-optimal methods, combining the optimal procedure and our heuristic methods, raise the success rate to at least 81.79(2)%, 78.22(3)%, and 40.06(2)% respectively.