Phase transition for Minesweeper

TL;DR

This paper establishes a phase transition in Minesweeper, showing that above a certain mine density the game is almost surely unsolvable, while below it, an efficient solving algorithm exists.

Contribution

The paper provides the first rigorous proof of a phase transition in Minesweeper related to mine density and solvability.

Findings

High mine density leads to unsolvability with high probability.

Below the critical density, Minesweeper can be solved in linear time.

Identifies a sharp threshold for solvability based on mine density.

Abstract

We prove a coarse phase transition for the game of Minesweeper: above a certain critical mine density, the game becomes unsolvable with high probability, whereas below the critical mine density it can be solved with a linear time algorithm.