Hostname: page-component-74656f9884-skzmx Total loading time: 0 Render date: 2026-11-05T23:36:10.319Z Has data issue: false hasContentIssue false

The Minesweeper Game: Percolation and Complexity

Published online by Cambridge University Press:  09 October 2002

ELCHANAN MOSSEL
Affiliation:
Institute of Mathematics, The Hebrew University of Jerusalem, Giv'at Ram, Jerusalem 91904, Israel and Microsoft Research, 1 Microsoft Way, Redmond, WA 98052, USA (e-mail: mossel@math.huji.ac.il)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

We study a model motivated by the minesweeper game. In this model one starts with the percolation of mines on the lattice ℤd, and then tries to find an infinite path of mine-free sites. At every recovery of a free site, the player is given some information on the sites adjacent to the current site. We compare the parameter values for which there exists a strategy such that the process survives to the critical parameter of ordinary percolation. We then derive improved bounds for these values for the same process, when the player has some complexity restrictions in computing his moves. Finally, we discuss some monotonicity issues which arise naturally for this model.

Information

Type
Research Article
Copyright
2002 Cambridge University Press