Minesweeper (computer game): Wikis

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A game in beginner board

Minesweeper is a single-player video game. The object of the game is to clear an abstract minefield without detonating a mine. The game has been written for many system platforms in use today, including the Minesweeper for the Windows platform, which has come bundled with versions of the operating system from 3.1 and on.

Contents

Overview

When the game is started, the player is presented with a grid of gray squares. The size of the grid is dependent on the skill level chosen by the player, with higher skill levels having larger grids. If the player clicks on a square without a mine, a digit is revealed in that square, the digit indicating the number of adjacent squares (typically, out of the possible 8) which contain mines. By using logic, players can in many instances use this information to deduce that certain other squares are mine-free (or mine-filled), and proceed to click on additional squares to clear them or mark them with flag graphics to indicate the presence of a mine.

The player can place a flag graphic on any square believed to contain a mine by right-clicking on the square. Right-clicking on a square that is flagged will sometimes, according to settings, change the flag graphic into a question mark to indicate that the square may or may not contain a mine. Right-clicking on a square marked with a question mark will set the square back to its original state. Squares marked with a flag cannot be cleared by left-clicking on them, though question marks can be cleared in the same manner as normal squares. If the question mark state is deemed unnecessary, it can be disabled so that right clicking on a flagged mine will set it directly to its original state.

In some versions, the expedient of middle-clicking (or clicking the left and right buttons simultaneously) on a number having at least as many adjacent flags as the value of the number reveals all the unmarked squares neighboring the number; however, the game is forfeit in the event a related flag was placed in error. Some implementations allow for the mouse to be moved with the right mouse-button depressed after flagging a mine; the player can then click on multiple squares while dragging with the right mouse-button. As an alternative to clicking both buttons at the same time players can also middle-click or shift-click on fully-flagged numbers.

Some implementations of Minesweeper will set up the board by never placing a mine on the first square clicked, or by arranging the board so that the solution does not require guessing. This approach was highlighted on the G4 television show Cheat!.

History

The basic gameplay style became a popular segment of the puzzle game genre during the 1980s, with such titles as Mined-Out (Quicksilva, 1983), Yomp (Virgin Interactive, 1983), and Cube. Cube was succeeded by Relentless Logic (or RLogic for short), by Conway, Hong, and Smith, available for MS-DOS as early as 1985; the player took the role of a private in the United States Marine Corps, delivering an important message to the U.S. Command Center. RLogic had greater similarity to Minesweeper than to Cube in concept, but a number of differences exist:

  • In RLogic, the player must navigate through the minefield, from the top left corner to the bottom right corner (the Command Center).
  • It is not necessary to clear all non-mine squares. Also, there is no mechanism for marking mines or counting the number of mines found.
  • The number of steps taken is counted. Although no high score functionality is included, players could attempt to beat their personal best score for a given number of mines.
  • Unlike Minesweeper, the size of the minefield is fixed. However, the player may still specify the number of mines.
  • Because the player must navigate through the minefield, it is sometimes impossible to win — namely, when the mines block all possible paths.

The gameplay mechanics of Minesweeper are included in a variety of other software titles, including:

  • The mini-game Vinesweeper implemented into the MMORPG RuneScape; in this iteration (written by Jagex developer Danny J), the Minesweeper gameplay is given a large multiplayer aspect and the 'game board' adopts a continually resetting timer. This allows for a never-ending game of Minesweeper where the skill is awarded assessed in points rather than 'game completion'.
  • The PC game Mole Control (developed by Remode); in this game, the minesweeper mechanic is integrated into a puzzle adventure game based in a village called Molar Creek, which has been overrun with exploding moles. You play the local inventor's assistant, who is tasked with clearing the village of exploding moles, and you can also take part in the Molar Creek Annual Mole Control competition in a Time Attack Mode.

Distribution and variants

Versions of Minesweeper are frequently bundled with operating systems and GUIs, including Minesweeper in Windows, KMines in KDE(Unix-like OSes), Gnomine in GNOME and MineHunt in Palm OS. Apart from the bundled versions, a huge number of clones of all shapes and sizes can be found on the Internet.

Variants of the basic game generally have differently shaped minefields in two and three dimensions, or various 2D layouts (such as triangular or hexagonal grids). For example, X11-based XBomb adds triangular and hexagonal grids, and Professional Minesweeper for Windows includes these and others.

A minigame in Sonic Battle is essentially a variation of Minesweeper.

Game analysis

Patterns and solving

There are many patterns of numbered squares that may arise during a game that can be recognized as allowing only one possible configuration of mines in their vicinity. In the interest of finishing quickly, it is often easiest to process the known patterns first, and continue on with the uncertain parts later. There are a few broad methods for solving problems in minesweeper games without guessing.

Single-square analysis

Example case 2
1 3 flag unopened
1 a b unopened
1 unopened unopened unopened
a and b must be mines; the only squares that can provide those demanded by the 3 are a and b.
Example case 1
flag 3 flag unopened
a b flag unopened
unopened unopened unopened unopened
a and b are safe to open, as the 3 is satisfied by adjacent mines.

There are two special cases that are of extra interest when solving a board that can be solved using analysis of only one square and its surrounding squares:[1]

  • If the number of unclicked (blank or flagged) squares adjacent to a numbered square is equal to the number on that square, all these unclicked squares must be mines.
  • For any numbered square, if the number of mines you've found adjacent to that square is equal to the number of the square, all other squares adjacent to that numbered square must be 'safe' (e.g. If you know the square to the right of a 1 is a mine, then you can deduce that all the other squares next to that 1 do not contain mines.)

Multiple square analysis

To solve more complex puzzles, one needs to consider more than one square at a time. Some strategies that involve considering more than one number at a time:

  • If you have two adjacent numbers, the difference between those numbers is equal to the difference in the number of mines for the 3 squares adjacent to each that are not adjacent to the other number. For example: if these numbers differ by 3, all of the adjacent squares to the higher number not shared by the other are mines, and all the opposite ones are safe.
  • In a similar method, sometimes it can be known that there are a certain number of mines in a certain number of squares (without necessarily knowing which are the mines and which are safe) and you can often utilise this information to find out information about other squares.

One method that is commonly used by minesweeper AIs is to consider the board as a constraint satisfaction problem.[2][3]

The variables/unknowns are the unopened squares, and the constraints are the adjacent squares that are opened. The algorithm consists of trying every combination of mines that satisfies all the numbers in the adjacent squares, and making a conclusion from there. For large puzzles, this is a time-consuming process for a computer, but expert minesweepers might be able to quickly see which squares need this procedure, and where one might expect it to succeed. The two rules above are such special cases.

Example
1 a unopened
1 2 b unopened
c d e unopened
unopened unopened unopened unopened

Example: A corner square and the 3 adjacent squares have been opened, and the numbers given revealed. The letters here are unopened squares and they are the variables.

Blindly trying every combination gives the 4 valid configurations (out of 25), namely {a,b,c,d,e} = {1,0,1,0,0}, {0,1,1,0,0}, {1,0,0,1,0} and {0,1,0,1,0}, where 1 represents a mine.

The only common number in all these configurations is that the variable e is never a mine. The conclusion is that in all possible valid configurations, e is safe, and one can safely open that square. Analogously, if a square is marked as mine in every valid combination, then the square must be a mine.

One can also think of this as a system of equations, where the variables must be in {0,1}. In the above example, the constraints gives that a+b=1, c+d=1 and a+b+c+d+e=2. The third equation can be reduced to 1+1+e=2 and hence the square e must be safe. This strategy is more similar to the human approach, but is harder to implement as a computer program.

Final analysis

Used at the end of a game, this can be used to clear a square when all other squares on the board are either safe or can be shown to be mines. Often these final squares are on walls or in corners.

In some versions of the game the number of mines on the field is known. Near the end when almost all the tiles are lifted, knowing the number of mines remaining can give some insight to otherwise unresolvable patterns.

Elements of guesswork

In all implementations of Minesweeper, it is possible for a grid to be generated which cannot be solved without an element of guessing. For instance, in the following situation:

Example
1 2 3 2 1
1 flag flag flag 1
1 3 a 3 1
1 b 1

The player must guess whether a or b is the mine.

The constraint satisfaction problem above might help a little to estimate the likelihood that a square is a mine; list all the valid combinations and count how many times each square is occupied by a mine. If the density of mines is known (or estimated during the game), the player can pick the square that is least likely to contain a mine.

Another apparent instance of required guessing is when an unclicked square is completely surrounded by either mines, or a combination of mines and the perimeter of the game window (the latter being much more common). In this case, since no numbers touch the unclicked square, a player has no information about the likelihood of the unclicked square being a mine. However, there is still a good strategy when facing this situation that will allow the player to avoid simple guessing: simply play the rest of the game and ignore this square. When the number of unclicked, unflagged spaces left equals the number of mines left unmarked, then all remaining spaces are mines. Some versions may automatically flag these spaces once all other squares in the game window have been clicked by the player, or reveal them once all flags have been placed.

Computational complexity

In 2000, Richard Kaye published a proof that it is NP-complete to determine whether a position in a Minesweeper game is consistent with some placement of mines.[4] Minesweeper is now mentioned in the Clay Mathematics Institute's unofficial description of the P versus NP problem.[5]

Measuring board difficulty

Beginner board with a 3BV of 8.

The difficulty of a given minesweeper board is often measured using the 3BV measure (abbreviated from Bechtel's Board Benchmark Value).

Method

The 3BV of a board names the minimum number of left clicks required to open up all squares without a mine of a Minesweeper field.

  • Each opening of a board counts as 1 3BV (white dots on the pictures).
  • Each square without a mine but a number which is not a border (white lines) of an opening counts as 1 3BV (green dots on the pictures).

The sum of the 3BV is the 3BV of the whole board.

3BV/s

3BV/s stands for 3BV per second.

Because the time that is needed to finish a Minesweeper board depends highly on the difficulty of the board, it may not be the best way to compare records. 3BV/s on the other hand does consider the difficulty of the Minesweeper board as well as the time needed to finish it. Among the best Minesweeper players, 3BV/s records are not nearly as important as time records, but they give a picture of how fast someone can play with regard to mouse-handling.

If flags are marked, it is possible to require fewer clicks than the 3BV of the respective board. Using only left clicks is called non-flagging (nf) whereas marking mines with right-clicks is called flagging-style.

In Pop Culture

CollegeHumor made a fake trailer for Minesweeper - The Movie.[6]

Weird Al mentions Minesweeper in his song White and Nerdy.

Criticism

In 2001, the Italian "International Campaign to Ban Winmine" voiced strong concern over the game, contending that it is an "offense against the victims of the mines" and those who risk their lives to clear them. They created their own "Winflower" game, and lobbied Microsoft to use it in place of Minesweeper in Windows 98.[7] As a reaction to this criticism, the version of Minesweeper included in Windows Vista and Windows 7 offers a mode in which the mines are replaced with flowers.[8]

See also

Notes

References

External links


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