![]() If you flag all mines touching a number, chording on the number opens the remaining squares. This can save you a lot of work! However, if you place the correct number of flags on the wrong squares, chording will explode the mines. The three difficulty levels are Beginner (8x8 or 9x9 with 10 mines), Intermediate (16x16 with 40 mines) and Expert (30x16 with 99 mines). The game ends when all safe squares have been opened. A counter shows the number of unflagged mines and a clock shows your time in seconds. Minesweeper saves your best time for each difficulty level. You also can play Custom games up to 30x24 with a minimum of 10 mines and maximum of (x-1)(y-1) mines. When a number touches the same number of squares those squares must be mines. You might notice that the four squares in the top left corner produce the fewest and smallest openings. Windows Minesweeper makes the first click safe by shifting the mine to the first empty square on the top row starting from the left corner. Windows Vista introduced guaranteed openings on the first click in which case you should always start in the middle. New players should start in the middle on all versions because despite losing more games in the first few clicks they will finish more games. Do you mind losing thousands of games an hour in the first three clicks to get bigger openings? For experienced players the best place to start is more complicated and depends on personal preference. ![]() Sometimes in Minesweeper you are forced to guess. New players guess because it is easier than solving, but sometimes guessing is unavoidable. The optimal guessing strategy depends on whether your goal is to win or to win quickly. This is the best approach when there is no possibility of obtaining further information. It can also be effective if you are happy losing in order to win fewer games more quickly. Solving the rest of the board can often eliminate the guess but many professionals guess immediately to avoid incurring time moving the mouse to an easier location. The second strategy is to guess only when you are forced to guess. If the squares touch other unopened squares solve the rest of the board first in the hope that approaching from a different direction will eliminate the guess.Ī third strategy is to practice playing with no flags so you become better at looking for empty squares. Players who enjoy flagging often make the mistake of guessing mines when it is equally important to open safe squares. The sixth strategy is to calculate probability. This is the best strategy for winning games but can be complicated and time consuming. Local probability is easy to calculate but global probability is much more difficult. For example, it is easy to calculate that one mine in two squares is 50:50 but what if probability depends on all possible mine arrangements for the rest of the board? Sean Barrett has written an excellent guide to Minesweeper Advanced Tactics. The following example considers all six strategies. The first strategy is to guess quickly and hope for the best. This approach will give the best score if you survive. The second strategy is solving the rest of the board to determine the number of mines remaining. There are 79 possible mine arrangements but only 1 solution has 9 mines. The third strategy opens a safe square but in this case there are none. The fourth strategy makes a useful guess. In this case there is one square (I) that solves the board if it is a 4 or 7. The fifth strategy guesses a square that does not touch a number (B, C, F, G) hoping Expert density of 0.206 comes to the rescue. The sixth strategy calculates global probability which ranges from 0.392 (D, K) to 0.798 (J). Minesweeper is won by opening all safe squares. On Intermediate a NF player needs to open 216 safe squares but an inefficient Flagger also needs to flag 40 mines. However, remember that chording can open multiple squares. NF players look for openings instead of mines. Openings propagate in all directions until they are surrounded by numbers.
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