Minesweeper Statistics: Mine Odds, Number 8, 3BV and First Clicks

Minesweeper by the numbers

Minesweeper is a game of deduction, but every board begins with randomness. We independently generated 350,000 standard-size boards to explore which clue numbers appear, how densely mines are packed, how much one opening click can reveal, and how challenging a typical layout is under the 3BV metric. The results are research examples, not a record of the visitors playing on this website.

The sample includes 100,000 Beginner boards, 100,000 Intermediate boards and 150,000 Expert boards. Every simulated game protected the first clicked square and all eight surrounding squares. That condition strongly affects opening sizes, so it is important when comparing the figures with other Minesweeper variations.

Board sizes and mine density

Beginner contains 10 mines in an 81-square grid, leaving 71 safe squares. Intermediate has 40 mines among 256 squares, with 216 safe squares. Expert has 99 mines in 480 squares, with 381 safe squares. Although the absolute number of mines changes substantially, the density—the share of covered cells containing mines—is a more useful first measure of difficulty.

Expert has a 20.63% mine density compared with 12.35% on Beginner. A crowded minefield produces more complicated local clues and smaller natural openings. Density alone does not determine how difficult an individual board is: the arrangement matters too, and a relatively sparse board can still leave a difficult forced guess.

How rare is an 8 in Minesweeper?

An 8 is a safe interior square surrounded by mines in every one of its eight adjacent squares. In our independent sample, 151 of 150,000 Expert boards contained at least one 8, approximately one board in 993. Four of 100,000 Intermediate boards contained an 8, and none appeared in 100,000 sampled Beginner boards.

These are observed frequencies from a finite sample, not guaranteed odds for all implementations. Zero observed 8s on Beginner does not mean that a Beginner 8 is mathematically impossible. Other generators and first-click rules may produce different frequencies. A board containing an 8 also does not guarantee that the player will reveal it before the game ends.

Which numbers appear most often?

A Minesweeper clue counts neighboring mines, not the total number of mines on the board. On the sampled Expert grids, 1 was the most common visible number, followed by 2, 3 and 4. Blank squares were also common; higher clues fell away rapidly as more of the eight neighbors had to be mines.

In the chart, percentages refer only to safe squares, including blank squares, across the Expert sample. The distribution does not show how often players personally encounter each number: many generated safe squares are never revealed in a lost game. Corner cells have only three neighbors and edge cells have five, which also changes the overall mix of clues.

What happens on the first click?

For this comparison, the first click is near the center of the board and the entire surrounding 3×3 area is guaranteed safe. That makes the first click a zero, which expands through nearby blank squares and reveals their numbered borders. In half of the sampled Expert games, the first click revealed at least 35 squares; the median was 48 on Beginner and 64 on Intermediate.

A large initial opening is helpful, but it does not prove the rest of the puzzle can be solved without guessing. Different versions of Minesweeper use different opening guarantees. If only the clicked cell is protected, a first click may reveal just a number rather than a wide opening. Do not compare first-click figures without checking the exact rule.

3BV: measuring the difficulty of a board

3BV means Bechtel's Board Benchmark Value. It estimates the minimum number of direct left-click actions needed to reveal all safe squares when the mine layout is already known: one click for each connected opening of zero cells, plus one for every numbered safe square not exposed by those openings. Chording and automation are not included in this definition.

Our median 3BV values were 14 for Beginner, 63 for Intermediate and 170 for Expert. This is a property of the board, not the player's personal skill. A timed run of 100 seconds on a board with 3BV 170 has a 3BV/s of 1.70, but identical completion times on different boards may reflect very different amounts of clicking and reasoning. The actual move counter in a game may count actions differently from 3BV.

Why no-guess odds are not win rates

A guess-free board is one that can be completed using logically forced safe moves from its starting position. An ordinary board may eventually present a genuine 50/50 choice where no clue distinguishes two squares. A game can still be won after a guess; the odds of solving without guessing are therefore not the same as the probability of winning.

We have intentionally not published a guess-free percentage here: determining one requires a specified solver, a clear definition of deduction, and a simulation that plays each board. Mine density or 3BV alone cannot produce that percentage. If you want to practise logic-only puzzles, try our No-Guess Minesweeper mode or follow the deduction examples in the guides.

How this simulation was created

We produced a new, independent sample rather than reproducing numbers from another website. Each board used the classic 9×9/10, 16×16/40 or 30×16/99 settings. A reproducible pseudo-random generator placed mines without replacement among all cells outside the center 3×3 protected area. We then counted every safe clue, the existence of a 7 or 8, connected zero regions, 3BV and the number of cells exposed by the first click.

The sample sizes were 100,000, 100,000 and 150,000 boards respectively, totaling 350,000. Numbers are rounded for readability. The downloadable data file hosted on this site contains the raw count summaries, seeds and method description so the published percentages can be checked. The study was prepared on 30 October 2026.

View the study data (JSON) →

What these figures cannot tell you

These figures describe the simulated boards, not the live leaderboard, a player's win rate or all possible Minesweeper generators. The live game has its own implementation and can create a different distribution of layouts. The simulation uses a protected 3×3 opening; a game protecting only one square is not directly comparable. No statistical sample can establish whether an extremely rare arrangement is impossible.

Percentages near zero are especially uncertain. An observed count of four Intermediate boards with an 8 is enough to establish that the pattern appeared in our sample, but not enough for a precise universal probability estimate. Use these numbers to understand the game, not to declare an individual score legitimate or suspicious. You can continue with our strategy guide, number guide, or the article dedicated to the number 8.