Minesweeper by the Numbers
We dealt 12,000,000 random boards with this site's own game code and played each one with a logic solver. Here is how often Minesweeper can be won without guessing, how hard a typical board is, and what the first click really gives you.
- of Beginner boards can be cleared without a single guess
- 81.3% of Beginner boards can be cleared without a single guess
- of Intermediate boards can be cleared without a single guess
- 54.2% of Intermediate boards can be cleared without a single guess
- of Expert boards can be cleared without a single guess (1 in 22)
- 4.5% of Expert boards can be cleared without a single guess (1 in 22)
- random deals, on average, before the no-guess generator finds a clean Expert board
- 22.5 random deals, on average, before the no-guess generator finds a clean Expert board
First click in the centre, with the click and its neighbours kept free of mines, as in normal play on
this site. 1,000,000 boards per setting, seed
play-minesweeper.games/stats/v1. A "guess" here means the solver described in the
methodology got stuck, so these are lower bounds.
How Often Can You Win Without Guessing?
Most Minesweeper losses that feel unfair come from a forced guess: a position where no number on the board can tell a safe cell from a mine. We counted how many random boards never reach such a position. On Beginner, most do. On Expert, with 20.6% of the grid mined, a guess-free board is the exception: 1 in 22.
| Difficulty | Mine density | Centre click | 95% interval | Corner click | 95% interval |
|---|---|---|---|---|---|
| Beginner | 12.3% | 81.3% | 81.24–81.39% | 73.5% | 73.39–73.56% |
| Intermediate | 15.6% | 54.2% | 54.08–54.28% | 44.9% | 44.84–45.03% |
| Expert | 20.6% | 4.5% | 4.45–4.53% | 3.2% | 3.17–3.24% |
Share of 1,000,000 boards per entry that the solver cleared from the first click without guessing. Intervals are 95% Wilson score intervals.
This is not the same as your chance of winning. A board that needs one guess is still won whenever the guess lands, so experienced players win more often than these figures suggest. What the numbers do tell you is how often a perfect player is at the mercy of luck at least once. That is the problem no-guess Minesweeper removes.
The First-Click Rule Changes the Odds
Every modern Minesweeper keeps your first click safe, but not in the same way. On this site, normal and no-guess games keep the clicked cell and its neighbours free of mines, so the first click always opens an area. The daily challenge has to give everyone the same board, so it only moves a mine off the clicked cell, much like the classic Windows versions. That small difference matters a lot:
| Board | First click | Click and its neighbours safe | Only the clicked cell safe | ||
|---|---|---|---|---|---|
| No guess needed | Cells opened (median) | No guess needed | Opens just 1 cell | ||
| Beginner | Centre | 81.3% | 48 | 27.1% | 66.9% |
| Beginner | Corner | 73.5% | 26 | 42.9% | 41.6% |
| Intermediate | Centre | 54.2% | 64 | 13.7% | 74.9% |
| Intermediate | Corner | 44.9% | 17 | 22.5% | 49.6% |
| Expert | Centre | 4.5% | 35 | 0.7% | 84.5% |
| Expert | Corner | 3.2% | 11 | 1.3% | 60.4% |
With only the clicked cell safe, the first click on Expert shows a lone number on 84.5% of boards from the centre, and the next click is usually a guess. Guaranteeing the whole neighbourhood turns every first click into an opening, which is why it raises the guess-free share in every setting we tested.
Where to click depends on the rule. When the neighbours are protected, the centre wins on every difficulty: the safe area is a full 3x3 block that can spread in every direction. When only the clicked cell is safe, a corner is the better bet on every difficulty, because a corner cell has only three neighbours and is far more likely to be a blank that cascades.
How Hard Is a Typical Board? 3BV Distributions
3BV (Bechtel's Board Benchmark Value) is the minimum number of left clicks needed to clear a board: one per opening plus one per number that no opening reaches. Speedrunners divide it by their time to get 3BV/s, so the same time is a better result on a high-3BV board. If you compare times on the leaderboard, this is how much the luck of the deal varies.
| Difficulty | Min | 10th pct | Median | Mean | 90th pct | Max | Mean, guess-free boards |
|---|---|---|---|---|---|---|---|
| Beginner | 1 | 9 | 14 | 14.3 | 20 | 41 | 14.1 |
| Intermediate | 21 | 49 | 63 | 63.1 | 78 | 124 | 63.1 |
| Expert | 93 | 146 | 170 | 170.4 | 195 | 272 | 169.5 |
Centre first click, click and neighbours safe. 1,000,000 boards per difficulty.
Openings and the First Click
An opening is a connected patch of blank cells; clicking any of them clears the whole patch and its numbered border. In normal and no-guess games on this site the first click always lands in one, and how big it is sets the tone of the game.
| Difficulty | Measure | Min | 10th pct | Median | Mean | 90th pct | Max |
|---|---|---|---|---|---|---|---|
| Beginner | Openings per board | 1 | 1 | 2 | 2.5 | 4 | 8 |
| Beginner | Cells opened by a centre click | 9 | 30 | 48 | 45.9 | 59 | 71 |
| Beginner | Cells opened by a corner click | 4 | 6 | 26 | 27.9 | 54 | 71 |
| Intermediate | Openings per board | 1 | 5 | 7 | 7.0 | 9 | 16 |
| Intermediate | Cells opened by a centre click | 9 | 21 | 64 | 64.4 | 108 | 185 |
| Intermediate | Cells opened by a corner click | 4 | 6 | 17 | 26.9 | 64 | 185 |
| Expert | Openings per board | 3 | 10 | 13 | 13.2 | 16 | 26 |
| Expert | Cells opened by a centre click | 9 | 12 | 35 | 40.4 | 75 | 216 |
| Expert | Cells opened by a corner click | 4 | 4 | 11 | 15.8 | 34 | 194 |
On Expert, a centre click opens 10.6% of the safe cells on average, but the spread is wide: one board in ten gives you 12 cells or fewer, another one in ten 75 or more. On Beginner, the first click occasionally clears the whole board in one go: 1 in 48,000 boards (21 of 1,000,000).
Which Numbers Show Up
On an Expert board, 18.9% of the safe cells are blank and 34.2% show a 1. The big numbers are rare: an 8, a cell surrounded by mines on all sides, turns up on 1 in 1,100 Expert boards.
| Difficulty | Boards with a 7 or 8 | Boards with an 8 |
|---|---|---|
| Beginner | 1 in 100,000 | none in 1,000,000 |
| Intermediate | 1 in 520 | 1 in 30,000 (33 boards) |
| Expert | 1 in 34 | 1 in 1,100 (900 boards) |
What It Costs to Deal a No-Guess Board
The no-guess mode works by rejection: it deals a random board around your first click, runs the solver, and deals again until a board passes. We ran the real generator 120,000 times. The number of deals follows directly from the guess-free shares above, so Expert is where the work is.
| Difficulty | First click | Deals, mean | Median | 90th pct | Max | Time, median | Time, 90th pct |
|---|---|---|---|---|---|---|---|
| Beginner | Centre | 1.2 | 1 | 2 | 6 | 0.04 ms | 0.13 ms |
| Beginner | Corner | 1.4 | 1 | 2 | 8 | 0.03 ms | 0.07 ms |
| Intermediate | Centre | 1.9 | 1 | 3 | 13 | 0.16 ms | 0.39 ms |
| Intermediate | Corner | 2.2 | 2 | 4 | 16 | 0.13 ms | 0.32 ms |
| Expert | Centre | 22.5 | 16 | 51 | 209 | 3.0 ms | 8.9 ms |
| Expert | Corner | 31.3 | 22 | 71 | 302 | 2.7 ms | 8.9 ms |
20,000 generator runs per row for the deal counts. Times are from 1,000 further runs per row on one thread of an Apple M4 Pro under Node v26.5.0; a phone is slower. The generator gives up after 400 deals; no run reached that limit, and the most any run needed was 302.
Methodology
- Boards. Beginner 9x9 with 10 mines, Intermediate 16x16 with 40 mines, Expert 30x16 with 99 mines. Each setting combines a difficulty, a first click in the centre (row 9, column 16 on Expert) or the top-left corner, and one of the two first-click rules above. 1,000,000 boards per setting, 12,000,000 in all.
- Dealing. Mines are placed by the same function the game uses: uniformly at random over every cell outside the protected area. For the daily-style rule, mines are placed over the whole grid and a mine under the click moves to the first free cell, as in the daily challenge.
- Solver. The site's no-guess checker plays from the first click using only what a player can see. It applies three rules until none fires: a number with as many hidden neighbours as missing mines has all of them as mines; a number with all its mines found makes its other neighbours safe; and the subset rule between two numbers, which covers the 1-1 and 1-2-1 patterns. When the frontier is exhausted it uses the total mine count. A board counts as guess-free only if this clears every safe cell.
- Metrics. 3BV and openings come from the same board analysis that powers the daily archive pages. Cells opened by the first click are counted by playing the click with the game's own reveal function. Percentiles use the nearest-rank method, so every value shown occurred in the sample.
- Randomness. Every block of boards uses its own seedrandom stream derived from the
master seed
play-minesweeper.games/stats/v1, so the counts are identical however many threads run. - Reproduce it. The whole simulation is one script,
node scripts/simulate-stats.mjs, which needs Node 23.6 or newer. The source is not public yet, but the method above is complete, and the seed fixes every count. The run that produced this page took 200 seconds on 13 threads and was generated on 2026-10-15. Every count should match exactly; only the timings depend on the machine.
Limitations
- The guess-free shares are lower bounds. The solver does not enumerate every arrangement of mines along the frontier, so some positions a full constraint solver would crack are counted as needing a guess. The true share of boards solvable without guessing is somewhat higher.
- Guess-free is not the same as winnable. Many boards that need a guess are still won, because the guess lands. This page does not estimate win rates with guessing.
- First-click rules differ between games. Other Minesweeper versions protect a different area, or none, and the centre of an even-sized board is a choice: we used row 9, column 16 on Expert.
- Sampling error. With 1,000,000 boards per setting, no 95% interval on a guess-free share is wider than 0.20 percentage points; the tails of the histograms (the very highest and lowest 3BV) are the least certain values.
Download and Cite
Download the full results as CSV: every summary on this page plus the exact histograms behind the charts, one row per value, for all 12 settings.
The data is published under CC BY 4.0: reuse it freely, with a link back to this page.
If you use these numbers, please cite:
Play Minesweeper (2026). Minesweeper by the Numbers. https://play-minesweeper.games/stats/ (simulation of 12,000,000 boards, seed "play-minesweeper.games/stats/v1", generated 2026-10-15).
Want to put the numbers to the test? Learn the rules in the how-to-play guide, drill the common patterns, play no-guess Minesweeper where every board is one of the clean ones, or compare your times on the leaderboard.
Minesweeper Statistics FAQ
- What are the odds of winning Expert Minesweeper without guessing?
- In our simulation of 1,000,000 Expert boards (30x16, 99 mines, first click in the centre), 4.5% could be cleared from the first click by logic alone, about 1 in 22. Every other board needed at least one guess somewhere. A guess is not a loss, so a strong player's real win rate is higher than this figure.
- How many Minesweeper boards are solvable without guessing?
- With the first click in the centre: 81.3% on Beginner, 54.2% on Intermediate and 4.5% on Expert. These are lower bounds: the solver uses the standard single-cell rules, the subset rule and the mine count, and a stronger solver would clear a few more boards.
- Does it matter where you click first?
- Yes. When the first click and its neighbours are kept free of mines, a centre click does better: 4.5% of Expert boards are guess-free from the centre against 3.2% from a corner. When only the clicked cell is guaranteed safe, the first click on Expert opens a single number on 84.5% of boards from the centre.
- What is a typical 3BV on Expert?
- The median Expert board in our sample has a 3BV of 170, and 80% of boards fall between 146 and 195. 3BV is the minimum number of left clicks needed to clear a board, and it is the yardstick behind the 3BV/s speed measure.
- How does the no-guess mode find a solvable board so fast?
- It deals random boards and runs the solver on each until one passes. On Expert that takes 22.5 deals on average with a centre click and 31.3 with a corner click, and the median board is ready in 3.0 ms on our test machine.
- Can I use this data?
- Yes. The data is free to reuse under CC BY 4.0: quote it, chart it or put it in a video, with a link back to this page as the source. The full results, including exact histograms, are in the CSV file linked on this page.