Minesweeper Openings: Where the Blanks Are and When to Chase Them

An opening in Minesweeper is a patch of blank squares (zeros: no mine touches them) that clears in one click, along with every number around its edge. An Expert board has about 13 openings, and together they uncover 58.8% of its safe squares. Blanks are most common in corners and along the edges, but when you are stuck, don't gamble for one: in our test, guessing for openings won 42.5% of Expert games, while always taking the safest square won 49.0%.

This guide shows what openings look like, how many each level has, where the blanks hide, and exactly how much an opening is worth when you have to guess. Every number comes from boards made by the same code as Poozee's Minesweeper, seeded so they can be replayed.

What is an opening in Minesweeper?

A blank (or zero) is a safe square with no mine among its eight neighbors. When you uncover one, the game opens all its neighbors for you, and any blank among them opens its own neighbors, until the chain stops at a ring of numbers. That whole patch is one opening.

Clicking any blank in the top-right opening uncovers 20 squares at once. The little top-left one is only 4 blanks, but it still opens 9 squares. Numbers that touch no blank are lone numbers: no opening will ever uncover them, so you click each one yourself. One click per opening plus one per lone number is the fewest clicks that clear the board, a count speed players call 3BV (this board's is 19; our chording guide explains it).

On Poozee your first click is always an opening: the mines are placed after it, never on it or next to it.

How many openings each level has

We counted every opening on 10,000 boards per level, with the first click in the middle:

"Openings" is the average per board (the middle 80% of boards had 1‑4 on Beginner, 5‑9 on Intermediate and 10‑16 on Expert), "First click" counts the squares the first click opens, and "Share opened" is the share of safe squares that some opening reveals, blanks and the numbers around them.

A few things stand out:

• On Beginner, the first click does most of the work. It opened 64.5% of the safe squares on average, and on 17.9% of boards the first click's opening was the only one.
• Expert boards always have more to find. No Expert board had fewer than 4 openings, and the first click opened only 10.6% of the safe squares. On 5.2% of Expert boards it opened nothing past the guaranteed 3x3 square around your click.
• Openings save a lot of clicks. On Expert the openings uncovered 224.0 squares per board for 13.1 clicks, a saving of 210.8 clicks over opening those squares one at a time. The other 41.2% of the safe squares are lone numbers, one click each.

Where the blanks are

A square is a blank only if it and all its neighbors are clear. A corner has 3 neighbors, a square on an edge has 5 and a square in the middle has 8, so a corner needs 4 clear squares, an edge square 6 and a middle square 9. That makes a big difference. Here is the exact chance that a square at least three steps from your first click is a blank, before any of its numbers show:

These follow from how the game places mines (uniformly among the squares away from your first click), and the 10,000 boards per level matched them to within half a point.

So openings hug the walls. On Expert, 62.3% of the openings other than the first had a blank on the edge of the board, although only 18.3% of the squares are on the edge.

At a real guess, numbers kill openings

The picture changes once numbers are on the board. We stopped a perfect logic player at every forced guess in 1,000 Expert games (2,718 moments when no square was provably safe) and worked out, for every covered square, the exact chance that it is a mine and the exact chance that clicking it opens an area:

A square next to a number almost never opens anything: the number usually means a mine is close by. Away from the numbers, the board still behaves like a fresh one: a covered corner opened an area about as often as a corner before the game started. At the first forced guess of each game there were still 3.43 unfound openings on the board on average, so they are out there. The question is what they are worth.

Should you guess for an opening?

An opening is tempting when you are stuck: one lucky click can uncover dozens of squares and a lot of new numbers. But the square most likely to open an area is rarely the safest one. At those same 2,718 Expert stuck moments, the safest square was a mine 17.9% of the time and opened an area only 4.4% of the time. The square most likely to open an area did so 30.8% of the time, but it was a mine 26.3% of the time. They were the same square in only 37.6% of the stuck moments.

Here is a real position where you face that choice:

Only 22 arrangements of the last 4 mines fit these numbers, and each is equally likely. Square a is a mine in 1 of them, square e in 2, and e is a blank in 15. We played every arrangement out: whichever square you open, if it is safe the numbers alone finish the board. So the opening at e buys nothing here. Opening a wins 21 games in 22 (95.5%), opening e wins 20 in 22 (90.9%).

To see whether that holds over whole games, we played the same boards with different guessing rules. Each player is perfect at logic, guesses only when nothing is provably safe, and differs only in which square it guesses:

Win rates on 10,000 Intermediate and 10,000 Expert games, the same boards for every rule. "Opening" rows take the square most likely to open an area among those at most 2, 5 or 10 percentage points likelier to be a mine than the safest square, or, in the last row, among every covered square.

On Beginner and Intermediate the rule barely matters, because forced guesses are rare: on 20,000 Beginner games every rule won between 96.1% and 96.2%, and even going all in for openings cost Intermediate only 0.6 points. On Expert, the more risk the player accepted for an opening, the more games it lost. Going all in for openings cut wins from 49.0% to 42.5%: it survived only 73.9% of its guesses against 81.5% for the safest square, and the openings it found didn't make up for it. Using openings only to break ties, or paying a point or two for one, made no measurable difference either way.

Pro tip: Decide by the chance of a mine first. Look for an opening only among squares that are as safe as your best option.

How to use openings

1. Click the middle first. Your first click is always an opening on Poozee, and our Minesweeper 50/50 guide measured that a middle start leaves the fewest guesses later.
2. Let logic find the rest. On Expert, most of the openings you haven't found yet will open from the numbers as you work along the edges. The Minesweeper patterns are how you get there without guessing.
3. When you must guess, compare the odds. A square away from the numbers is often about as safe as anything on the board (19.8% on average on Expert), but a square next to a number can be much safer or much riskier.
4. Break ties toward openings. Among squares with the same chance of a mine, pick the one most likely to be a blank: a corner away from the numbers beats an edge, and an edge beats the middle. In our test that didn't change Expert win rates measurably, but the guesses it picked opened an area 8.1% of the time, against 4.2% for a random one of the safest squares.
5. Don't pay for an opening. If the square that might open an area is riskier than your safest choice by more than a point or two, take the safe one.

Keep playing

Try it on a real board: open Minesweeper on Expert, count the openings you find, and when you get stuck, check the odds before you reach for a corner. If you're new to the game, start with how to play Minesweeper, and when a guess comes down to two squares, our guide to Minesweeper 50/50s shows how to tell a true coin flip from a position you haven't solved yet.