What is 3BV?

Definition

3BV (pronounced "three-BV") stands for Bechtel's Board Benchmark Value, named after Nick Bechtel who introduced it to the Minesweeper community. It measures the minimum number of left-clicks required to clear a board completely — without using flags — assuming perfect play.

A higher 3BV means a harder board: more individual clicks are required even from a player who knows exactly where every mine is.

How 3BV is Calculated

Every non-mine cell on a Minesweeper board falls into one of two categories:

• Opening cells — cells with a value of 0 (no adjacent mines). Clicking any cell in a connected group of zeros reveals the entire group and all its numbered border cells in a single click. Each such connected region counts as 1 point toward 3BV, regardless of how many cells it contains.
• Isolated numbered cells — cells with a value of 1–8 that are not adjacent to any zero-cell opening. These cannot be revealed by flood-fill; each one requires its own click. Each isolated numbered cell counts as 1 point toward 3BV.

Therefore: 3BV = (number of distinct openings) + (isolated numbered cells)

Derived Metrics

3BV/s (3BV per second)

Speed metric: 3BV ÷ time_in_seconds. Measures how many "clicks worth of board" a player clears per second. The world's fastest players exceed 10 3BV/s on Expert boards.

Efficiency (%)

3BV ÷ total_clicks × 100. Measures how economically a player used their clicks. 100 % efficiency means every click contributed directly to clearing the board. Chording (revealing numbered cells via a surrounding flag cluster) can push efficiency above 100 % if done skillfully.

3BV and Board Difficulty

For a fixed board size, 3BV varies with mine count in a characteristic curve:

• Very few mines — almost all cells are zero-value openings. One click reveals nearly the entire board. 3BV ≈ 1.
• Moderate mines — the board is divided into several opening regions plus many isolated numbered cells. 3BV is highest here.
• Many mines — no opening regions form; every non-mine cell is adjacent to at least one mine. 3BV = number of non-mine cells, but there are few non-mine cells left.

The standard Beginner (9×9, 10 mines) board has an average 3BV of ~45, while Expert (16×30, 99 mines) boards average ~200–250. The maximum possible 3BV equals the number of non-mine cells — achieved when every non-mine cell is adjacent to a mine.

Topology Effects

On Cylinder boards (left↔right wrap) and Toroid boards (all-edges wrap), every cell has more neighbors. This generally increases the likelihood that zero-value openings form, which lowers 3BV compared to the same board in Standard topology — the same mines produce larger flood-fill regions. You can explore these effects in the calculator below.

Experimenting with 3BV

The best way to develop an intuition for 3BV is to design boards yourself. The Board Generator lets you place mines on a grid of any size and instantly see the resulting 3BV for Standard, Cylinder, and Toroid topologies — updating live as you add or remove mines. You can also open any generated board directly as a Mosaic puzzle or share it via the replay link.

As an example, here is a 9×9 board with 10 mines arranged to achieve the maximum possible 3BV for that mine count — every non-mine cell is adjacent to at least one mine, so there are no openings and every cell must be clicked individually:

▶ Play the maximum-3BV Beginner board (9×9, 10 mines)