Dice Roller

One die is flat. Two are not.

A single six-sided die is uniform: every face has exactly a one-in-six chance. Add a second and that stops being true of the total.

There is only one way to roll 2 — both dice showing 1. There are six ways to roll 7: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1. So 7 comes up six times as often as 2.

With two dice the distribution is a triangle, peaking at 7. With three or more it starts to look like a bell curve, which is the central limit theorem showing up in a board game.

What that means in practice

• In backgammon and Monopoly, the middle numbers dominate. Properties six or eight squares from a common starting point get landed on most.
• Rolling 3d6 for a character statistic gives 10 or 11 about a quarter of the time, and an 18 once in 216 rolls.
• 2d6 and 1d12 are not the same. Both span 2–12, but one is flat and the other is peaked. Any game that treats them interchangeably is broken.

The d20, and why it feels swingy

A twenty-sided die is uniform, which is exactly why single-d20 systems feel so random. A +2 bonus is a 10 % shift, and skill moves the odds far less than the die does. Systems that roll several dice and sum them feel more consistent, because the total clusters.

Physical dice are not perfectly fair

Standard moulded dice have hollowed pips, so the 6 face is very slightly lighter than the 1 — which biases them a little towards 6. Casino dice are made with flush, density-matched inlays and sharp edges for exactly this reason, and they are replaced frequently as they wear.

A digital roll has none of these problems, and none of the satisfaction.

Common uses

• Tabletop games when the dice are lost.
• Board games on a train.
• Teaching probability, where rolling a hundred times and watching the shape appear is more convincing than any explanation.
• Settling something quickly.

Questions people ask

Why is 7 the most common roll with two dice?

Because there are six ways to make it and only one way to make 2. The total of two dice forms a triangle peaking at 7.

Is 2d6 the same as 1d12?

No. Both cover 2–12, but 1d12 is flat and 2d6 peaks in the middle. Treating them as equivalent breaks a game's maths.

Are physical dice fair?

Not quite. Hollowed pips make the 6 face lighter, biasing standard dice slightly. Casino dice use flush, density-matched inlays.

Why does a d20 feel so swingy?

Because it is uniform. Every result is equally likely, so the die dominates over modifiers. Summing several dice clusters the total.

What does 3d6+2 mean?

Roll three six-sided dice, add them together, then add two. Set the boxes above to 3, 6 and 2.

Where the randomness comes from

Every result on these pages uses crypto.getRandomValues, your browser's cryptographically secure random generator, seeded by the operating system from genuinely unpredictable physical sources.

That is deliberately not Math.random(), which most tools use. Math.random is a deterministic algorithm producing numbers that look random; given enough output, its future values can be predicted. For a dice game that does not matter. For a prize draw, a password or anything anyone might want to game, it does.

The numbers are also produced by rejection sampling rather than by taking a remainder. Taking a random 32-bit number modulo 6 slightly favours the lower faces, because 2³² does not divide evenly by 6. The bias is small and it is real, and discarding the leftover tail removes it completely.

Nothing leaves the page

Results are generated in your browser and are not transmitted or stored. Reload the page and they are gone — which matters most on the password generator.