Dice Probability Explained: d4 to d20

One die: every face is equally likely

A fair die with N sides gives each number a 1 in N chance. On a d6 that is 1/6 (about 16.7%); on a d20 it is 1/20 (5%).

The average roll of one die is (1 + N) ÷ 2: 3.5 for a d6, 10.5 for a d20.

Two dice: the middle is most common

Two d6 have 36 equally likely combinations. A total of 7 can be made six ways (1+6, 2+5, 3+4, 4+3, 5+2, 6+1), so its chance is 6/36 = 1/6. A total of 2 or 12 can be made only one way each, so it is 1/36.

The more dice you add, the more the totals bunch around the average — which is why 3d6 rarely rolls an 18.

The common dice and what they're used for

Tabletop games use a standard set:

• d4 and d6 — small damage rolls and board games
• d8, d10 and d12 — larger damage rolls; two d10 can make a percentile roll
• d20 — the main roll in many role-playing games

Past rolls don't change the next one

Rolling three 1s in a row does not make a 6 'due'. Each roll is independent, so the odds reset every time. Streaks are a normal part of randomness.

Rolling online

Pick a die type, choose how many dice (up to 20), and press Roll. The roller shows each die and the total.

It uses your browser's standard random function — fine for games and practice, but not certified for gambling or prize draws.