What makes a dice roll "fair"
A fair die gives every face an equal chance of landing face-up — 1 in 6 for a standard cube, 1 in 20 for a D20, and so on. Physical dice can drift from that ideal over time: a chipped corner, uneven manufacturing, or a slightly warped edge all nudge the odds, which is part of why competitive tabletop players sometimes use precision-milled dice.
A digital roller sidesteps the manufacturing problem entirely by generating a random number in software rather than depending on a physical object's balance. Every roll here draws from a fresh random value each time, so past rolls have no influence on what comes next — the same logical independence a perfectly balanced physical die would have.
Odds for a single roll, by die type
For any single fair die, the probability of any one specific face is simply 1 divided by the number of sides:
| Die | Chance of any one face | Average roll |
|---|---|---|
| D4 | 25% (1 in 4) | 2.5 |
| D6 | 16.7% (1 in 6) | 3.5 |
| D8 | 12.5% (1 in 8) | 4.5 |
| D10 | 10% (1 in 10) | 5.5 |
| D12 | 8.3% (1 in 12) | 6.5 |
| D20 | 5% (1 in 20) | 10.5 |
| D100 | 1% (1 in 100) | 50.5 |
The average roll is just (sides + 1) ÷ 2 — useful for estimating expected damage or scores before you ever pick up the dice.
Why rolling multiple dice isn't flat like a single die
One die gives every outcome equal odds, but add a second die and that stops being true — because more combinations of two dice add up to the middle values than to the extremes. Two six-sided dice (2d6) is the classic example:
| Total | Ways to roll it | Probability |
|---|---|---|
| 2 or 12 | 1 | 2.8% |
| 3 or 11 | 2 | 5.6% |
| 4 or 10 | 3 | 8.3% |
| 5 or 9 | 4 | 11.1% |
| 6 or 8 | 5 | 13.9% |
| 7 | 6 | 16.7% |
Seven comes up more than any other total simply because there are six different combinations of two dice that add to it (1+6, 2+5, 3+4, 4+3, 5+2, 6+1), while only one combination makes 2 or 12. Roll more dice together and the curve gets smoother and more bell-shaped — this is the same idea behind the multiple-dice mode's statistics panel, which shows the mean, minimum, maximum, and standard deviation of whatever combination you roll.
If you want to explore that curve in more depth — probabilities, combinations, expected values — the Probability Calculator breaks down the math further.
Reading dice notation: 2d6+3 and similar
Tabletop rulebooks describe rolls in shorthand: a number, the letter "d", another number, and sometimes a modifier — for example 3d8+2. Break it into three parts:
- The first number is how many dice to roll.
- The number after "d" is how many sides each of those dice has.
- Anything after a + or − sign is a flat modifier added to (or subtracted from) the total after all the dice are added together.
So 3d8+2 means: roll three eight-sided dice, add their results together, then add 2 to the sum. The Custom Dice mode above handles exactly this pattern — set the sides, the count, and the modifier, and it computes the total the same way a game master would.
Which dice tabletop games actually use
- D20 systems (Dungeons & Dragons, Pathfinder): a single D20 resolves most actions, with D4 through D12 covering weapon and spell damage.
- Percentile rolls: often two D10s read together — one for the tens digit, one for the ones — to produce a result from 1 to 100, which is exactly what the D100 option simulates directly.
- Yahtzee and most classic board games: five or more D6s rolled at once, which the Multiple Dice mode handles by setting the count to match.
Whatever the count or die type your table uses, matching it here just means picking the right numbers rather than needing a different tool per system.