Dice Roller & Probability Calculator
Roll standard dice notation with cryptographic randomness, or compute the exact probability of any dice pool.
Result
Probability distribution
Histogram
How dice notation works
Standard dice notation dates back to the earliest tabletop RPGs and is used in everything from D&D to board game rulebooks:
NdS— roll N dice with S sides.2d6rolls two six-siders.+Mor-M— add or subtract a flat modifier.1d20+5= d20 + 5.khN— keep the highest N dice.4d6kh3is the classic D&D ability score roll (roll 4, drop the lowest).klN— keep the lowest N. Used for "disadvantage" style checks.
Why probability beats intuition
People are terrible at estimating dice odds. A few facts that trip everyone up:
- 2d6 averages 7, not 6 — because the number of ways to roll 7 (six combinations) dwarfs any other sum.
- 4d6-drop-lowest averages 12.24, not 10.5 like 3d6. That's why D&D uses it — heroes are meant to be above average.
- Advantage on a d20 (2d20kh1) shifts the average from 10.5 to ~13.83 — roughly equivalent to a +3.3 bonus, but bigger when you're near the target and smaller at the extremes.
- The chance of at least one hit on 3 attacks at 65% each is 1 − 0.35³ = 95.7%. Independent chances stack quickly.
FAQ
What is dice notation?
Dice notation is a short way to write a dice roll: NdS means 'roll N dice with S sides each'. So 3d6 rolls three six-sided dice. Modifiers are added: 1d20+5 rolls a d20 and adds 5. Keep-highest is written kh (4d6kh3 = roll 4d6 and keep the highest 3, the classic D&D ability score roll).
Are the rolls truly random?
Yes — this uses the browser's crypto.getRandomValues, which produces cryptographically secure random numbers. It's far better than Math.random for anything where fairness matters. No results are ever sent to a server.
How does probability mode differ from rolling?
Rolling gives you one random result. Probability mode computes the exact distribution of every possible outcome — mean, minimum, maximum, and the chance of hitting or beating any target. Useful for RPG combat planning, board game analysis, and homework.
What sizes of dice are supported?
Any positive integer of dice and sides — d4, d6, d8, d10, d12, d20, d100, or exotic dice like d3 or d1000. The probability distribution is fast for typical dice pools (up to a few hundred dice); for anything larger it will still work but may take a moment.