Dice Roller
Roll fair virtual dice — a single d6, 2d6 for board games, or a d20 with a modifier for tabletop RPGs. Then simulate thousands of rolls to see how the observed totals line up with the exact probabilities.
Simulate Many Rolls vs. Exact Odds
Rolls 2d6 repeatedly and compares the share of each total with its exact probability.
Related Calculators
Dice Probability Calculator
Find exact odds of rolling a dice sum exactly, at least, or at most a target value.
Random Number Generator
Generate true-random integers or decimals in any range, with or without repeats, and sort or copy the results.
Expected Value Calculator
Calculate E(X), variance, and standard deviation of a discrete random variable.
Learn More
Central Limit Theorem
Learn why sample means become normally distributed, how standard error shrinks with sample size, and where the theorem powers everyday inference.
Expected Value Explained
The probability-weighted average behind every gamble: worked raffle, dice, and insurance examples, the law of large numbers, and where EV alone falls short.
Dice Notation Explained
Games write dice as NdS+M: roll N dice with S sides each and add the modifier M. So 2d6 means two six-sided dice, 1d20+5 means one twenty-sided die plus 5, and 3d8−2 means three eight-sided dice minus 2. The roller above accepts every standard polyhedral die — d4, d6, d8, d10, d12, d20, and d100 (percentile dice).
Average of NdS+M = N × (S + 1) / 2 + M
Minimum = N + M, Maximum = N × S + M
Variance of NdS = N × (S² − 1) / 12
Worked Example: Why 7 Is the Most Common Roll of 2d6
Two six-sided dice produce 6 × 6 = 36 equally likely ordered outcomes.
- A total of 2 needs (1,1) — 1 way, so P(2) = 1/36 ≈ 2.78%.
- A total of 7 comes from (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) — 6 ways.
- P(7) = 6/36 = 1/6 ≈ 16.67%, the highest of any total.
- The average is 2 × (6 + 1) / 2 = 7, matching the peak.
Run the simulation with 2d6 and 10,000 rolls: the share of 7s typically lands within about a percentage point of 16.67%. Adding more dice makes the distribution look more and more like a bell curve — the central limit theorem in action.
Are Virtual Dice Fair?
Each face is drawn with crypto.getRandomValues() using rejection sampling, so every face of every die has exactly equal probability and rolls are independent. Physical dice, especially cheap ones with drilled pips and rounded edges, are often measurably biased. For exact probabilities of reaching a target — like at least 15 on 3d6 — use the dice probability calculator.
Frequently Asked Questions
How do I roll a d20 online?
Set the number of dice to 1 and choose d20, or tap the 1d20 shortcut, then press Roll. Add a modifier such as +5 for an attack roll; the total already includes it.
What is the probability of rolling a natural 20?
1/20, or 5%, on a single d20 roll. With advantage (rolling twice and keeping the higher), the chance of at least one 20 rises to 1 − (19/20)² = 9.75%.
What is the most likely total with two dice?
7, with probability 6/36 ≈ 16.7%. Totals of 2 and 12 are the least likely at 1/36 each. Use the simulation panel to see the full triangular distribution.
Is this dice roller random enough for games?
Yes. It uses the browser's cryptographically secure random generator with rejection sampling to avoid modulo bias, which makes it fairer than most physical dice.
Why do simulated results differ from the exact probabilities?
Any finite number of rolls fluctuates around the true probabilities. The gap shrinks roughly in proportion to 1/√(number of rolls), so 100,000 simulated rolls track the exact column far more closely than 100 do.
Embed This Calculator
Add this free calculator to your course page or LMS.
Adjust the height value to fit your page.