Monte Carlo check
Run the probability-lab expression many times with the same secure random source and compare the observed event rate.
—No simulation yet.
ROLL · BUILD · UNDERSTAND
Dice Roller
Roll one die, a mixed tabletop pool, or full RPG notation. Results use browser Web Crypto with rejection sampling, and the probability lab shows what the same roll should do in theory.
d4→d100plus custom dice
Web Cryptobias-safe mapping
localno account
ROLL WORKBENCH
Build a roll your way
RPG NOTATION
R = rollType the whole roll
Examples: 1d20+5, 2d6+1d8+3, 2d20kh1, 4d6kh3, 4d6dl1. Use kh/kl to keep or dh/dl to drop.
MIXED DICE POOL
Tap dice to build a pool
Pool is empty. Tap a die above.
ROLL BREAKDOWN
Every die, including discarded dice
Your dice will appear here.
EXACT PROBABILITY LAB
Know the odds before you roll
For ordinary dice sums, compute the exact discrete distribution instead of estimating it.
PROBABILITY58.333%21 / 36 for 2d6 ≥ 7
EXPECTED TOTAL7range 2–12
MOST LIKELY716.667%
Exact distribution currently supports additive/subtractive dice groups and flat modifiers without keep/drop operators, with a bounded state range for browser safety.
SIMULATION & FAIRNESS
Compare theory with repeated rolls
Single-die fairness snapshot
Roll one selected die 5,000 times and inspect its frequency spread and χ² snapshot. Random samples will never be perfectly flat.
—No fairness sample yet.
DAILY DICE MATH
One probability question per UTC day
This is a deterministic learning puzzle, not a random roll.
TODAY'S ROLL—
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Choose an answer.
ROLL HISTORY
Keep the last 30 rolls in this browser
No rolls yet.
DICE NOTATION GUIDE
Read the expression before the dice hit the table
Count · sides · modifier
Roll two six-sided dice, add their faces, then add 3. The possible total is 5 through 15.
Keep highest
Roll two d20s and keep the higher result. This is the familiar advantage pattern. kl1 keeps the lower.
Drop lowest
Roll four d6s, discard the lowest, and total the other three. dh1 drops the highest instead.
Fair mapping matters
Each face is chosen with rejection sampling from crypto.getRandomValues(), avoiding simple modulo bias when the number of sides does not divide the raw integer range.
Randomness method, scope & limitations
Secure browser randomness
Actual rolls use crypto.getRandomValues(). The mapper rejects the small tail of 32-bit values that would make a plain remainder uneven, then maps the accepted value to a die face.
No silent fallback
If Web Crypto is unavailable, rolling is disabled instead of silently switching to Math.random().
Probability lab
The exact lab uses discrete convolution for ordinary additive dice expressions. Keep/drop notation can still be rolled, but is intentionally excluded from the exact-distribution calculator on this version so the page does not pretend to solve a different sample space.
Scope
This is a local dice and probability tool for tabletop games, classrooms, practice, and everyday random decisions. It is not an audited physical random-number source and is not intended for gambling, regulated drawings, cryptographic key generation, or other high-stakes outcomes.