Dice Roller

Tabletop dice notation compresses a complete rolling instruction into a short expression. In 2d6+3, the first number is the number of dice, the number after d is the number of faces on each die, and the final modifier is added after the dice are resolved.

Keep and drop rules make the instruction richer. 4d6kh3 rolls four six-sided dice and keeps the three highest die totals. 8d10dl2-1 rolls eight ten-sided dice, drops the two lowest totals, then subtracts one. Advantage or disadvantage is different: the whole expression is evaluated twice, and the higher or lower final total is selected.

Reroll

Replace an original low face once when it is at or below a chosen threshold.

Explosion

Add another face when the current face matches the trigger, continuing while the trigger repeats.

Seed

Text that initializes a deterministic sequence so the same configuration can be replayed.

Simulation

One complete evaluation of the configured expression for estimating an outcome distribution.

A single roll answers what happened now. Repeating the same expression many times answers a different question: how often each total appeared under that configuration. The observed success rate becomes more stable with more simulations, but it remains an estimate from one generated sample and cannot promise the next outcome.

Fair face selection means every integer from 1 through the die’s side count has equal chance on each draw. The draws use replacement, so rolling a six does not make the next six more or less likely. Keep/drop, reroll, explosion, and advantage rules deliberately reshape the final-total distribution even though each underlying face draw stays uniform.

Random dice are suitable for games, teaching, probability practice, and informal design checks. They carry no monetary value and are not a certified draw for wagering, regulated prizes, cryptographic secrets, or decisions that require independent audit and participant verification.

How to Use This Tool:

Enter the dice rule first, then decide whether you need one outcome, an estimated distribution, or a repeatable sequence.

1. Choose a Preset or enter a Roll expression such as d20, 2d6+3, or 4d6kh3.
2. Select Single roll, Advantage, or Disadvantage. The latter two evaluate the complete expression twice before selecting a total.
3. Open Advanced only when needed. Set 1 to 5,000 simulations, an optional target comparison, one-time low-face rerolls, exploding dice, or a seeded sequence.
4. Roll the dice and inspect the total. Use the roll trace when keep/drop, reroll, or explosion rules make the result hard to explain, and read the distribution against the actual simulation count.

Interpreting Results:

The latest total already includes the selected keep/drop rule, modifier, rerolls, explosions, and roll mode. When a target is present, the latest Pass or Miss applies only to that selected total.

The success percentage covers every completed simulation and uses the chosen comparison operator exactly. For example, ≥ 15 includes 15 while > 15 does not. A seeded rerun is comparable only when the expression, modes, thresholds, target, simulation count, and seed all stay unchanged.

Technical Details:

Valid notation contains one dice term with 1 to 2,000 dice and 2 to 100,000 sides. It may include one kh, kl, dh, or dl rule and one signed integer modifier from −10,000,000 to 10,000,000. A drop rule must leave at least one die.

Rule Core:

Each random sample u lies from 0 inclusive to 1 exclusive. A face is selected by taking the integer part of u × sides and adding 1, giving every supported face the same interval width.

1. Draw the original face for each die.
2. If that face is at or below the reroll threshold, draw once more and discard the original face from the die total.
3. If the current face equals the explosion trigger, keep drawing and adding faces until a different face appears or the per-die explosion limit is reached.
4. Apply keep/drop to the completed die totals, not merely the last visible faces.
5. Add the kept die totals and the signed modifier. For advantage or disadvantage, repeat all prior steps and select the higher or lower complete total.

Formula Core:

When a target is supplied, the empirical success rate is the number of simulated totals satisfying the exact operator divided by the number of simulations.

No target leaves success count and rate at zero because no pass/fail question was asked. That zero must not be read as a measured 0% chance.

System mode requests unsigned 32-bit values from the browser’s cryptographic random generator when available, then maps them uniformly to faces. If that interface is unavailable, it falls back to the browser’s ordinary pseudorandom generator. Seeded mode hashes the seed into a 32-bit starting state and uses a deterministic Mulberry32 sequence; it is intended for reproducibility, not secrecy.

Work is bounded to 250,000 face operations, including additional reroll and explosion draws. Each original die may explode at most 100 times, and the base dice count multiplied by simulations and the one- or two-expression roll mode must fit the same workload ceiling.

Limitations and Fairness Notes:

• An observed distribution is not the exact mathematical probability distribution, especially with few simulations or rare exploding chains.
• Seeded sequences are predictable and should never be used for security, wagering, or adversarial draws.
• System mode depends on the browser environment and can fall back to non-cryptographic randomness when the stronger interface is unavailable.
• Roll settings and the session log stay in the current browser session; no remote draw service certifies the outcomes.

Worked Examples:

References:

• Web Cryptography Level 2, getRandomValues method, World Wide Web Consortium.