Random Dice Roller

A random dice roller simulates any pool of polyhedral dice: the d4, d6, d8, d10, d12, and d20 of tabletop games, the percentile d100, or a custom die with anywhere from 2 to 1000 sides. Each die lands on a whole number from 1 to its number of sides with equal chance. The values come from the browser's pseudo-random number generator, which is uniform enough for games and classroom work but is not a cryptographic source.

A roll follows standard dice notation, NdS+M: N dice with S sides each, plus a flat modifier M that may be negative. 3d8+2 means three eight-sided dice summed, then 2 added; 1d20-1 means one twenty-sided die minus 1. The number of dice runs from 1 to 100, and up to 100 separate rolls can be produced in one batch, each listed with its own expression and total. A custom die count above 1000 sides is held at 1000, and the expression shown with each result always names the die that was actually rolled.

The total of NdS+M ranges from N + M to N x S + M, and its average over many rolls is N x (S + 1) / 2 + M, because one die averages (S + 1) / 2. Every individual die is listed next to the total, so mechanics the roller does not perform itself, such as dropping the lowest die or counting dice that beat a target number, can still be read off the values. The statistics summarize the stored history of up to 100 rolls: how many rolls are recorded, the average total, and the lowest and highest totals seen. Settings can hide the individual dice, the history, or the statistics without discarding anything.

The running average converges on the expected value only over many rolls; ten rolls of 2d6 can easily average 5 or 9. Mixing different expressions in one history blends their totals, so the average of a d4 roll and a d20 roll describes neither die, and clearing the history between experiments keeps the statistics meaningful.

3d8+2 ranges from 3 + 2 = 5 to 24 + 2 = 26, with an expected total of 3 x 4.5 + 2 = 15.5. 2d6 has 36 equally likely pairs; its expected total is 2 x 3.5 = 7, and 7 is also the most frequent single result at 6 of 36.

Polyhedral dice appear across tabletop games, classroom exercises, decision-making, and creative projects. A configurable roller that handles any die type and keeps a record of results replaces a bag of physical dice and several single-purpose apps.

• Tabletop RPGs: Roll 2d6+3 for a Powered by the Apocalypse move, 4d6 for an ability score with the lowest of the four listed dice set aside, or 8d6 for a high-level fireball. Weapons and spells that call for d4, d8, d10, d12, and d20 pools all come from the same roller.
• Board Games: Replace lost or missing dice by rolling any standard size. The history settles disputes about lucky streaks across several turns.
• Classroom Probability: A hundred rolls in one batch show the average settling toward the expected value: 3.5 for 1d6, 5.5 for 1d10, and 10.5 for 1d20. Comparing a single die with a sum of dice illustrates uniform versus summed outcomes.
• Decision Making: Assign options to numbered outcomes and roll a die with matching sides to pick at random. A d20 handles up to twenty choices; the custom die extends to 1000.
• Game Design Prototyping: Test damage curves and encounter balance by rolling large pools with modifiers. The minimum and maximum across a session reveal extreme outcomes that could break gameplay.
• Creative Writing Prompts: Map plot elements, character traits, or settings to die faces and roll to generate random story seeds. Combining several dice types layers the randomization.
• Wargaming: Roll large pools of d6 for attack and defense resolution. The history log lets players verify contested rolls after the fact.
• Party Games: Settle disputes, assign tasks, or hand out forfeits with a quick roll visible to everyone on a shared screen.