Dice Roller
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A dice roller simulates rolling one or more dice with any number of sides — standard d6, or polyhedral dice (d4, d8, d10, d12, d20, d100) used in tabletop RPGs. Results follow a uniform distribution (equally likely outcomes) for a single die.
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Tip: For probability: P(rolling at least N on a d20) = (20 − N + 1) / 20. Rolling a 15 or higher: (20−15+1)/20 = 6/20 = 30% chance.
- 1Rolling 1 die: each face has 1/n probability
- 2Rolling multiple dice: sum follows a bell curve (central limit theorem)
- 3Notation: 2d6 = roll two 6-sided dice and sum them
- 4Average of nd6 = n × 3.5 (average of one d6)
| Die | Sides | Range | Average | Common use |
|---|---|---|---|---|
| d4 | 4 | 1–4 | 2.5 | Damage (small weapons) |
| d6 | 6 | 1–6 | 3.5 | Most common die |
| d8 | 8 | 1–8 | 4.5 | Longsword damage |
| d10 | 10 | 1–10 | 5.5 | Percentile (with d%) |
| d12 | 12 | 1–12 | 6.5 | Great axe damage |
| d20 | 20 | 1–20 | 10.5 | D&D attack rolls |
| d100 | 100 | 1–100 | 50.5 | Percentile rolls |
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Fun Fact
The d20 is one of the oldest gaming implements — icosahedral (20-sided) dice carved from serpentine stone have been found in Egypt dating to 304–30 BCE. Dungeons & Dragons popularized the d20 system in 1974.
References
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