How the Dice Roll Simulator Works
I built this simulator because dice are one of the oldest and most elegant random number generators in human history — and the probability math behind them is genuinely fascinating. Whether you are rolling for a tabletop RPG, a board game, or just need a quick random number, understanding what the dice are actually doing makes the game more interesting.
For a single fair die with n sides, every face has an equal probability of 1/n. When you roll multiple dice and sum the results, the distribution changes from uniform to a bell curve shape — this is the central limit theorem in action.
- Single d6 probability per face:
1/6 ≈ 16.7% - Sum of 2d6: 7 is the most likely outcome at
6/36 ≈ 16.7% - Sum of 3d6 (classic character stats): peaks near 10–11, range 3–18
- Expected value of a dn:
(n + 1) / 2
What Dice Are Used in Tabletop Games?
Different game systems use different dice pools to achieve very different probability curves. Knowing these helps you understand why certain game mechanics feel the way they do.
- d20 (D&D ability checks): flat distribution — every result from 1–20 is equally likely, making outcomes feel swingy and dramatic
- 2d6 (Powered by the Apocalypse): bell curve centred on 7, which is why a 7–9 "partial success" is the most common result
- Percentile (d100): two d10 read as tens and units, giving exact 1% probabilities — common in WFRP and Call of Cthulhu
- 4d6 drop lowest (D&D character creation): shifts the average well above 10.5, producing heroic characters
Frequently Asked Questions
Is this truly random?
This simulator uses JavaScript's Math.random(), which is a pseudo-random number generator (PRNG). It is more than random enough for games, but it is not cryptographically secure. For true randomness in security contexts you would need a hardware random number source, but for rolling a d20 to see if you hit the dragon, it is perfectly fine.
What does "advantage" mean in dice terms?
In D&D 5e, rolling with advantage means you roll two d20s and take the higher result. This shifts the effective probability significantly upward — the expected value of the higher of two d20 rolls is approximately 13.8, compared to 10.5 for a single roll. Roll twice using this simulator and keep the best result to simulate it.
Can I use this for board games that need multiple dice?
Absolutely. Select the die type and the number of dice to roll simultaneously. The simulator will show you each individual die result as well as the total sum, making it useful for any game from Monopoly (2d6) to Yahtzee (5d6) to complex wargames with large dice pools.