Dice Roller | D4 to D100 with Advantage

Roll any combination of dice including D4, D6, D8, D12, D20, D100, or fully custom sides. Supports advantage, disadvantage, drop-lowest, modifiers, probability distribution charts, and full roll history.

Quick Presets

Die type

Quantity

Sides (dN)

Modifier (+/−)

Roll mode

R or Space = roll · Esc = reset

What Is the Dice Roller | D4 to D100 with Advantage?

Every die is a physical random number generator. A fair n-sided die(denoted dN or DiceN) produces each integer from 1 to n with equal probability 1/n. This is the discrete uniform distribution, no outcome is more likely than any other.

When you roll multiple dice and sum the results, the distribution of outcomes is no longer flat. Rolling 2d6 gives 36 equally likely combinations, but they do not map uniformly to the 11 possible sums (2–12). Sums near the middle (7) can be made many more ways than extreme values (2 or 12). More dice means a more pronounced bell shape, this is the Central Limit Theorem at work.

Advantage and disadvantage (introduced in D&D 5th Edition) change the effective probability curve dramatically. Rolling 2d20 and keeping the highest shifts the average from 10.5 to approximately 13.8, a +3.3 effective bonus. Disadvantage (keep lowest) drops it to 7.2, roughly a −3.3 penalty. These are not linear modifiers; they compress the distribution toward the middle.

Formula

Dice Probability Formulas

Single Die, Uniform Distribution

P(X = k) = 1/n for k ∈ {1, 2, …, n}

E[X] = (n + 1) / 2 (expected value)

Var(X) = (n² − 1) / 12 (variance)

Every face is equally likely, this is a discrete uniform distribution.

Multiple Dice, Sum Distribution

E[X₁ + X₂ + … + Xₘ] = m · (n + 1) / 2

Var(sum) = m · (n² − 1) / 12

The sum of m independent d-n dice has mean m(n+1)/2. By the Central Limit Theorem, the distribution becomes bell-shaped as m grows.

Advantage / Disadvantage (D&D 5e)

P(max(X₁,X₂) ≤ k) = (k/n)² (advantage CDF)

E[max(X₁,X₂)] = (2n+1)/3 (advantage mean ≈ 13.8 for d20)

E[min(X₁,X₂)] = (n+2)/3 (disadvantage mean ≈ 7.2 for d20)

Rolling with advantage is roughly equivalent to a +3.3 bonus on a d20.

Die	Sides (n)	Min	Max	Expected value	Std deviation
D4	4	1	4	2.5	1.12
D6	6	1	6	3.5	1.71
D8	8	1	8	4.5	2.29
D10	10	1	10	5.5	2.87
D12	12	1	12	6.5	3.45
D20	20	1	20	10.5	5.77
D100	100	1	100	50.5	28.87

How to Use

1Select the die type: Click D4, D6, D8, D10, D12, D20, or D100, or type any number of sides in the Sides field. Supports any custom die from D2 to D1000.
2Set quantity and modifier: Enter how many dice to roll (1–20) and an optional flat modifier to add or subtract from the total.
3Choose a roll mode: Normal = standard roll. Advantage = 2d20 keep highest. Disadvantage = 2d20 keep lowest. Drop Lowest = rolls your dice and discards the smallest (classic for D&D ability scores).
4Roll: Click the Roll button or press R or Space. Each die shows its individual face value; the total, percentile, and stats update instantly.
5Read the results: The result box shows each die face, the total (including modifier), min/max/expected values, and your roll's percentile within the distribution.
6Check the distribution chart: The bar chart shows the probability of every possible sum for your configuration. The highlighted bar is your current roll.
7Review history: The last 12 rolls are listed. Click Clear to wipe the history or Reset to start completely fresh.

Example Calculation

Example 1, D&D Attack Roll (1d20 + 5)

›Select D20, Quantity 1, Modifier +5. Click Roll.
›If the die shows 14, total = 14 + 5 = 19.
›To hit Armour Class 15 you need a total of 15 or more, a roll of 10+ on the die succeeds.
›Probability of hitting AC 15 = P(d20 ≥ 10) = 11/20 = 55%.
›Switch to Advantage mode to roll 2d20 and keep the higher, now P(hitting AC 15) rises to ~79.75%.
›Natural 20 regardless of modifier = Critical Hit. Natural 1 = Critical Fail (automatic miss).

Example 2, D&D Ability Score Generation (4d6 Drop Lowest)

›The classic method: roll 4d6 and discard the lowest die, then sum the remaining three.
›Select D6, Quantity 4, mode "Drop Lowest". Click Roll.
›Example roll: [6, 4, 1, 3] → drop 1 → 6+4+3 = 13.
›Possible range: 3 (rolling 1,1,1,1 then dropping one 1) to 18 (rolling three 6s).
›The expected value of 4d6dl1 ≈ 12.24, compared to 10.5 for a straight 3d6.
›Repeat 6 times to generate a full set of ability scores for STR, DEX, CON, INT, WIS, CHA.

Example 3, Board Game Damage (2d6 + 3)

›Select D6, Quantity 2, Modifier +3. Click Roll.
›Minimum damage: 1+1+3 = 5. Maximum: 6+6+3 = 15. Expected: 7+3 = 10.
›The most likely single result is 10 (7 on 2d6 is the most probable sum).
›P(total ≥ 12) = P(2d6 ≥ 9) = 10/36 ≈ 27.8%, roughly a 1-in-4 chance.
›The distribution chart immediately shows the bell curve centred around 10.
›Useful for Catan resource trades, Axis & Allies combat, or any game using 2d6 with a modifier.

Understanding Dice Roller | D4 to D100 with Advantage

Probability Quick Reference, Common Rolls

Roll	Range	Expected	Common use
1d4	1–4	2.5	Dagger, magic missile, D&D cantrip
1d6	1–6	3.5	Shortsword, fireball (×8), Catan production
2d6	2–12	7.0	Greatsword damage, Risk battle, Monopoly move
3d6	3–18	10.5	Traditional D&D ability score method
4d6dl1	3–18	12.2	D&D 5e ability score generation (drop lowest)
1d8	1–8	4.5	Longsword, D&D cleric/druid hit die
1d10	1–10	5.5	Halberd, ranger hit die
1d12	1–12	6.5	Greataxe, barbarian hit die
1d20	1–20	10.5	D&D attack roll, saving throw, skill check
2d20 adv	1–20	13.8	D&D advantage, roll 2d20 keep highest
2d20 dis	1–20	7.2	D&D disadvantage, roll 2d20 keep lowest
1d100	1–100	50.5	Percentile rolls, wild magic tables, random events

Popular Dice Combinations by Game

›Dungeons & Dragons 5e: Uses the full polyhedral set (D4, D6, D8, D10, D12, D20, D100). The D20 drives the core resolution mechanic, roll + ability modifier vs a Difficulty Class (DC).
›Pathfinder 2e: Same polyhedral set as D&D. Uses three degrees of success, critical success (beat DC by 10+), success, failure, critical failure (miss by 10+).
›Catan (Settlers): 2d6 for resource production. The 7 is the robber trigger, and it is the most probable sum (6/36 ≈ 16.7%). Good Catan strategy accounts for the bell curve.
›Risk: Attacker rolls up to 3d6, defender rolls up to 2d6. Both sides take the highest die and compare, the higher wins, with ties going to the defender.
›Yahtzee: Five D6s, rerolled in combinations. The full house, large straight, and Yahtzee (five of a kind) all have calculable probabilities using combinations.
›Shadowrun / World of Darkness: These systems roll pools of D6s or D10s and count successes (results ≥ threshold), not sums. The distribution of successes follows a binomial distribution.

Frequently Asked Questions

What does "NdS" or "3d6" mean in dice notation?

›"NdS" is standard tabletop dice notation: N = number of dice, S = number of sides.
›"3d6" means roll three 6-sided dice and sum the results. Range: 3 to 18, expected: 10.5.
›"1d20+5" means roll one 20-sided die and add 5. Used for attack rolls and skill checks in D&D.
›The "d" stands for "die" or "dice". It originates from wargaming notation in the 1970s.
›Common shorthand: "a D20" refers to the die type; "1d20" refers to a single roll of that die.

What are the standard dice used in tabletop roleplaying games?

›D4 (tetrahedron): used for daggers, magic missiles, and small weapon damage.
›D6 (cube): the most familiar die; used in Dungeons & Dragons, Catan, Yahtzee, and most board games.
›D8 (octahedron): used for longswords, hit dice for clerics and rangers in D&D.
›D10 (pentagonal trapezohedron): used for damage rolls and percentile dice (two D10s = D100).
›D12 (dodecahedron): used for greataxe damage and barbarian hit dice in D&D.
›D20 (icosahedron): the signature die of D&D, used for all attack rolls, saving throws, and skill checks.
›D100 (percentile): two D10s (one tens digit, one units digit) generate 1–100. Used for wild magic surges, random tables.

How does advantage and disadvantage work in D&D 5e?

›Advantage: roll 2d20, take the higher. This significantly improves your chance of success.
›Disadvantage: roll 2d20, take the lower. This significantly hurts your chance of success.
›Average with advantage: ~13.83. Average with disadvantage: ~7.17. Normal d20 average: 10.5.
›Advantage is roughly equivalent to a +3.3 flat bonus for most target numbers.
›Multiple sources of advantage don't stack, you still roll 2d20. Same for disadvantage.
›Advantage and disadvantage cancel each other out exactly, no matter how many sources you have.

Why does rolling more dice create a bell curve?

›A single die produces a flat, uniform distribution, every result equally likely.
›When you sum two dice, there are more ways to make a middle value than an extreme one.
›For 2d6: there is only 1 way to roll 2 (two 1s) but 6 ways to roll 7, making 7 six times more likely than 2.
›With more dice, the distribution approaches a normal (Gaussian) bell curve. This is the Central Limit Theorem.
›4d6 drop lowest generates ability scores that cluster between 10–14, rarely reaching 3 or 18.
›This is why high-level D&D damage rolls (e.g., 8d6 for a fireball) are fairly predictable, rarely landing near extremes.

What is a critical hit and critical fail on a D20?

›Natural 20 (rolling a 20 on the die itself, before modifiers) = critical hit in D&D.
›On a critical hit, most damage dice are doubled, roll all damage dice twice.
›Natural 1 (rolling a 1) = critical fail, automatic miss regardless of modifiers.
›These rules only apply to attack rolls in most D&D editions, not to skill checks by default.
›Some house rules extend critical success/fail to skill checks (e.g., a 20 always succeeds, a 1 always fails).
›Probability of a natural 20 = 1/20 = 5%. You should see one roughly every 20 attacks on average.

How do flat modifiers affect dice rolls?

›A flat modifier shifts the entire distribution up or down by a fixed amount.
›It does not change the shape of the distribution, it just moves the centre.
›Example: 1d20+5 has range 6–25 and expected value 15.5 vs 1–20 and 10.5 for bare 1d20.
›In D&D, modifiers come from ability scores, proficiency bonus, magical items, and spells.
›A +1 modifier always provides exactly +1 to every possible outcome, it is a simple linear shift.
›Compare this to advantage, which reshapes the distribution non-linearly.

Can I use this for non-RPG purposes?

›Yes, virtual dice are useful for any game or randomisation task.
›Board games: Catan (2d6), Monopoly (2d6), Risk (d6 battles), Backgammon (2d6).
›Teaching probability: use the distribution chart to demonstrate the Central Limit Theorem visually.
›Decision making: roll a die to randomly pick from N options (use a custom dN die).
›Party games: "Spin the die" for choosing tasks, dares, or trivia categories.
›Game design: prototype new games using custom dice (D3, D7, D13) not available physically.

Is the random number generator truly random?

›This roller uses JavaScript's Math.random(), which is a pseudo-random number generator (PRNG).
›It uses the Xorshift128+ or similar algorithm, seeded from system entropy at startup.
›For all practical purposes, games, teaching, decision-making, it is indistinguishable from true randomness.
›True randomness (hardware entropy) is only meaningful for cryptographic uses. For dice rolling, PRNG is perfectly sufficient.
›Each roll is independent of the last, the die has no "memory" of previous results (the gambler's fallacy).
›If you need cryptographically secure randomness, use the Web Crypto API, but this is unnecessary for games.

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