Dice Roller

How Dice Rolling Works

A dice roller is a tool that simulates the random outcome of throwing polyhedral dice, generating a uniformly distributed integer from 1 to the number of faces. Dice have been used for games and decision-making for over 5,000 years — the oldest known dice, dating to approximately 3000 BCE, were found in southeastern Iran. Modern tabletop role-playing games like Dungeons & Dragons (D&D), first published by TSR in 1974, popularized the use of polyhedral dice beyond the standard six-sided cube.

The standard RPG dice set includes seven shapes: d4, d6, d8, d10, d12, d20, and d100. Each corresponds to a Platonic solid or related polyhedron. The d20 is the most iconic, used for attack rolls, ability checks, and saving throws in D&D 5th Edition. This digital roller uses a pseudorandom number generator to ensure perfectly uniform probability — each face has an exactly equal chance of appearing.

How Dice Notation Works

Standard dice notation follows the format NdS+M, where N is the number of dice, S is the number of sides, and M is an optional modifier. The formula for the result is:

Result = (sum of N rolls, each 1 to S) + M

Each variable is defined as follows:

• N (number of dice): How many dice to roll. "2d6" means roll two six-sided dice.
• S (sides): The number of faces on each die. Standard options are 4, 6, 8, 10, 12, 20, and 100.
• M (modifier): A fixed bonus or penalty added to the total. "+5" means add 5 after summing the dice.

Worked example: Rolling 2d6+3 with results of 4 and 5. Subtotal = 4 + 5 = 9. Modifier = +3. Grand total = 12. This notation originated with D&D and is now universally used across tabletop RPGs and game design.

Key Terms You Should Know

• Natural 20 (nat 20): Rolling a 20 on a d20 before modifiers. In D&D 5e, a natural 20 on an attack roll is an automatic critical hit, dealing double damage dice.
• Critical failure (nat 1): Rolling a 1 on a d20. In D&D, this is an automatic miss on attack rolls regardless of modifiers.
• Advantage/Disadvantage: Rolling 2d20 and taking the higher (advantage) or lower (disadvantage) result. Statistically shifts the average by about +3.33 or -3.33.
• Percentile dice (d100): Two d10s rolled together to generate 01-100. Used for random tables, loot generation, and percentage-based systems.
• Exploding dice: A mechanic where rolling the maximum value lets you roll again and add. Used in systems like Savage Worlds and Shadowrun.

Dice Probability Reference

Understanding dice probabilities helps players evaluate risk. The average roll for any single die is (max + 1) / 2. For multiple dice, the distribution forms a bell curve centered on N × (S + 1) / 2. According to AnyDice, a widely used dice probability tool, the following statistics apply:

Practical Examples

Example 1 — D&D attack roll: A level 5 fighter with +7 to hit rolls 1d20+7 against an enemy with AC 16. The d20 shows 11. Total = 11 + 7 = 18, which beats AC 16. The attack hits. For damage, the fighter rolls 1d8+4 (longsword + Strength) and gets 6 + 4 = 10 damage.

Example 2 — Fireball damage in D&D: A wizard casts fireball, dealing 8d6 fire damage. Rolling 8d6 gives 3, 5, 2, 6, 4, 1, 5, 3 = 29 damage. The average for 8d6 is 28, so this is a slightly above-average roll. Targets make a Dexterity saving throw for half damage. Use our probability calculator to check the odds of beating specific DCs.

Example 3 — Board game turn: In Monopoly, you roll 2d6 to move. Results of 4 and 4 (doubles) mean you move 8 spaces and roll again. The most common total is 7 (16.67% probability), which is why properties 7 spaces from "Go to Jail" (like the orange properties) get landed on most frequently. Use our statistics calculator to analyze roll distributions.

Tips for Tabletop Gaming

• Use advantage strategically: In D&D, advantage increases your chance of rolling 15+ from 30% to 51%. Seek advantage through flanking, the Help action, or class features like Reckless Attack.
• Know your average damage: When choosing between weapons, compare average damage. A greatsword (2d6+mod) averages 7+mod, while a greataxe (1d12+mod) averages 6.5+mod. The greatsword is statistically better in most situations.
• Save modifiers for key rolls: Abilities that add to rolls (like Bardic Inspiration) are most valuable when the target DC is close to your base roll average. Adding 1d8 to a d20 roll increases success probability most when you need 9-16 to succeed.
• Use digital rollers for speed: Rolling 8d6 for fireball or 10d10 for meteor swarm is slow with physical dice. Digital rollers calculate instantly and maintain accuracy over large numbers of dice.
• Track roll history: Use the history feature to settle disputes about previous rolls. Some groups also use roll history to detect suspiciously lucky physical dice that may need to be tested for bias.