How to Roll Custom Dice
Start by selecting how many dice you want to roll—anywhere from 1 to 15. Next, decide whether all dice should have the same number of sides. If they do, use the uniform dropdown to set them all at once. If you need mixed dice (for instance, rolling 2d6 alongside 1d20), select the custom option and configure each die individually.
Each die can range from 4 sides up to 120, giving you flexibility for non-standard game mechanics. Once your dice configuration is set, toggle the roll checkbox to execute the simulation. Results appear instantly with individual die outcomes and the total.
Probability and Expected Value
When rolling multiple dice, the expected value—the average outcome over many rolls—follows a predictable pattern. For a single fair die with n sides numbered 1 through n, the expected value is the sum of all possible outcomes divided by the number of sides.
Expected Value = (1 + 2 + 3 + ... + n) ÷ n = (n + 1) ÷ 2
Total Expected Value (multiple dice) = Expected Value per die × Number of dice
n— Number of sides on a single dieNumber of dice— Total count of dice being rolled
Understanding Polyhedral Dice and Geometry
Standard gaming dice correspond to Platonic solids—three-dimensional shapes where all faces are identical regular polygons and all vertices align uniformly. These geometric properties ensure fair probability distribution across outcomes.
- 4-sided (d4): Tetrahedron—four triangular faces
- 6-sided (d6): Cube—six square faces
- 8-sided (d8): Octahedron—eight triangular faces
- 12-sided (d12): Dodecahedron—twelve pentagonal faces
- 20-sided (d20): Icosahedron—twenty triangular faces
Odd-sided dice (like d10) often use prism geometry, while even-sided non-Platonic dice employ trapezohedra or dipyramids to maintain balanced probability.
Common Pitfalls When Rolling Custom Dice
Avoid these mistakes when configuring and interpreting your rolls.
- Forgetting to Toggle the Roll Checkbox — Setting up dice without activating the roll function returns no results. Always ensure the checkbox is ticked to execute the simulation. Untick it to disable rolling without losing your configuration.
- Misunderstanding Probability Skew in Unequal Dice Pools — Rolling 1d4 plus 1d20 creates an asymmetrical distribution where results cluster unevenly. The total won't follow a bell curve like rolling multiple identical dice would. Verify your mechanic design matches your intended outcome range.
- Neglecting Extreme Outliers in Small Sample Sizes — A single roll of 15d120 can produce results from 15 to 1800, but you're seeing one sample. Run dozens of rolls to understand actual frequency distributions before drawing conclusions about odds.
- Exceeding Browser Computational Limits — While the calculator supports up to 15 dice with 120 sides each, simulating extremely high-count rolls repeatedly may slow your device. Batch your rolls sensibly if testing statistical distributions.
Core Dice Sets for Tabletop Gaming
Most tabletop RPGs rely on seven standard polyhedral dice, commonly sold as a single set. These form the foundation of games like Dungeons & Dragons, Pathfinder, and countless indie RPGs:
- d4 (tetrahedron): Low-variance damage or saves
- d6 (cube): Classic six-sided die, base mechanic
- d8 (octahedron): Medium damage rolls
- d10 (prism): Percentile mechanics when paired with d100
- d12 (dodecahedron): Higher damage scaling
- d20 (icosahedron): Primary mechanic for attack rolls and checks
- d100 (percentile die): Percentage-based skill resolution
This calculator extends beyond standard sets, letting you experiment with non-traditional dice counts and sizes for custom rule systems.