Roll any dice configuration from d2 to d1000 with modifiers, keep modes, exploding dice, and minimum face values. Full statistical analysis and frequency charts.
Not every situation calls for standard polyhedral dice. Sometimes you need a d7, a d30, or even a d100. Maybe you're designing a custom RPG system, running a probability experiment, or simulating events with non-standard outcomes. The Custom Dice Roller handles any configuration from d2 to d1000 with any number of dice.
Beyond basic rolling, this tool supports modifiers, keep-highest/lowest mechanics, exploding dice (reroll on max), and adjustable minimum face values (so you can create d6s starting from 0 instead of 1). Quick presets cover common configurations like 2d6, 3d8, 1d20, and 4d10.
Every roll produces detailed individual die results, kept dice, and totals. The face frequency chart shows observed vs. expected distributions, and a built-in reference table covers all standard polyhedral dice with their statistics and geometric shapes. Check the example with realistic values before reporting. Use the steps shown to verify rounding and units. Cross-check this output using a known reference case.
Standard dice rollers limit you to common polyhedral shapes. Our custom roller removes all restrictions — any number of dice, any number of sides, with advanced mechanics like exploding dice and keep-best built in. It's the universal dice tool for game designers, probability students, and creative RPG systems.
The face frequency analysis also validates that digital dice produce uniform results, and the reference table makes it easy to compare statistical properties across dice types. Whether you're playtesting a new system or just curious about d37 probability, this tool has you covered.
For NdS (N dice with S sides): Expected value = N × (1+S)/2. Variance = N × (S²−1)/12. Standard deviation = √(Variance). Range: N to N×S (before modifier).
Result: 3d8+5 → [2, 6, 7] + 5 = 20
Rolling 3 eight-sided dice gave 2, 6, and 7 (sum 15). Adding the +5 modifier yields 20. The expected value for 3d8+5 is 18.5.
The NdS+M notation is universal in tabletop gaming. It extends to complex expressions like 4d6kh3 (roll 4d6, keep highest 3) and 2d10! (2d10 with exploding). While our tool uses drop-downs for readability, the underlying mechanics match any notation system.
Some systems extend further: Anydice uses expressions like "output 3d6+2d8", FATE uses special d6 with +/−/blank faces, and dice pool systems count successes rather than summing. Understanding these variations helps when designing or analyzing game mechanics.
A single die produces a uniform (flat) distribution. Adding multiple dice creates a bell curve: 2d6 forms a triangle, 3d6 approaches a normal curve, and 10d6 is nearly indistinguishable from Gaussian. This is the central limit theorem in action — the sum of many independent random variables tends toward normality regardless of the underlying distribution.
The speed of convergence depends on the die size. Smaller dice (d4, d6) converge faster because their underlying distribution is already symmetric and compact. Larger dice (d20, d100) need more dice before the bell curve emerges.
When designing RPG mechanics, the choice of dice profoundly affects feel. A d20 system (like D&D) has high variance — a skilled fighter can roll 1 and fail spectacularly. A 3d6 system (like GURPS) clusters results around 10-11, making skill levels more deterministic. Pool systems (roll Nd6, count successes) scale gracefully and reward investment linearly. Understanding these tradeoffs is essential for balanced game design.
Any die from d2 (coin flip) to d1000. While physical dice beyond d120 don't exist, digital dice can have any number of sides with perfectly equal probability.
NdS+M means roll N dice with S sides each and add modifier M. For example, 2d6+3 means roll two six-sided dice and add 3 to the sum.
When a die shows its maximum value, you roll an additional die. If that also maxes out, you keep rolling. All results are summed. This creates theoretically unbounded results.
Roll more dice than you need and only count the best N results. This shifts the average upward and is used for advantage in D&D 5e and many other RPG systems.
Some systems use d6 with values 0-5 instead of 1-6. Setting the minimum to 0 makes the lowest face 0, which is useful for certain probability calculations and game designs.
Yes! Set sides to 100 for a true d100 roll. This is equivalent to rolling two d10 dice (one for tens, one for units) but more convenient.