Custom Dice Roller Calculator - Roll Mixed Polyhedral Dice

The custom dice roller calculator is a browser tool that rolls 1 to 15 polyhedral dice at once, picks the face count per die, and returns the individual face values, the total sum, and the expected value.

• • Tabletop role-playing sessions: Roll a D&D attack with 1d20 plus modifiers, ability scores with 4d6, or a save with 2d10 plus 1d4 without hunting for the right physical die.
• • Board game nights without a full dice tray: Replace lost or short physical dice for Catan, King of Tokyo, or Yahtzee and read the total alongside individual face values.
• • Probability and statistics class demos: Show students the expected value of a pool and the theoretical minimum and maximum totals for any mix of polyhedral shapes.
• • Monte Carlo simulation warm-ups: Use the seeded xorshift generator to reproduce a specific batch, which makes it easy to share a Monte Carlo sample with a study group.

Each die in the pool can use a different face count, and the supported shapes range from a tiny 3-sided prism up to a 120-faced disdyakis triacontahedron. The calculator records every individual face so you can read the roll the way you would on a real table, not as a single opaque total.

When you only need a pair of standard six-sided dice, the 2 Dice Roller Calculator keeps the same click-to-roll workflow but focuses on the classic 36-outcome probability table.

Each die in the pool rolls independently using a seeded xorshift32 generator. The total is the sum of every face, and the theoretical expected sum is the sum of (sides + 1) divided by 2 across the pool.

• N: Number of dice in the batch, integer from 1 to 15
• sides_i: Face count of the i-th die, chosen from the supported shape list
• face_i: Independent uniform integer from 1 to sides_i drawn for die i
• Total: Sum of every face in the batch
• Expected sum: Sum of (sides_i + 1) / 2, the long-run average of the total

The minimum possible sum is N, the maximum is the sum of the largest face on each die, and the expected value sits at the midpoint of those two bounds because the uniform distribution on 1..sides is symmetric.

According to Wolfram MathWorld, the expected value of a single fair n-sided die is (n + 1) divided by 2 and the variance is (n squared minus 1) divided by 12.

When the question shifts from a single roll to the exact probability of a sum, the Two Dice Probability Calculator returns the count of favorable ordered pairs divided by 36 for any sum from 2 to 12.

Four short ideas anchor the rest of the page. They cover the math behind a single die, the way multiple dice combine, and the role of the seed.

For a deeper view of how independent events combine, the Probability Calculator lets you compute AND, OR, and conditional probabilities with the same uniform-draw assumption.

Use the custom dice roller in five steps. The defaults already roll a standard D&D attack pool, so most users only adjust the face list.

1. 1 Set the number of dice: Type how many dice you want in the batch into the Number of Dice box. The default of 5 covers most tabletop needs.
2. 2 List the face counts for each die: Type the face count for every die into the Face Count per Die box, separated by commas. Use 4, 6, 8, 10, 12 for a D&D attack pool, or a single number such as 6 to roll that shape N times.
3. 3 Pick a seed if you want to reproduce the roll: Leave the seed at the default 42 for a casual batch or change it to any integer between 0 and 999999 so the same sequence can be replayed later.
4. 4 Read the results panel: The Total Sum tile shows the sum of every face. The other rows show the minimum and maximum possible sums, the expected sum, and the mean face value of this batch.
5. 5 Audit the individual faces: Scroll to the per-die face table below the inputs. The list is labelled Die 1, Die 2, and so on so a D&D player can read the attack roll and the damage roll in the same view.

For a D&D greatsword attack with a +5 modifier, set dieCount to 2, faces to 20, 6 (1d20 + 1d6 for damage), and leave the seed alone. The total sum plus your +5 modifier gives the attack and damage.

When the next question is whether the attack hit and the damage roll both landed in target ranges, the And Probability Calculator handles the joint probability without forcing you to enumerate each pair by hand.

Five concrete reasons this custom dice roller earns its place next to your physical dice tray or your probability textbook.

• • Mixed-shape pools in one click: Roll a d20, a d6, and a d4 in a single batch instead of grabbing three dice and adding the results by hand.
• • Full per-die readouts: Every individual face is visible, so a D&D player can read the raw d20 and the damage roll separately instead of treating the total as opaque.
• • Expected value alongside the roll: The expected sum is computed for your exact pool, which lets you compare a single batch to its long-run average without a statistics book.
• • Reproducible via seed: A specific seed always produces the same dice sequence, so a study group or a teacher can share a Monte Carlo sample by sharing one integer.
• • Browser-only, no install: Runs on any modern browser including Chromebooks and tablets, so it works in a classroom, a board-game cafe, or on a phone at the table.

For a single independent event with only two outcomes, the Coin Flip Probability Calculator handles the uniform-coin counterpart to this dice roller.

Five factors drive how the displayed total relates to its theoretical range, and three caveats keep the result honest.

• • The xorshift32 generator is fast and reproducible but is not cryptographically secure. Use a different tool when true randomness is required, such as cryptographic key generation.
• • The face list is parsed as integers, so face counts that are not in the supported shape list (such as d9 or d11) are silently coerced to a d6 to keep the roll valid. This is the same fallback most online dice rollers use, but it can hide a typo.
• • The calculator models each die as a fair uniform shape. Loaded dice, biased dice, or non-standard label distributions are not modeled.

According to Wikipedia, common polyhedral dice include tetrahedra, cubes, octahedra, dodecahedra, icosahedra, pentagonal trapezohedra, and prisms for odd-sided designs.

When you want to study how a series of independent draws cluster into streaks, the Coin Flip Streak Calculator uses the same uniform-draw idea on a two-sided outcome.