A dice probability heatmap visually represents the likelihood of each possible outcome when rolling one or more dice. Each square uses color intensity to show how probable a particular result is — darker or more intense colors indicate higher chances. It’s an intuitive way to grasp the distribution at a glance, much faster than reading raw numbers.

We enumerate all possible dice roll combinations (using dynamic programming for efficiency) and count how many lead to each outcome. The probability is then the count divided by the total number of equally likely outcomes (sides^{dice count}). For sum and product this uses exact counting; for max and min closed-form formulas are applied: P(max=k) = (kⁿ - (k-1)ⁿ) / sidesⁿ.

The operation completely changes the distribution shape. Sum tends toward a central bell curve, while product generates a right‑skewed distribution with many small values and very few huge ones. The heatmap instantly shows these differences, helping you understand how game mechanics (like damage multipliers) behave.

This version focuses on identical dice for a clean heatmap. For mixed dice, the distribution becomes multidimensional. We recommend using our tool for each die type separately and then combining them mentally or using our advanced dice roller (coming soon).

They are exact, based on deterministic counting of all possible combinations. We use high-precision arithmetic and display percentages rounded to two decimal places. Fractions are also shown as exact simplified ratios (e.g., 1/6) wherever possible.

The most probable sum is 7, with a probability of 16.67% (1/6). You can check this instantly by selecting d6, count=2, and operation Sum in the calculator above.

Yes, we treat each ordered outcome as distinct (e.g., rolling (2,3) is different from (3,2)). This is the standard convention in probability and matches real physical dice rolls.