A generic die emerging from a transparent bowl of random colored beads. Original AI-generated artwork produced for GreenCalc; not a measured diagram or empirical data display.
A random integer still needs an unbiased mapping
A virtual die needs a random source and a rule that maps source values to die faces. Even when source integers are uniform, reducing them modulo the number of sides can introduce a small bias if the source range is not an exact multiple of that side count. Some remainders then receive one more source value than others.
See the issue in a tiny example
Suppose a toy source returns integers 0 through 9 with equal probability. Taking the remainder modulo six maps 0 and 6 to face index 0, 1 and 7 to index 1, 2 and 8 to index 2, and 3 and 9 to index 3. Indices 4 and 5 have only one source value each. The first four faces are twice as likely as the last two.
Reject the incomplete final block
To produce six equal outcomes from that toy source, accept only values 0 through 5 and redraw values 6 through 9. Every accepted face then has one equally likely source value. The Dice Roller Calculator applies this principle to uniform 32-bit browser cryptographic random integers. It accepts the largest initial range divisible by the number of sides, then maps the accepted remainder to faces 1 through s.
Know what the implementation establishes
This mapping removes modulo bias under the assumed uniform source. It does not provide an independently certified gambling service, a seeded reproducible simulation or evidence about physical dice. A short batch can still look uneven because uniform probability does not require balanced observed counts. The tool displays only a bounded preview of large batches while computing totals from all generated dice. Read the simulation-comparison guide to assess observations against a theoretical mean. For exact event probabilities under the same fair-dice model, use the probability calculator instead of inferring a rare probability from a handful of rolls.
Check the model behind your result
Use the Dice Roller Calculator for the supported calculation and review its stated assumptions before interpreting the output. Find related tools in the Statistics category, or browse the GreenCalc homepage for other calculation topics.
By GreenCalc Editorial Team · Updated 2026-10-26