Dice Roller

The bias in this dice roller, and exactly how big it is

Most pages like this one claim to be fair and leave it there. Here is the actual arithmetic.

Each die is rolled by asking the browser for a cryptographically random 32-bit number and taking the remainder when divided by the number of sides. That is the standard approach and it carries a known flaw: unless the number of sides divides 2³² exactly, some faces get one more of the 4,294,967,296 possible source values than the others.

For a six-sided die, 4,294,967,296 divided by 6 leaves a remainder of 4, so four faces are backed by 715,827,883 source values and two are backed by 715,827,882. The favoured faces are more likely by a factor of about 1.0000000005, which is to say by about one part in two billion. For a twenty-sided die the remainder is 16 and the excess is about one part in a billion. The largest case this tool allows, a 1,000-sided die, is about one part in six million.

To notice the d6 bias with any confidence you would need to roll on the order of a billion billion times. It is real, it is disclosed here because you should be told, and it does not matter for any game. If it ever did matter, the fix is to reject source values that fall in the uneven tail and draw again, which is what Node’s crypto.randomInt does.

Dice are fair. Sums of dice are not, and that is the point

One d6 gives every face the same chance. Three of them do not. There are 216 possible combinations of 3d6, and only one of them totals 3, while 27 of them total 10 and 27 total 11. A ten is twenty-seven times more likely than a three.

This is why tabletop systems roll several small dice rather than one big one. 3d6 clusters hard around the middle and makes extremes rare; a single d18 would make 3 and 10 equally likely. If you are designing something and want results to bunch, add dice. If you want a flat spread, use one die with more faces.

The same reasoning explains why a modifier is not the same as a bigger die. On this page the modifier is added once to the total, not to each die, so 3d6+2 shifts the whole curve up by two and leaves its shape alone.

What this page does with input you did not expect to give it

• The number of dice is capped at 100 and the number of sides at 1,000, and both caps are applied silently after your input is accepted. Ask for 500 dice and you get 100, with no message.
• Fewer than two sides is refused rather than clamped, because a one-sided die is not a die. You will see "Enter valid dice."
• A blank or non-numeric modifier counts as zero. The modifier is the only field where nonsense is quietly treated as nothing.
• The rolls are listed in the order they were generated, not sorted, so you can see the individual results that made the total.
• Nothing is sent anywhere. The rolling happens in your browser and no result is stored between visits.

Sources

• The browser’s cryptographic random source: crypto.getRandomValues(). developer.mozilla.org
• An example of range generation that removes the bias by rejection rather than modulo: Node.js crypto.randomInt(). nodejs.org/api/crypto
• Why the fallback is not good enough for secrets: Math.random(). developer.mozilla.org

The figures on this page were computed from this tool’s own code on 9 October 2026. Where a probability is marked as simulated, it came from 20,000 simulated runs and is an estimate, not an exact value.