Dice Roller

How the Dice Roller works

Dice roller: choosing a name that fits

A physical die is fair when every face is equally likely, and the same test applies to a virtual one. Software dice fail that test in two ways: a poor source of randomness, and a biased way of turning that randomness into a face. This page avoids both, and here is exactly how.

Where the randomness comes from. JavaScript offers two random sources. Math.random() is a pseudo-random generator seeded once when the page loads; in modern browsers it is xorshift128+, which is fast and passes statistical tests but is not designed to be unpredictable. Someone who sees a few hundred outputs can reconstruct its state and predict the rest. crypto.getRandomValues() draws from the operating system's cryptographic generator, the same source used to make encryption keys, which is continuously reseeded from hardware noise and cannot be predicted from previous output. For a dice game between friends Math.random() would be fine; for anything where someone might care about the outcome enough to cheat, it is not, and there is no cost to using the strong source, so this page always does.

Turning random bits into a fair face. The generator gives 32 random bits, a number from 0 to 4,294,967,295. The naive way to get a D6 is to take that number modulo 6, but 4,294,967,296 is not divisible by 6, so the faces 1 through 4 each get one more chance than 5 and 6. The bias is tiny (about one part in a billion) but it is real, and for a D100 or a custom 37-sided die it grows. The fix is rejection sampling: discard any raw value in the leftover range at the top and draw again. This page does that, so every face has exactly the same probability whatever the die size.

Reading the results. The total is what most games want. The average per die is shown against the expected average, which is (sides + 1) ÷ 2, so 3.5 for a D6 and 10.5 for a D20; over a handful of rolls it will wander a long way from that, over a hundred it should be close. That is a useful reminder about how randomness feels: streaks of high or low rolls are normal, and a fair die produces them regularly. A D20 rolled on its own also flags a natural 20 or natural 1, since most tabletop systems treat those specially.

Modifiers and notation. The output uses standard dice notation: 2d6 + 3 means two six-sided dice plus three. The modifier is added once to the total, not to each die, which is how every mainstream tabletop system reads it. To roll several different dice at once, roll them separately; this page keeps to one die type per roll so the individual results stay readable.

Custom dice. Choose Custom and enter any number of sides from 2 upwards. A 2-sided die is a coin; a 3-sided one is what you get from a D6 divided by two and rounded up; anything else is whatever your game needs. Rejection sampling means an odd number of sides is exactly as fair as an even one.

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