Dice Roller & Probability Distribution Simulator

One real roll, plus the math behind what to expect over time

Rolling 2 six-sided dice produced faces 4 and 1 for a total of 5 in this run -- a genuine random result, different every time you roll, alongside the theoretical mean of 7.00 that 2d6 converges toward over many, many rolls.

That mean of 7 comes from a simple formula: n x (sides + 1) / 2 = 2 x (6+1)/2 = 7. It's the average you'd expect if you rolled 2d6 thousands of times and averaged every result -- any single roll, like this one landing on 5, is just one sample from a distribution centered on that mean, not a deviation from a 'correct' answer.

With 2d6 specifically, not every total is equally likely -- 7 is the single most common total (achievable via six different combinations: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1), while extremes like 2 or 12 are the least common (only one combination each), which is exactly why 7 is also the theoretical mean.

Why one roll doesn't prove anything about fairness

Uniform faces via crypto.getRandomValues. Mean is n times (sides+1)/2. Each die uses a cryptographically secure random source specifically to ensure every face has a genuinely equal 1-in-6 chance on every roll, with no bias toward any particular number -- a meaningfully higher randomness quality than some simpler pseudo-random implementations provide.

A single roll landing on 5 (below the mean of 7) tells you nothing about whether the dice are fair -- genuine randomness produces plenty of variance around the mean, and it would actually be more suspicious, not less, if every roll landed suspiciously close to 7.

For actually verifying fairness or exploring the true probability distribution, running many rolls and checking whether the frequency of each total converges toward its theoretical probability is the correct approach -- a small number of manual rolls is inherently too noisy a sample to draw conclusions from.

Related probability and randomness tools

For a simpler two-outcome random event with the same underlying randomness quality, the Coin Flip Frequency Counter runs the same kind of trial at larger scale to check convergence toward 50/50.

If the goal is picking randomly from a custom list rather than simulating dice, the Random List / Name Picker uses the same quality of cryptographic randomness for that different purpose.

Frequently Asked Questions (FAQ)