Fairness Score
A percentage from 0–100% showing how close your roll distribution is to a perfectly fair die. 100% means every face appeared exactly equally. It's derived from the chi-squared statistic, normalised so it's easy to read at a glance.
- 90–100% — Excellent, very uniform
- 75–89% — Good, fairly uniform
- 50–74% — Fair, some deviation (normal for small samples)
- 25–49% — Poor, clearly biased
- 0–24% — Very poor, heavily skewed
Don't read too much into a low score with fewer than 30 rolls — randomness is clumpy by nature.
Total Rolls
How many rolls you've recorded in this session. The more rolls you have, the more reliable the stats become. Around 30+ rolls is a good minimum for meaningful chi-squared results.
Mean
The average of all your roll values, calculated as the sum of all values divided by the count. For a fair D6, the expected mean is 3.5. If your mean is significantly higher or lower, one side of the die may be favoured.
Median
The middle value when all your rolls are sorted from lowest to highest. Half your rolls are below this number and half are above. For a fair die, the median should be close to the mean.
Standard Deviation
Measures how spread out your rolls are from the mean. A low standard deviation means rolls cluster tightly around the average; a high one means they're more spread out. For a fair D6, the expected standard deviation is about 1.71.
Most / Least Common
The face value that appeared the most (or least) often in your rolls. In a small sample it's normal for these to differ — with enough rolls of a fair die, all faces should appear roughly equally.
Chi-Squared Test (χ²)
A statistical test that compares your actual roll frequencies against what you'd expect from a perfectly fair die. The result is a number — lower is closer to random.
- Looks fair — your rolls are consistent with a fair die (p-value above 0.05). No evidence of bias.
- Slightly biased — there's a mild indication your rolls aren't perfectly random (p-value 0.01–0.05). Could just be small sample size.
- Strongly biased — your rolls differ significantly from what a fair die would produce (p-value below 0.01). The die or rolling method may be biased.
The "degrees of freedom" (df) is the number of face values minus one. It's used alongside the chi-squared statistic to calculate the p-value.
What does "random" look like?
True randomness is clumpier than people expect. Even with a perfectly fair die, you'll see streaks, clusters, and gaps — that's normal. Don't read too much into patterns in small samples (under ~30 rolls). The chi-squared test accounts for sample size, so trust it over your intuition about whether something "looks" random.