Dice Fairness Test
Testing a die means asking whether the spread of results is more uneven than chance would explain. A chi-square test answers exactly that, and its limits matter as much as its answer: a few dozen rolls cannot detect a mild bias at all, and a result below the threshold is not proof of fairness — only a failure to find evidence against it.
What this generator does
Compares your recorded counts against the uniform expectation with a chi-square goodness-of-fit test, using the critical value for the right number of degrees of freedom at the five per cent level.
How to use this tool
- Roll the die a few hundred times and record how often each face came up.
- Enter the counts, one per face.
- Read the statistic against its threshold.
- Note how many rolls it would take to detect a small bias.
Understanding the controls
- Counts per face
- How many times each face came up, in order, separated by commas. Any number of faces from 2 to 20 works, so this covers polyhedral dice as well as ordinary ones.
Common use cases
- Testing a die you suspect is loaded
- Checking a set of dice before a tournament
- Teaching the chi-square goodness-of-fit test with familiar data
- Understanding why casual testing cannot detect small biases
- Comparing recorded rolls against a uniform expectation
How this generator works
If the die is fair, every face should come up the same number of times on average. The chi-square statistic adds up the squared difference between what was observed and what was expected, divided by the expected count, across every face. Large values mean the spread is more uneven than chance readily produces. Before display the statistic is recomputed from the counts, the expected counts are confirmed to sum to the rolls made, and the verdict is checked against the threshold.
Randomness and fairness
Nothing here is random. A set of counts gives exactly one statistic — this tests rolls you have made rather than making any.
For how randomness is produced across the whole site, see how Generate Random works.
Limitations and good to know
- Failing to find bias is not proof of fairness. Detecting a die that favours one face by ten per cent takes thousands of rolls, not dozens.
- The test needs a reasonable expected count per face — below about five it becomes unreliable.
- It detects an uneven spread, not which face is favoured or by how much.
- A five per cent threshold means a fair die fails this test one time in twenty, which is worth remembering before condemning one.
Privacy and your data
The test runs in your browser and the counts you enter are never transmitted, stored or included in analytics.
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