How to Use Math to Perform a Dice Test for Fairness

Whether you’re a tabletop role-player, a board-game enthusiast, or a collector of premium dice, there’s one question that often comes up: “Is my die fair?” A fair die should give each possible face an equal chance of appearing, but imperfections in manufacturing, material density, or even just wear and tear can create subtle biases.

Many people turn to the saltwater float test—but for heavy metal dice or uniquely shaped dice, that method simply doesn’t work. If you really want to know whether your dice are trustworthy, you’ll need a more reliable dice test: one that’s rooted in mathematics, not guesswork.

This guide will walk you through exactly how to test your dice using 1,000 rolls, Bayesian probability, and Chi-Square analysis—methods that have been used to test high-end dice like the Rule Dice's Serpent’s Dagger Dice series.

Why the Saltwater Float Test Isn’t Enough

The saltwater float test involves dissolving salt in water until your plastic die floats. You then observe whether a certain face drifts upward more often, which could suggest imbalance. The problem?

Metal dice sink—making the test impossible.
Even for plastic dice, micro-variations in surface texture, bubbles in resin, or changes in temperature can affect results.
The test provides only qualitative observations, not quantitative proof.

If you’re serious about fairness testing, you need something more precise.

The Math-Based Dice Test Method

Step 1: Gather Materials

You’ll need:

The die you want to test (e.g., D6, D20)
A flat rolling surface
A way to ensure rolls are random (dice tower, cup, or consistent hand throw)
A tally sheet, spreadsheet, or dice-logging app
Access to online statistical tools (Bayesian analysis calculator, Chi-Square tester)

Bayesian D&D Dice Analysis test tool: https://evjrob.shinyapps.io/bayesian-dnd/

Die Fairness Tester: https://dicefairness.johnellmore.com/

Step 2: Perform 1,000 Rolls

The golden rule of statistical reliability: more data = more accuracy.

Roll the die 1,000 times.
Record the result of every single roll.
Keep conditions consistent—same surface, same rolling method.
If possible, have more than one person roll to reduce human bias.

Why 1,000?
With a 20-sided die, each face should appear ~50 times in 1,000 rolls. That’s enough to identify patterns while still being feasible to perform in a day.

Step 3: Analyze with Bayesian Probability

Bayesian analysis allows us to update our belief about the fairness of a die based on observed results.

Input your roll counts into a Bayesian dice fairness calculator (like evjrob’s online tool).
The tool will output a probability distribution showing how likely it is that your die is unbiased.
For example, when the Serpent’s Dagger D20 was tested, results clustered tightly around the “perfect fairness” mark—suggesting no significant bias.

Why Bayesian?
Unlike raw frequency counts, Bayesian methods incorporate uncertainty and give you a range of probabilities, not just a yes/no answer.
Bayesian D&D Dice Analysis test tool: https://evjrob.shinyapps.io/bayesian-dnd/

Step 4: Validate with the Chi-Square Goodness-of-Fit Test

This is a classic statistical test used in everything from genetics to quality control. You can just use the data of step 3.

Formula:
$\chi^2 = \sum \frac{(O - E)^2}{E}$
Where $O$ is observed counts and $E$ is expected counts (e.g., 50 per face in a 1,000-roll D20 test).
Compare your $\chi^2$ value to a critical value table for your degrees of freedom (number of faces minus 1).
If your $\chi^2$ is below the threshold, you cannot reject the hypothesis that your die is fair.

In the Serpent’s Dagger example, both the D20 and D6 passed with results well within the fairness threshold.
Die Fairness Tester: https://dicefairness.johnellmore.com/

Step 5: Interpret Results

Passing both tests → Your die is statistically fair.
Failing one or both tests → Your die may have a bias—though it could also be due to chance if your sample size is small. Consider re-testing.
Slight deviations → All dice have tiny imperfections; the key is whether they’re statistically significant.

Real-World Example: The Serpent’s Dagger Dice

A real test was performed on both a D20 and D6 from the Serpent’s Dagger metal dice set.

Rolls: 1,000 for each die
Method: Manual rolling with recorded results
Bayesian outcome: High probability of fairness
Chi-Square outcome: No statistically significant bias detected

The conclusion? The dice were fair—good news for anyone using them in competitive or narrative play.

Serpent’s Dagger Dice Set: https://ruledice.com/products/serpent-s-dagger-dice-set

Advantages of This Approach

Works for any material – Plastic, resin, or metal.
Objective and repeatable – Anyone can verify your results.
Statistically rigorous – Recognized methods used in scientific studies.
Fun experiment – Great for gaming clubs or as a group challenge.

Quick DIY Dice Test Checklist

Select die to test
Prepare rolling area and recording method
Roll 1,000 times
Log results accurately
Run Bayesian analysis
Run Chi-Square test
Interpret results and share with your gaming group

Final Thoughts

While the saltwater float test might be a fun curiosity, it doesn’t hold up for heavy dice or when you need hard proof. By using 1,000-roll datasets, Bayesian probability, and Chi-Square testing, you can get a clear, mathematical answer to whether your dice are fair.

If you love your dice as much as you love the games you play, this method will give you confidence that every roll is truly left to chance.

How to Use Math to Perform a Dice Test for Fairness