Do the Dice Hate You?

“I never roll above a 7.”

It is the most common complaint at any D&D table, and it always feels true. Someone fumbles a critical save, drops to the floor, and declares the dice cursed. The table nods. A legend is born.

But a feeling is not evidence. Across three active campaigns, every digital roll has been logged to a database since 2023 — over five thousand of them. That turns an article of faith into a testable hypothesis: are the dice actually unfair to anyone, or does it just feel that way?

Where the numbers come from

Every roll made on D&D Beyond is captured by its game-log API, pulled with a lightweight sync script, and upserted into a Postgres database on Supabase. One in-game attack often becomes two rows — a to-hit and a damage roll — linked by a shared roll ID. The raw die faces are preserved in a JSON column, which is what makes a fairness audit possible at all.

Cleaning a messy real-world log

A roll archive is not a tidy dataset. Three decisions did most of the work, and each one matters for the result.

1 · Only true 1d20 rolls count

The fairness question is about a single fair die. So the analysis keeps only single-d20 rolls used for attacks, checks, saves, and raw d20s — the rolls that should follow a clean uniform distribution.

2 · Advantage and disadvantage are excluded — deliberately

Rolling two d20s and keeping the higher (advantage) or lower (disadvantage) is not a uniform distribution. Advantage skews high; disadvantage skews low. Folding those rolls into the base rate would manufacture a bias that the die itself never had. Excluding them is the difference between measuring the dice and measuring the rules.

3 · Known data quirks, handled

A handful of legacy rows stored the die values as a double-encoded JSON string rather than an array; DM-controlled monsters appear in the log as their own “characters”; and a few early rows have no recorded values at all. Each was filtered explicitly rather than silently averaged over.

WITH d20 AS (
  SELECT (individual_values->>0)::int AS face
  FROM ddb_rolls
  WHERE dice_notation LIKE '1d20%'        -- single die only
    AND jsonb_typeof(individual_values) = 'array'  -- skip legacy/null
    AND jsonb_array_length(individual_values) = 1   -- no adv/disadv
    AND roll_type IN ('to hit','check','save','roll')
)
SELECT face, COUNT(*) FROM d20 GROUP BY face ORDER BY face;

The full extraction query. After filtering, 3,246 clean single-d20 rolls remained for analysis.

The dice are fair. Boringly fair.

If a d20 is fair, all twenty faces should land roughly equally often — about 162 times each across 3,246 rolls. Here is what actually happened.

So at the level of the whole table, there is no curse and no blessing. The random number generator is doing its job. Which raises the obvious objection…

“Fine — but I’m still cursed.”

Fair overall doesn’t mean fair for everyone. So we split the rolls by character — every player and DM-run creature with at least 30 single-d20 rolls — and looked at how often each one fumbled a natural 1.

Run a binomial test on each character and two names cross the usual p < 0.05 line:

Case closed? Not quite. There’s a trap in testing nineteen characters two ways each — that’s 38 separate significance tests. At a 5% threshold, you expect about 1.9 of them to flag by pure luck, even if nothing is wrong. We found exactly two. That is the number randomness predicts.

This is the quiet lesson hiding in a joke dataset: search hard enough through random data and you will always find something that looks significant. The discipline is knowing it isn’t.

What this can’t see

• Physical dice are invisible. Some players roll real dice that never touch D&D Beyond. Their rolls aren’t in the archive — an expected gap, not a sync failure, but it means “every roll” really means every digital roll.
• Advantage and disadvantage sit out. They’re excluded from the base-rate test on purpose. A separate analysis could measure how much the rules — not the dice — bend the odds.
• DM-run creatures share the character list. Monsters Addison rolls for appear alongside player characters. For a fairness audit every fair-die roll counts equally, but they aren’t all “players.”
• Memory isn’t in the data. The archive records outcomes, not how they felt. The gap between the two is the whole story — and it’s the one thing the numbers can’t measure.