D4–D20 ENTROPY INSTRUMENT

Die Check

Every fair die roll picks one of N equally likely outcomes. Choose a die below, log your rolls, and this instrument runs the standard randomness battery — entropy, uniformity, streaks, and correlation — to see whether it's behaving like an honest source of randomness.

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Readout

Four independent checks. A fair, well-shaken die should pass all four.

Face frequency

Observed count per face against the expected uniform count (dashed).
within expected range ≥2σ from expected ≥3σ from expected
View as table

How to read this

Shannon entropy

Measures how much information each roll actually carries, in bits. A perfect die delivers log₂(sides) bits per roll — 2.00 for a d4, 3.32 for a d10, 4.32 for a d20. A biased die favors some faces, which makes rolls more predictable and pulls this number down. Needs a reasonable sample (roughly 4× the number of faces) before the estimate settles.

Uniformity — χ² goodness-of-fit

Compares the observed face counts against the count you'd expect if every face were equally likely. Reported as a p-value: high means "no evidence of favoritism," low means some face is coming up far more (or less) than chance allows. This test needs roughly 5 rolls per face (about 100 for a d20, 20 for a d4) to have any real power — below that, treat it as a rough read.

Runs test — streakiness

Classifies each roll as "high" or "low" relative to the midpoint of the die's range and counts how many unbroken streaks (runs) appear. Real dice produce a predictable number of runs; a die (or a person faking rolls) that alternates too neatly or clumps too much will show a suspiciously low or high run count.

Serial correlation

Checks whether one roll predicts the next — for instance a die that tends to land near its previous face, or a person unconsciously avoiding repeats. Reported as a correlation coefficient near zero for independent rolls.