Most d20 dice are notably imbalanced

I recently saw the question asked How accurate are the d20 dice used in role playing games? on the skeptics stack exchange website.

There's a very persuasive and popular video of Lou Zocchi speaking about his GameScience dice. Essentially the sharper the edges on the die the more fair and balanced the roll, and the difference is a notable one.

Over at 1000d4 there's a closeup of Zocchi's dice comparison chart and an excellent article with their own updated comparison of GameScience dice dimensions to other manufacturers. His dice are indeed highly consistent.

The Awesome Dice blog conducted a thorough comparison of a GameScience d20 with a Chessex d20 rolling them 10,000 times each. The GameScience die is more fair except the number 14 rolls significantly less often because the opposite side has a chunk of plastic from being snipped off the mold. (Rounder dice like the Chessex have this but it's polished away with the rounding of the corners.)

So his dice are better than most, but still don't offer the equal access to every number we tend to expect from a die.

Delta's D&D Hotspot demonstrates how to use Pearson's chi-squared test to determine if a die is imbalanced. Around this time last year I conducted my own test with these methods, rolling an Orange, Purple, and Green Chessex d20 500 times each (a minimum for this test). In the following spreadsheets if the result is higher than the fairness limit for the number of rolls, the die is imbalanced.

Chessex Orange, Green, and Purple

The results were frightening. My intuitive "feel" of the die wasn't superstitious but actually quite correct! My Purple d20 really is strongly biased in favor of rolling 1's and 20's. Also the Green d20 has a very noticeable deformation on the 17, opposite the 4. When the die is showing 4, it wobbles unevenly. The data shows this bias away from 4 quite clearly.

What does it all mean? Cheap dice do in fact suffer from a dramatic imbalance, Lou Zocchi was correct. Though even his have a bias against 14. Thus I haven't switched to his die, instead I now use a pseudorandom number generator

Rolling Pebble, Pebble watch app

that I know to have a uniform distribution. Choosing die specific to the situation feels too much like cheating. It's an unfortunate discovery but true nevertheless.


Orange 638 < 754 Balanced (Probably)

Green 1,940 > 754 Imbalanced

Purple 858 > 754 Imbalanced