All dice are not created equal. At least that is the claim of the few manufacturers that produce "precision" dice. And they appear to be right, although how meaningful this is in the context of D&D is debated. What are we talking about here?
A die's fairness is measured, at least in one understanding, by how close its roll result is truly random. For example, you roll a d20. There should be a 5 percent chance of getting a 20. Not 4.575 percent, but 5.000 percent. Each number on a d20 should have a 5 percent chance of showing on a roll.
This perfect randomness exists only in the pure world of abstraction. Or more interestingly you could say that the Platonic solid icosahedron is the eternal form upon which inferior earthly material copies are based. Yikes.
So how do mortals muck up perfect randomness? One issue is how dice are rolled. This is discussed elsewhere. Another is the material and manufacturing process used to make dice. Let's look at that.
Icosahedron. Author of the image:
Bacground photo by Inactive on Unsplash at unsplash.com/photos/ihbqhutI9x4.
MATERIAL, MANUFACTURING & "PRECISION" DICE
Whether metal, plastic, stone, or glass, if the material of a die has air bubbles, impurities, or some other unevenness in weight, then the die is not balanced. Even if perfectly shaped, if one side of the die is heavier than its other sides, then the heavier side will have a greater chance of being on bottom when the die comes to a rest. Or at least common sense suggests this. One academic appears to disagree.
Another issue is shape. In theory, the distance between every opposite pair of faces of a die must be identical. If it is not, then the die will be asymmetrical and will not roll with perfect randomness. The faces of a die must be identical. This brings us to the great debate between Louis Zocchi, founder of Gamescience, and almost everyone else in the dice business. Well, it's not really a debate (except among bloggers). Zocchi has pugnaciously but entertainingly asserted the superiority of his dice for over 40 years. The rest of the industry (and there's a lot of them) appears bemused and silent.
Most plastic dice are injection molded -- molten material is injected into a mold. Here is the problem according to Zocchi. Most dice companies place the molded die in a tumbler to polish off the sprue (excess material that solidifies in the passage through which molten material is introduced into a mold) and the flash (excess material attached to a molded item usually at the seam of the mold). Then the entire die is painted and put in a tumbler again, this time to rub off the paint except for the portion trapped in the number indentations. The die is then tumbled again with extra fine abrasion to polish off the scratches caused by the prior tumbling. Here is the rub. Tumbling softens the edges of a die, and does so irregularly. Some edges are rubbed down more than others. Violà - an irregularly shaped die!
Zocchi does not use a tumbler. Hence his dice have sharp edges, are produced unpainted, and have a small sprue mark. The yellow die below is from Gamescience (yes, it's pretty old). It's hand-inked. Even given its age, you can sill see the sharp edges. The green die is a basic tumbled die, with significantly rounded edges. Zocchi's claim is that such irregularly worn-down edges and the often oblong shape of tumbled dice are not as symmetrically shaped as his dice and thus do not roll as true as his dice. Some manufacturers of metal dice, also usually injection molded, reiterate Zocchi's sermon about the sinfulness of tumbling. For example, see Die Hard Dice.
Zocchi's claim appears to be true -- see the Daniel Fisher video, the Awesome Dice Blog article, and the 1000d4 blog article -- but the meaningfulness of the difference between his dice and tumbled dice is debated. See the interesting videos and articles below on the topic, as well as some more esoteric forays into dice fairness.
Gravity Dice manufactures computer calibrated, aluminum machined (not injection molded) precision polyhedral dice. I am not aware of any randomness tests with them, but my guess is that they win hands-down. I couldn't resist and bought two d20. (See the die on the right.) They feel and look beautiful and I bet they are close to perfect. They are, understandably, more expensive than plastic dice.
What about using casino quality d6? They are machined out of quality resin and made as close to the heavenly-Platonic standard as possible. Not a surprise - in Las Vegas it is not a +1 longsword at stake but billions of real dollars exchanging hands every year. One academic recommends using them in gaming. This is common sense. I think they are not commonly used in D&D because, to the extent players know about them, they clash with the aesthetics of RPG industry dice and the gain in accuracy is not worth it. I have 16mm casino-quality dice, which are smaller than most regular casino dice, and like them very much.
VIDEOS & ARTICLES
Google "precision dice" or "D&D Dice" or "polyhedral dice" and you will get many hits. Below are just a sample of some of the more interesting ones.
Louis Zocchi, founder of Gamescience, explains in his entertaining way why his dice are more accurate than tumbled dice. Filmed at GenCon 2015.
In this Awesome Dice Blog article dated September 3, 2012, the authors discuss a randomness test done on dice. The Gamescience dice rolled truer, but the authors question the meaningfulness of the difference.
In this DakaDaka website article (republished), from 2008, a teacher at Arizona State University conducts a scientific experiment on dice. One result, on material and balance, is counterintuitive. He recommends casino-style dice for gaming.
Part 2 of Stanford University Professor Persi Diaconi's fascinating foray into the theoretical and practical issues of fairness in polyhedral dice.
Daniel Fisher applies the saltwater test to dice to measure balance, and measures the width of dice. Gamescience dice proves more balanced and symmetrical. Filmed on July 29, 2015.
In this 1000d4 blog article dated February 14, 2013, Alan De Smet and Eva Schiffer measure the sides of d20s. Gamescience proves more symmetrical.
In this video (part 1), Stanford University Professor Persi Diaconi explains theoretical and practical issues of fairness in polyhedral dice. Fascinating and an unusual foray for gamers, to say the least.
If the two videos of Professor Diaconi were not enough, then treat yourself to a paper ("Fair Dice") by him and Professor Joseph B. Keller in The American Mathematical Monthly.