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On a regular six sided die (d6) the face with six pips has more material removed than the face with one pip during the engraving process. Does this worsen the distribution of outcomes (make the die biased)?

On a regular d6 the sum of opposing face's pips is 7 so the sum of removed material is even for opposing faces. Does this counter the effect of unequal removed material?

When designing my own dice I tend to look for "numerical beauty" in the placement of faces (like the sum of 7 on the standard die). Should I consider removed material during the engraving process instead?

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    The amount removed by pairs of opposite faces may be the same in total for all pairs, but that is largely irrelevant, since no such pairs are balanced (except trivially when all sides are the same).
    – Nij
    Nov 24, 2022 at 9:18
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    Separately, there is a reason casino dice aren't engraved (and are transparent, and subject to very careful testing). Obviously it does affect the balance. But that effect may well be irrelevant again compared to the imbalance due to other causes.
    – Nij
    Nov 24, 2022 at 9:24
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    Technically, even small dots of paint instead of engraving will unbalance the die.
    – Hackworth
    Nov 24, 2022 at 14:36
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    If you want all the pips to look the same size, you can engrave to a different depth on each face so that the same amount of material is removed.
    – Weather Vane
    Nov 26, 2022 at 19:49
  • @WeatherVane Sounds good, I try have equal surface area as my vendor only supports one depth. I would go for printed dice then if I really need fair dice.
    – aggsol
    Nov 28, 2022 at 9:07

1 Answer 1

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Are engraved dice unbalanced or biased?

Most customers do not think much about how fair their dice are.

Does this worsen the distribution of outcomes (make the die biased)?

Yes, slightly. I've included some research below on Chessex and Gamescience dice to show how much.

Does this counter the effect of unequal removed material?

No. In the case of casino dice there is a lot of work put into making them as close to fair as possible. They are better than your typical die, but still not perfectly random.

Should I consider removed material during the engraving process instead?

If you intended market is customers very concerned with how fair the dice are, you will need to look to the casino dice process. But my advice is not worry too much about it. Most people will likely never notice them being off slightly.

I've included analyses here.

There have been many comparisons of dice in the past, here is one comparing Chessex (leader by quantity) and Gamescience ("High Impact Precision Dice").

A casual analysis of the results suggests that neither die is rolling randomly.

While neither die rolled true, it’s certain that the Chessex die rolled less true, with a greater degree of deviation from the expected range across more of the dice faces. Interestingly, the GameScience die actually rolled very close to true except for the number 14 which rolled vastly less often than it should have, farther off than any face of the Chessex d20.

They noticed a flashing from the manufacturing process that may explain the low number of times the die landed on a 14:

this flashing is on the 7 face — directly opposite the 14

A far more detailed analysis has been done by WKU:

They had some conclusions:

All dice are unfair because they cannot be precisely manufactured with uniform density and dimensional correctness. However, the number of rolls required to detect the unfairness of a casino die manufactured to a few ten thousandths of an inch tolerance is very high.

The manner in which a die is rolled makes a large difference in the face probabilities. It varies with surface and the manner in which it is rolled, that is, dice cup to felt, drop from a height to a hard surface, or rolling in a dice tower.

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    You are right, they can never get them 100% fair but they can get them close enough that it isn't going to matter much and most people won't notice it.
    – Joe W
    Dec 27, 2022 at 4:21
  • How does that differ from what I said or is that you agreement with my post? I updated to make it a bit more clear I'm saying people won't care much if they are off slightly.
    – James Risner
    Dec 27, 2022 at 4:23
  • It is disagreeing with your post, as the question is asking if a specific process for making a set of dice is unbalanced/biased not if you can make a dice 100% fair. And if you look at the science behind dice making them as fair as possible also needs to consider the method that they are rolled with and the surface that they are rolled on. People are able to make dice that are relatively fair with engraving and filling the holes in with material to balance the dice.
    – Joe W
    Dec 27, 2022 at 4:30
  • I've directly answered each of their questions in the original post now in an attempt to make it more clear what I was trying to highlight. Thank you
    – James Risner
    Dec 27, 2022 at 4:43
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    You have done better at answering the question after your most recent edits and I read your answer at first as just saying it doesn't matter.
    – Joe W
    Dec 27, 2022 at 14:39

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