whitebeard wrote:What is the spec you are looking for with these dice? You are currently testing against a perfect random process, but how good is "good enough"?
I ask this because the more samples you collect, the greater the precision to which you are able to show that ANY die is not perfect. If you roll a million times, you could show that a die which is great for all practical purposes is outside of 5 sigma of a perfect die. In short, perfect should not be your objective.
I don't require perfection. If i invent monsters, if i make equipment, if i make a quest, i work under the assumption that in a game of Heroquest, you will not see differences smaller than 10%. That's because you do not roll often enough to "feel" the difference. That's different for games like 40k, but we're at the Heroquest forum here.
For example, if i make new equipment; making the next weapon a little bit more than 10% stronger than the one before, is for me kind of a prerequisite before i even think about producing and printing a new card.
To avoid hitting the 10% border accidentally with a die just because I don't want to test eternally, I would wish him to undercut that "feeling" border by half - so up to 5% away from the perfect die would be acceptable for me.
I know now, that those normal mass-produced dice are likely to cross this border more often than not.

You could avoid the entire problem if everybody round the table uses one common set of dice, so that every time you roll, you choose randomly among the dice set and it's failures. Only, that mitigation doesn't work at my home and in my experience because people take a "lucky" die and keep it for the rest of the evening. "That's my die now!"



How bad are these dice really?
Bad. I see 3x more failures than expected. They are bad. Not a little bit, but really really bad. But i see light: The failure seems to be connected to the color. So sorting out and throwing away the failing sets should be easy.
Also, you have omitted the constraint in one of your assertions. It's not terribly important, but it does change the expected value for the number of results outside of a sigma value. Once you have one side which registers an extreme value (because of randomness or because of defect), the liklihood that the other sides will be wrong is not random. So there is not a 7.9% chance that a perfect die shows outside of 2.2 sigma, it is even lower.
I took only the most extreme % and calculated: How probable is it that at least one side shows extremes like that? So that's 100% - ((100% - extreme side) pow 6).
Now, to reduce the dice rolling work, i would like to calculate "how probable is it that this die shows more (or less) than the mean 4 out of 5 times?"
Worst case, i have to go with 50% 4 out of 5 times, best case i can somehow incorporate the Z-value/sigma that i have there.
