[RPG] Dice Rolling Method Fairness


Recently, in D&D sessions I have been rolling poorly (nothing over 10), and thus tried ways to improve my rolling. I was using a plastic solo cup last session, and got really good results compared to normal. I would place the die with the 20 facing down while holding the cup upright. I then spin the cup in a circular motion, slowly tilting it to about horizontal, then slamming it down on the table to get the result(kind of like Yahtzee). I don't personally think this has any real advantage to rolling normally, but one of my friends said that rolling in a consistent method would essentially make the rolls less random, which would be considered cheating. I know some people will not let others touch their die, or start all their rolls with a 20 facing up, but I thought that was more superstition than a tangible change. Recently I found this article that rolls would not be completly random but it doesn't notate any specific methods used for the motion of the dice. It does imply that changing the situation in which the dice are rolled can affect the outcome or probability.

So my questions are:

  • Does the physical rolling method change the odds of the dice in a significant way?
  • Is simply seeking for a method to improve rolling considered cheating?

Best Answer

This is a classic clustering fallacy

Wikipedia defines the clustering fallacy as:

...the tendency to erroneously consider the inevitable "streaks" or "clusters" arising in small samples from random distributions to be non-random.

Basically, a perfectly random die will have long (potentially very long) steaks of seemingly non-random behavior, either very high or very low. Therefore, your observation of low rolls in multiple sessions could simply be true random variation. Streaks, both high and low, might not be common, but you'll definitely notice them a lot more than more varied behavior. After all, a sequence of exactly 19,20,19 will be a lot more noticeable than a 3, 16, 9, even though the exact probability of both sequences is the same.

The only way to truly know if any method or die is biased or not is to do dozens of identical rolls and look at the resulting distribution. Additionally, everything from the die itself to the rolling surface to your throwing technique is going to affect the roll.

How random does it need to be?

Moreover, how random is random enough? If you read the paper that your article is citing, they say that for a 6-sided die that bounces 4-5 times, the probability that the die lands on the face that's the lowest at the beginning is about 20%, whereas the expected random value is about 16%. Would you notice a 4 percentage point difference on a d6 roll?

For a more concrete personal example, I have a gold d20 that that has a very strong bias toward rolling 20s, according to the saltwater flotation method. However, when I use this "golden" d20, I don't actually notice a greater proportion of 20s showing up in my rolls.

Therefore, the answer to your first question is yes: rolling methods do affect the roll, but unless you're using actual loaded dice, the difference is too small to matter. This means that the answer to your second question is also no, as well.