As an actual Masters of Statistics, let's do this.
1. You must have 100 or more d20 rolls. Not the pass/fail value, the actual roll result. For practical purposes, the actual count needs to be a multiple of 20, so 100, 120, 140, etc. rolls.
2. You must pick them in an unbiased manner, i.e., you can't wait until you have a set of several low (or high) rolls in a row and then start keeping track. Or sample some, then ignore some, then start sampling again. Or run multiple tests and choose the results you want. There are LOTS of other ways to consciously or unconsciously bias the results, also, too many to go into here. Suffice it to say that if you are actually looking for a specific result, you are more likely to find it.
3. Go to
https://www.icalcu.com/stat/chisqtest.html4. The expected values for 100 rolls would be 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 in their format, or 5 of each number. Or all 6s for 120 rolls, all 7s for 140 rolls, etc.
5. The actual value would be the count of 1s, followed by the count of 2s, followed by the count of 3s, etc. So something like 4 8 3 5 6 3 5 6 10 4 4 2 0 6 5 8 6 4 4 7 would indicate 4 1s, 8 2s, 3 3s, etc.
6. Stack the rows as it shows in the site example. (Or if you want to use my sample data, just copy and paste from below.) Calculate.
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
4 8 3 5 6 3 5 6 10 4 4 2 0 6 5 8 6 4 4 7
7. The P-value is the likelihood that the actual rolls come from a completely unbiased die. By convention, if it is 0.05 or less, you have significant evidence that the rolls are biased.
8. For an interesting thought exercise, how do you think the numbers above come out? Write it down. Then do the calculation. Surprised at the result?
P-value 0.902413853239. In other words, no significant evidence of a bad distribution, despite the 10 9s and the 0 13s in the list.
9. Stop griping until you do the actual test.
There are lots of other tests you can do looking for various things, but the number of ways to do things wrong far exceeds the number of ways to do things right.
