Gotta account for a null hypothesis.

The null would be that it is a fair die (average roll 10.5). Your test is whether the true result is significantly less than 10.5 based on a sample of 100 with a mu of 8.8. Let’s call it an alpha of 0.05

So we have to run a left tail one-sample t-test.

Unfortunately, this data set doesn’t tell me the standard deviation – but that could be determined in future trials. For now, we’ll have to just make an assumption that the D20 is fair. For a fair D20, the standard deviation should be be sqrt( ([20-1+1]^2 -1)/12) or roughly sqrt(33.25)

We can run that t-test in a simply python script:

import numpy as np
from scipy import stats as st

h0 = 10.5

sample = np.random.normal(loc=8.88, scale=(np.sqrt(33.25)), size=100)

t_stat, p_val = st.ttest_1samp(sample, h0)

print(f"T-statistic: {t_stat:.4f}")
print(f"P-value: {p_val:.4f}")

Of course, I had to randomize this a bit since I don’t have access to the full data from the true sample. That would make for a better bit of analysis. But at least assuming I didn’t make a serious dumb here, 100 rolls averaging 8.88 would seem to suggest that the you can reject your null hypothesis of this being a fair die at a typical alpha of 0.05.

Then again, the way I wrote this script is GUARANTEED to be an unfavorable result since the way I randomized it REQUIRES the average end up 8.88, which is, of course, less than 10.5. Your real world testing would not have this constraint.

How many dice did you test, and can we see the rest of the spreadsheet?

100 rolls is a staggeringly small sample size for a set with 20 possible outcomes, I would take this with a grain of salt (or a lot of salt in a glass of water? ;) )

In any case it’s fun to do some experimenting like this, thanks for sharing!

This is good work.

Neat. What was your sample size?

You need to include N rolls in your summary

Edit: nvm it’s in the title

IMO unfavourable dice are much more fun