Note that if your only goal was to test whether the dice was loaded, using a test against only one outcome (in this case, only 6s) is not the best way.
Use either a Kolmogorov-Smirnov test[1] or the Anderson-Darling test[2].
The intuition is that these tests are more powerful because they take the difference between the entire empirical distribution minus the expected probability mass distribution. You're using 'all the numbers' simultaneously to check for cheating.
Funnily enough, I first learned about these tests a nearly a decade ago, precisely because I wanted to know whether Settlers dice were loaded.
I think for this case (with 6 discrete outcomes) you could just use Pearson's Chi-Square test. What you describe is general enough for continuous distributions.
Use either a Kolmogorov-Smirnov test[1] or the Anderson-Darling test[2].
The intuition is that these tests are more powerful because they take the difference between the entire empirical distribution minus the expected probability mass distribution. You're using 'all the numbers' simultaneously to check for cheating.
Funnily enough, I first learned about these tests a nearly a decade ago, precisely because I wanted to know whether Settlers dice were loaded.
[1] https://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_tes...
[2] https://en.wikipedia.org/wiki/Anderson%E2%80%93Darling_test