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The usual gut reaction for statistical significance is that n*p should be 20, or 20 rolls per face. 100-150 should be statistically significant.

You can't assign significance to a sample size alone.

A sample size of 10 can be significant (if it were 10 1's for example), and a sample size of 100,000 can be not significant, for example if you were to roll 4,953 1's.

i believe the op meant "Statistical power"

Yes, if these graphs had confidence intervals they would be a lot more informative.

As the author -- I agree! I did some preliminary work to make confidence intervals, but didn't get around to updating the writeup.

These are my draft updated charts: http://www.markfickett.com/tmp/dice/chart.html

I used bootstrapped subsamples to generate the confidence intervals: https://github.com/markfickett/dicehistogram/blob/master/sum...

One of the dangers, especially with statistical tests of uniformity, is that they often over detect departures from uniformity when using large samples.