Graduate Using Statistics to Test for Normality of Pi

[WWGD]

Is there a " reasonable" way to test for the normality of $\pi$ , i .e., that every digit occurs with the same frequency? Someone suggested randomly sampling strings of size 20 and outputting the frequency. Then I guess we could average the frequencies among samples , use a chi-squared test. Assuming random sampling can be done, is this a sound way of testing?

 

[FactChecker]

Yes. The Chi-squared goodness of fit test can be used to test if the digits are from a uniform distribution.

 

[BWV]

Is normality dependent upon the base - is it possible for there to be a pattern in one base that then appears random in another?

anyway, here is one method that showed normality out to 22.5 trillion base 10 decimal places and an equivalent number of hexideximal ones

https://arxiv.org/pdf/1612.00489.pdf