Refutation of claims such as “Pi is less random than we thought”.

We begin with an allegory, a fanciful tale in which you plan to assess the randomness of pi. You use the digits of pi to simulate the result of flipping a coin—0,1,2,3,4 for heads, 5,6,7,8,9 for tails. After 3000 flips, the number of heads should be close to 1500, with standard deviatio