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Knowledgeable crypto practitioners do not calculate $\pi$ using a Monte Carlo method to determine if a series of numbers are random. The test alluded to in the question is a general-purpose randomness test for random number generators with output a real number expected to be uniform of the range $[0\dots1[$. The test consists of drawing pairs $(x,y)$, and ...

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I think that I've realised why you might calculate pi. It's easy. x^2 + y^2 = 1 is a simple calculation, thus fast. If you picked another 2 dimensional shape with a non trivial perimeter, you'd have a harder time estimating which side of the perimeter a point had fallen.

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Answered (I think pretty well) by this Reddit thread: All tests of RNGs are based on a "null hypothesis", meaning if they fail, they show the RNG may be flawed. But if they pass, it does not mean it is good. Therefore, the question should be re-worded as "what values constitute failing the ENT tests". Entropy: compressibility > 10% is probably a pretty ...

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