Refutation of claims such as "Pi is less random than we thought"

by George Marsaglia.

Abstract: An article by Tu and Fischman in a Physics journal has led to worldwide reports that Pi is less random than we thought, or that Pi is not the best random number generator, or that Pi seems good but not the best. A careful examination of the Tu and Fischman procedure shows that it is needlessly complicated and can be reduced to study of the average value of (U2-U1)(U2-U3) for uniform variates U produced by a RNG, (but not on their distribution). The authors' method of assigning a letter grade, A+,A,B,C,D,E to a sample mean, based on its distance from the expected value, suggests naivety in the extreme. Application, in the present article, to the first 960 million digits of the expansion of Pi shows that they perform as well as other RNGs on not only the average for (U2-U1)(U2-U3), but on the more difficult test for their distribution, consistent with results previously shown in this journal that Pi does quite well on far more extensive and difficult-to-pass tests of randomness.

Key Words: LSTests of Randomness, Pi, Diehard Tests, Random Number Generators

George Marsaglia,

Editor: Joseph W. McKean,

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