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Couldn't you run the same test (say) a few thousand times, then look at the distribution of numbers? Statistically they should be distributed evenly and be equally likely to appear for large enough runs.

Any number or group of numbers that are consistently over/under represented should point to a bias as far as I can tell.

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For large enough runs, 0, 1, 2, ..., max, 0, 1, ... etc exhibits that behaviour. Thus, a PRNG that fails your proposal is bad, but passing it doesn't meanthat the PRNG is good. A test suite like diehard (or the moderner version dieharder) runs tests for uniform distribution as well as a lot of others, but even then, a pass is only saying "any glaring nonrandomness can't be detected by this suite".

Thanks, that's true but my comment was mostly a response to the "three million zeroes and a single four" as a valid random sequence comment. I wasn't suggesting it as a generic method to test the quality of a PRNG.

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