Hacker News Reader

Comment by lsc36 | Hacker News Reader

1. You don't turn PRNG into "true" RNGs simply by picking seeds from environmental randomness. The seed is just the initial state, as long as the output is generated by a deterministic algorithm, by definition it's a PRNG. At the very best you can make a CSPRNG, but not a "true" RNG.

2. The dice roll example is not uniform distribution, I think this is a common pitfall when generating random integers of a range. `randomNumber % 6` results in a slight bias towards 0 and 1, since 2^31 % 6 == 2, there are more numbers in the range [0, 2^31-1] that map to 0 and 1 than those that map to 2...5. To make it uniform, for example, you should always discard if `randomNumber < 2` and regenerate another number for use.

View on HN

#2 reminds me of Benford's Law, which I recently learned about and find truly fascinating.

https://en.wikipedia.org/wiki/Benford%27s_law

Interesting.

On first pass, Benford’s Law looks a lot like Zipf’s Law.

What differentiates Benford’s Law from Zipf’s Law?

From https://en.wikipedia.org/wiki/Zipf%27s_law :

> It has been argued that Benford's law is a special bounded case of Zipf's law,[22] with the connection between these two laws being explained by their both originating from scale invariant functional relations from statistical physics and critical phenomena.[24] The ratios of probabilities in Benford's law are not constant. The leading digits of data satisfying Zipf's law with s = 1 satisfy Benford's law.

Thank you!

I’ll take some time to try and better understand your post.

Re 2.: OTOH, the bias is extremely tiny, there's only 2 out of 2^31 cases which are problematic, or one in a billion. A generic RNG obviously shouldn't do it this way, but for most applications it would be good-enough really.

The article claims that "it is indeed a uniform distribution" so I wanted to point it out.

To make a dice roll uniform, wouldn’t it be easier to do randomNumber % 8 and only use it if it is from 0 to 5, and discard and re-roll otherwise?

(Since we can reasonably assume that randomNumber is a binary number, and thus would be balanced over 8 values instead of 6.)

That depends on the modulus being divisible by 8, which is not always the case. A common example is modulus = 2^31 - 1 [0] which is prime.

[0] https://en.wikipedia.org/wiki/Linear_congruential_generator#...

Ah very true, an often ignored thing, thank you for sharing!

Reply on news.ycombinator.com