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Comment by stevebmark | Hacker News Reader

The first one looks more random to me? It has more runs. There was some article (can't remember the source) about generating a random coin flip - the way to tell the difference between a real physical coin flip and a computer is that the real physical flip will have a lot of runs, like 10 times in a row where you get heads. A computer random will attempt to "even out" the spectrum. The two images presented in the article looked similar to these but were reversed, true random looked more like a pattern, while computer generated random looked more like even noise.

TL;DR long strings of repeated results are a sign of true randomness. Am I misinterpreting the relationship between that and this article?

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That's true in general, but note that the runs should show up in 2 dimensions in the image. The second one appears clumpy, which exactly what it should look like. People tend to avoid runs, which would make it look more uniform. The first one has an obvious bias because it doesn't look the same in the x direction as in the y.

Randomness looks like white noise. You can't distinguish computer randomness (provided that it's a proper PRNG) from physical coin flips. Computers don't "even out spectrum". The longer the coin flip run, the less likely it is to happen, e.g. you would need on average 2046 coin throws to get 10 heads in a row.

TL;DR probability theory

(If you have free time and want to have some fun, throw a coin and draw a picture recording throws. I once generated a password by throwing a coin for more than hundred or times — each bit taking more than 1 throw to avoid biases — https://en.wikipedia.org/wiki/Fair_coin#Fair_results_from_a_...)

> Computers don't "even out spectrum"

Not "on purpose", of course. But with a bad PRNG, the probability of 10 heads in a row is lower compared to a proper PRNG so in a sense the bad one is "evening out spectrum"

Yeah, it can also be higher. Or lower. Or bad PRNG can give the same number every time. Flipping a biased coin can also produce bad randomness. I'm not going to mention every edge case in my comment ;-)

Computers are trying not to produce results different from fair coin flips.

Those lines are showing up because the old algorithm can't produce all possible values in the 0-1 range. 32 bits of internal state simply aren't enough for that.

The problem is highlighted by the images in this article:

http://jandemooij.nl/blog/2015/11/27/math-random-and-32-bit-...

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