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Random number generators commonly found in default libraries are actually pseudo-random number generators. Nevertheless, more sophisticated options exist to gather entropy from "truly"-random sources such as atmospheric noise, thermal noise, electromagnetic and quantum phenomena.

Speed of random number generation is important, as for instance Monte Carlo simulations need a large amount of random numbers. Since speed can be the bottleneck and Monte Carlo simulations are used in many fields, an improvement in random number generation speed translates into real-life value generated.

What about the quality of the randomness? Are there real-life applications in which the random number generation quality is the bottleneck? That is, are there situations in which an improvement in quality (or generation cost for a given quality) of random-number generation over the state of the art would result in real-life value generated?

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    $\begingroup$ Stream ciphers? $\endgroup$
    – Pseudonym
    Feb 20, 2023 at 13:00

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There have certainly been situations where the periodicity of some pseudo-random number generators along with simplifications during use and exceptional observers have caused issues -- the obvious one that comes to mind is the guy who could predict where the "randomized" Press Your Luck gameboard would land.

As far as more modern applications, I think one big concern is any time that you have two systems using similar pseudo-random number generators "against" each other. Whether these are simple game AIs or generative adversarial networks, you risk a chance of similarity in the number generation process, creating more false positive "successes" than would normally happen by chance.

Furthermore, because any pseudo-random generative process is inherently "predictable" given enough time and resources, how would you know if an AI was able to learn what algorithm you were using, or just abstracting it to outcomes from your number generator? This has applications from games to encryption to even just learning tasks -- you can't tell if an AI is answering your questions "intelligently" in a multiple choice test if it is just determining which answer slot will be the next one chosen randomly as the "correct" slot without reading the question.

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