Random number

In mathematics and statistics, a random number is either Pseudo-random or a number generated for, or part of, a set exhibiting statistical randomness.
In common understanding, it's that all have an equal chance; conversely, none have an advantage.
Algorithms and implementations.
A 1964-developed algorithm is popularly known as "the Knuth shuffle" or "the Fisher–Yates shuffle" (based on work they did in 1938). A real-world use for this is sampling water quality in a reservoir.
In 1999, a new feature was added to the Pentium III: a hardware-based random number generator. It has been described as "several oscillators combine their outputs and that odd waveform is sampled asynchronously." These numbers, however, were only 32 bit, at a time when export controls were on 56 bits and higher, so they weren't state of the art.
Common understanding.
In common understanding, "1 2 3 4 5" is not as random as "3 5 2 1 4" and certainly not as random as "47 88 1 32 41" but "we can't say authoritavely that the first sequence is not random ... it could have been generated by chance."
When a police officer claims to have done a "random .. door-to-door" search, there is a certain expectation that members of a jury will have.
Real world consequences.
Flaws in "randomness" have real-world consequences.
A 99.8% randomness was shown by researchers to negatively affect an estimated 27,000 customers of a large service and that the problem was not limited to just that situation.