For example, applications in cryptography usually have strict requirements, whereas other uses (such as generating a "quote of the day") can use a looser standard of pseudorandomness.
Many randomizing devices such as dice, shuffling playing cards, and roulette wheels, seem to have been developed for use in games of chance.
Electronic gambling equipment cannot use these and so theoretical problems are less easy to avoid; methods of creating them are sometimes regulated by governmental gaming commissions.
It has been alleged that some gaming machines' software is deliberately biased to prevent true randomness, in the interests of maximizing their owners' revenue; the history of biased machines in the gambling industry is the reason government inspectors attempt to supervise the machines—electronic equipment has extended the range of supervision.
Fifth century BC Athenian democracy developed out of a notion of isonomia (equality of political rights), and random selection was a principal way of achieving this fairness.
Although it may seem strange to those used to modern liberal democracy, the Athenian Greeks considered elections to be essentially undemocratic.
In addition, allotment prevented the corrupt practice of buying votes as no one could know who would be selected as a magistrate, or to sit on a jury.
Allotment, also called sortition, is today used in the selection of jurors in Anglo-Saxon legal systems like the UK and United States.
These applications are useful in auditing (for determining samples - such as invoices) and experimental design (for example in the creation of double-blind trials).
For example, an experiment might collect X-rays from an astronomical source and then analyze the result for periodic signals.
Pseudo-random numbers are frequently used in simulation of statistical events, a very simple example being the outcome of tossing a coin.
A ubiquitous use of unpredictable random numbers is in cryptography, which underlies most of the schemes which attempt to provide security in modern communications (e.g., confidentiality, authentication, electronic commerce, etc.).
To illustrate, imagine if a simple 32 bit linear congruential pseudo-random number generator of the type supplied with most programming languages (e.g., as the 'rand' or 'rnd' function) is used as a source of keys.
Even if a better random number generator is used, it might be insecure (e.g., the seed might be guessable), producing predictable keys and reducing security to nil.
Truly random numbers are absolutely required to be assured of the theoretical security provided by the one-time pad — the only provably unbreakable encryption algorithm.
Often people mistake order for randomness based on lack of information; e.g., Jackson Pollock's drip paintings, Helen Frankenthaler's abstractions (e.g., "For E.M.").
At one point in the novel, Diderot speaks directly to the reader: Now I, as the author of this novel might have them set upon by thieves, or I might have them rest by a tree until the rain stops, but in fact they kept on walking and then near night-fall they could see the light of an inn in the distance.
Other examples include selecting, or generating, a "Random Quote of the Day" for a website, or determining which way a villain might move in a computer game.