Randomness has many uses in science, art, statistics, cryptography, gaming, gambling, and other fields. For example, random assignment in randomized controlled trials helps scientists to test hypotheses, and random numbers or pseudorandom numbers help video games such as video poker.

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These uses have different levels of requirements, which leads to the use of different methods. Mathematically, there are distinctions between randomization, pseudorandomization, and quasirandomization, as well as between random number generators and pseudorandom number generators. 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.

Random numbers have uses in physics such as electronic noise studies, engineering, and operations research. Many methods of statistical analysis, such as the bootstrap method, require random numbers. Monte Carlo methods in physics and computer science require random numbers.

Random numbers are often used in parapsychology as a test of precognition.

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.).

For example, if a user wants to use an encryption algorithm, it is best that they select a random number as the key. The selection must have high entropy (i.e., unpredictability) to any attacker, thus increasing attack difficulty. With keys having low entropy (i.e., relatively easily guessable by attackers), security is likely to be compromised. 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. There will only be some four billion possible values produced before the generator repeats itself. A suitably motivated adversary could simply test them all; this is practical as of 2010, using readily available computers. Even if a linear congruential RNG is used with 1000-bit parameters, it is a simple exercise in linear algebra to recover the modulus m, and the constants a and b, where x' = ax +b (mod m), given only five consecutive values. 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. (A vulnerability of this sort was famously discovered in an early release of Netscape Navigator, forcing the authors to quickly find a source of "more random" random numbers.) For these applications, truly random numbers are ideal, and very high quality pseudo-random numbers are necessary if truly random numbers, such as coming from a hardware random number generator, are unavailable.

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. Furthermore, those random sequences cannot be reused and must never become available to any attacker, which implies a continuously operable generator. See Venona for an example of what happens when these requirements are violated when using a one-time pad.

For cryptographic purposes, one normally assumes some upper limit on the work an adversary can do (usually this limit is astronomically sized). If one has a pseudo-random number generator whose output is "sufficiently difficult" to predict, one can generate true random numbers to use as the initial value (i.e., the seed), and then use the pseudo-random number generator to produce numbers for use in cryptographic applications. Such random number generators are called cryptographically secure pseudo-random number generators, and several have been implemented (for example, the /dev/urandom device available on most Unixes, the Yarrow and Fortuna designs, server, and AT&T Bell Laboratories "truerand"). As with all cryptographic software, there are subtle issues beyond those discussed here, so care is certainly indicated in actual practice. In any case, it is sometimes impossible to avoid the need for true (i.e., hardware-based) random number generators.

Since a requirement in cryptography is high entropy, any published random sequence is a poor choice, as are such sequences as the digits in an irrational number such as the φ or even in transcendental numbers such as π, or e. All are available to an enterprising attacker. Put another way, in cryptography, random bit streams need to be not only random, but also secret and hence unpredictable. Public or third-party sources of random values, or random values computed from publicly observable phenomena (weather, sports game results, stock prices), are almost never cryptographically acceptable. Their use may be tempting, but in reality, they permit easier attacks than attacking the cryptography.

Since most cryptographic applications require a few thousand bits at most, slow random number generators serve well—if they are actually random. This use of random generators is important; many informed observers^[who?] believe every computer should have a way to generate true random numbers.

Some aesthetic theories claim to be based on randomness in one way or another. Little testing is done in these situations, and so claims of reliance on and use of randomness are generally poorly based in definite theory and more on an impression of randomness from technical fields.

An example of a need for randomness sometimes occurs in arranging items in an art exhibit. Usually this is avoided by using a theme. As John Cage pointed out, "While there are many ways that sounds might be produced [i.e., in terms of patterns], few are attempted". Similarly, the arrangement of art in exhibits is often deliberately non-random. One case of this was Hitler's attempt to portray modern art in the worst possible light by arranging works in worst possible manner.^{[citation needed]} A case can be made for trying to make art in the worst possible way; i.e., either as anti-art, or as actually random art.

Dadaism, as well as many other movements in art and letters, has attempted to accommodate and acknowledge randomness in various ways. 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."). Thus, in some theories of art, all art is random in that it's "just paint and canvas" (the explanation of Frank Stella's work).

Similarly, the "unexpected" ending is part of the nature of interesting literature. An example of this is Denis Diderot's novel Jacques le fataliste (literally: James the Fatalist; sometimes referred to as Jacques the Fatalist or Jacques the Servant and his Master). 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. [not an exact quote]

Diderot was making the point that the novel (then a recent introduction to European literature) seemed random (in the sense of being invented out of thin air by the author, not in a modern technical sense). See also Eugenio Montale, Theatre of the Absurd.

Randomness in music includes John Cage's chance-derived Music of Changes, stochastic music, aleatoric music, indeterminate music, or generative music.

Random numbers are also used in situations where "fairness" is approximated by randomization, such as selecting jurors and military draft lotteries. In the Book of Numbers (33:54), Moses commands the Israelites to apportion the land by lot.

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.

Weaker forms of randomness are also closely associated with hash algorithms and in creating amortized searching and sorting algorithms.

• Black swan theory
• Flipism