Randomness
In common usage, randomness is the apparent or actual lack of definite pattern or predictability in information.
[1][2] A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination.
[note 1] For example, when throwing two dice, the outcome of any particular roll is unpredictable, but a sum of 7 will tend to occur twice as often as 4.
In statistics, a random variable is an assignment of a numerical value to each possible outcome of an event space.
[2] According to Ramsey theory, pure randomness (in the sense of there being no discernible pattern) is impossible, especially for large structures.
Many ancient peoples threw dice to determine fate, and this later evolved into games of chance.
[7][8] Beyond religion and games of chance, randomness has been attested for sortition since at least ancient Athenian democracy in the form of a kleroterion.
It was only in the 16th century that Italian mathematicians began to formalize the odds associated with various games of chance.
[10] The early part of the 20th century saw a rapid growth in the formal analysis of randomness, as various approaches to the mathematical foundations of probability were introduced.
The modern evolutionary synthesis ascribes the observed diversity of life to random genetic mutations followed by natural selection.
[14][15][16] Several authors also claim that evolution (and sometimes development) requires a specific form of randomness, namely the introduction of qualitatively new behaviors.
For instance, insects in flight tend to move about with random changes in direction, making it difficult for pursuing predators to predict their trajectories.
Pioneers of this field include Andrey Kolmogorov and his student Per Martin-Löf, Ray Solomonoff, and Gregory Chaitin.
This allows surveys of completely random groups of people to provide realistic data that is reflective of the population.
Noise consists of numerous transient disturbances, with a statistically randomized time distribution.
Randomness can be seen as conflicting with the deterministic ideas of some religions, such as those where the universe is created by an omniscient deity who is aware of all past and future events.
This is one of the rationales for religious opposition to evolution, which states that non-random selection is applied to the results of random genetic variation.
In most of its mathematical, political, social and religious uses, randomness is used for its innate "fairness" and lack of bias.
The ability to produce random numbers fairly is vital to electronic gambling, and, as such, the methods used to create them are usually regulated by government Gaming Control Boards.
In fact, randomness has been used for games of chance throughout history, and to select out individuals for an unwanted task in a fair way (see drawing straws).
Computational solutions for some types of problems use random numbers extensively, such as in the Monte Carlo method and in genetic algorithms.
These include measures based on frequency, discrete transforms, complexity, or a mixture of these, such as the tests by Kak, Phillips, Yuen, Hopkins, Beth and Dai, Mund, and Marsaglia and Zaman.
[26] Quantum nonlocality has been used to certify the presence of genuine or strong form of randomness in a given string of numbers.
[27] Popular perceptions of randomness are frequently mistaken, and are often based on fallacious reasoning or intuitions.
However, it is fallacious to apply this logic to systems designed and known to make all outcomes equally likely, such as shuffled cards, dice, and roulette wheels.
However, an analysis of the probability spaces would reveal that the contestant has received new information, and that changing to the other door would increase their chances of winning.
