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Statistical randomness
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<p>A numeric <a href="/facts/Sequence/gV2S4uqp">sequence</a> is said to be statistically random when it contains no recognizable <a href="/facts/Pattern/mzD7uLQa">patterns</a> or regularities; sequences such as the results of an ideal <a href="/facts/Dice/qBnylzwJ">dice roll</a> or the digits of <a href="/facts/Pi/vC0UBj1q">π</a> exhibit statistical randomness. </p><p>Statistical randomness does not necessarily imply "true" <a href="/facts/Randomness/QJQBoEX5">randomness</a>, i.e., objective <a href="/facts/Predictability/FNSpNGQF">unpredictability</a>. <a href="/facts/Pseudorandomness/kfs1wfhY">Pseudorandomness</a> is sufficient for many uses, such as statistics, hence the name <i>statistical</i> randomness. </p><p><i>Global randomness</i> and <i>local randomness</i> are different. Most philosophical conceptions of randomness are global—because they are based on the idea that "in the long run" a sequence looks truly random, even if certain sub-sequences would <i>not</i> look random. In a "truly" random sequence of numbers of sufficient length, for example, it is probable there would be long sequences of nothing but repeating numbers, though on the whole the sequence might be random. <i>Local</i> randomness refers to the idea that there can be minimum sequence lengths in which random distributions are approximated. Long stretches of the same numbers, even those generated by "truly" random processes, would diminish the "local randomness" of a sample (it might only be locally random for sequences of 10,000 numbers; taking sequences of less than 1,000 might not appear random at all, for example). </p><p>A sequence exhibiting a pattern is not thereby proved not statistically random. According to principles of <a href="/facts/Ramsey_theory/CzLLM2j8">Ramsey theory</a>, sufficiently large objects must necessarily contain a given substructure ("<a href="/facts/Complete_disorder_is_impossible/xamFTKCf">complete disorder is impossible</a>"). </p><p>Legislation concerning <a href="/facts/Gambling/Hgw4a9DH">gambling</a> imposes certain standards of statistical randomness to <a href="/facts/Slot_machine/n5FBPkbq">slot machines</a>. </p>