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Gambler's Fallacy
The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the belief that, if an event (whose occurrences are Independent and identically distributed random variables, independent and identically distributed) has occurred less frequently than expected, it is more likely to happen again in the future (or vice versa). The fallacy is commonly associated with gambling, where it may be believed, for example, that the next dice roll is more likely to be six than is usually the case because there have recently been fewer than the Expected value, expected number of sixes. The term "Monte Carlo fallacy" originates from an example of the phenomenon, in which the roulette wheel spun black 26 times in succession at the Monte Carlo Casino in 1913. Examples Coin toss The gambler's fallacy can be illustrated by considering the repeated toss of a fair coin. The outcomes in different tosses are statistically independent and the probability of getti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independent And Identically Distributed Random Variables
Independent or Independents may refer to: Arts, entertainment, and media Artist groups * Independents (artist group), a group of modernist painters based in Pennsylvania, United States * Independentes (English: Independents), a Portuguese artist group Music Groups, labels, and genres * Independent music, a number of genres associated with independent labels * Independent record label, a record label not associated with a major label * Independent Albums, American albums chart Albums * ''Independent'' (Ai album), 2012 * ''Independent'' (Faze album), 2006 * ''Independent'' (Sacred Reich album), 1993 Songs * "Independent" (song), a 2007 song by Webbie * "Independent", a 2002 song by Ayumi Hamasaki from '' H'' News media organizations * Independent Media Center (also known as Indymedia or IMC), an open publishing network of journalist collectives that report on political and social issues, e.g., in ''The Indypendent'' newspaper of NYC * ITV (TV network) (Independent Televi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Daniel M
Daniel commonly refers to: * Daniel (given name), a masculine given name and a surname * List of people named Daniel * List of people with surname Daniel * Daniel (biblical figure) * Book of Daniel, a biblical apocalypse, "an account of the activities and visions of Daniel" Daniel may also refer to: Arts and entertainment Literature * ''Daniel'' (Old English poem), an adaptation of the Book of Daniel * ''Daniel'', a 2006 novel by Richard Adams * ''Daniel'' (Mankell novel), 2007 Music * "Daniel" (Bat for Lashes song) (2009) * "Daniel" (Elton John song) (1973) * "Daniel", a song from '' Beautiful Creature'' by Juliana Hatfield * ''Daniel'' (album), a 2024 album by Real Estate Other arts and entertainment * ''Daniel'' (1983 film), by Sidney Lumet * ''Daniel'' (2019 film), a Danish film * Daniel (comics), a character in the ''Endless'' series Businesses * Daniel (department store), in the United Kingdom * H & R Daniel, a producer of English porcelain between 1827 and 18 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A Priori And A Posteriori
('from the earlier') and ('from the later') are Latin phrases used in philosophy to distinguish types of knowledge, justification, or argument by their reliance on experience. knowledge is independent from any experience. Examples include mathematics,Some associationist philosophers have contended that mathematics comes from experience and is not a form of any ''a priori'' knowledge () tautologies and deduction from pure reason. Galen Strawson has stated that an argument is one in which "you can see that it is true just lying on your couch. You don't have to get up off your couch and go outside and examine the way things are in the physical world. You don't have to do any science." () knowledge depends on empirical evidence. Examples include most fields of science and aspects of personal knowledge. The terms originate from the analytic methods found in '' Organon'', a collection of works by Aristotle. Prior analytics () is about deductive logic, which comes from ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exchangeable Random Variables
In statistics, an exchangeable sequence of random variables (also sometimes interchangeable) is a sequence ''X''1, ''X''2, ''X''3, ... (which may be finitely or infinitely long) whose joint probability distribution does not change when the positions in the sequence in which finitely many of them appear are altered. In other words, the joint distribution is invariant to finite permutation. Thus, for example the sequences : X_1, X_2, X_3, X_4, X_5, X_6 \quad \text \quad X_3, X_6, X_1, X_5, X_2, X_4 both have the same joint probability distribution. It is closely related to the use of independent and identically distributed random variables in statistical models. Exchangeable sequences of random variables arise in cases of simple random sampling. Definition Formally, an exchangeable sequence of random variables is a finite or infinite sequence ''X''1, ''X''2, ''X''3, ... of random variables such that for any finite permutation σ of the indices 1, 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Empirical Evidence
Empirical evidence is evidence obtained through sense experience or experimental procedure. It is of central importance to the sciences and plays a role in various other fields, like epistemology and law. There is no general agreement on how the terms ''evidence'' and ''empirical'' are to be defined. Often different fields work with quite different conceptions. In epistemology, evidence is what Justification (epistemology), justifies beliefs or what determines whether holding a certain belief is rational. This is only possible if the evidence is possessed by the person, which has prompted various epistemologists to conceive evidence as private mental states like experiences or other beliefs. In philosophy of science, on the other hand, evidence is understood as that which ''Scientific method#Confirmation, confirms'' or ''disconfirms'' Hypothesis#Scientific hypothesis, scientific hypotheses and arbitrates between competing theories. For this role, evidence must be public and uncont ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayesian Inference
Bayesian inference ( or ) is a method of statistical inference in which Bayes' theorem is used to calculate a probability of a hypothesis, given prior evidence, and update it as more information becomes available. Fundamentally, Bayesian inference uses a prior distribution to estimate posterior probabilities. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the dynamic analysis of a sequence of data. Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law. In the philosophy of decision theory, Bayesian inference is closely related to subjective probability, often called "Bayesian probability". Introduction to Bayes' rule Formal explanation Bayesian inference derives the posterior probability as a consequence of two antecedents: a prior probability and a "likelihood function" derive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bias (statistics)
In the field of statistics, bias is a systematic tendency in which the methods used to gather data and estimate a sample statistic present an inaccurate, skewed or distorted ('' biased'') depiction of reality. Statistical bias exists in numerous stages of the data collection and analysis process, including: the source of the data, the methods used to collect the data, the estimator chosen, and the methods used to analyze the data. Data analysts can take various measures at each stage of the process to reduce the impact of statistical bias in their work. Understanding the source of statistical bias can help to assess whether the observed results are close to actuality. Issues of statistical bias has been argued to be closely linked to issues of statistical validity. Statistical bias can have significant real world implications as data is used to inform decision making across a wide variety of processes in society. Data is used to inform lawmaking, industry regulation, corp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blackjack
Blackjack (formerly black jack or ''vingt-un'') is a casino banking game. It is the most widely played casino banking game in the world. It uses decks of 52 cards and descends from a global family of casino banking games known as " twenty-one". This family of card games also includes the European games '' vingt-et-un'' and pontoon, and the Russian game . The game is a comparing card game where players compete against the dealer, rather than each other. History Blackjack's immediate precursor was the English version of '' twenty-one'' called ''vingt-un'', a game of unknown provenance. The first written reference is found in a book by the Spanish author Miguel de Cervantes. Cervantes was a gambler, and the protagonists of his " Rinconete y Cortadillo", from ''Novelas Ejemplares'', are card cheats in Seville. They are proficient at cheating at ''veintiuno'' (Spanish for "twenty-one") and state that the object of the game is to reach 21 points without going over and that the ac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Card Counting
Card counting is a blackjack betting strategy, strategy used to determine whether the player or the dealer has an advantage on the next hand. Card counters try to overcome the casino house edge by keeping a running count of high and low valued cards dealt. They generally bet more when they have an advantage and less when the dealer has an advantage. They also change playing decisions based on the composition of the deck and sometimes play in teams. Basics Card counting is based on statistical evidence that high cards (aces, 10s, and 9s) benefit the player, while low cards, (2s, 3s, 4s, 5s, 6s, and 7s) benefit the dealer. High cards benefit the player in the following ways: # They increase the player's probability of hitting a Blackjack, which often pays out at 3 to 2 odds (although some casinos pay at 6 to 5). # Doubling down increases expected value. The elevated ratio of tens and aces improves the probability that doubling down will succeed. The most common hand values that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joker (playing Card)
The Joker is a playing card found in most modern French-suited playing cards, French-suited card decks, as an addition to the standard four Playing card suit, suits (Clubs, Diamonds, Hearts, and Spades). Since the second half of the 20th century, they have also been found in Spanish-suited playing cards, Spanish- and Italian playing cards, Italian-suited decks, excluding stripped decks. The Joker originated in the United States during the American Civil War, Civil War, and was created as a Trump (card games), trump card for the game of Euchre. It has since been adopted into many other card games, where it often acts as a Wild card (cards), wild card, but may have other functions such as the top trump, a skip card (forcing another player to miss a turn), the lowest-ranking card, the highest-value card, or a card of a different value from the rest of the pack (see e.g. Zwicker (card game), Zwicker which has six Jokers with this function). By contrast, a wild card is any card that m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permutation
In mathematics, a permutation of a set can mean one of two different things: * an arrangement of its members in a sequence or linear order, or * the act or process of changing the linear order of an ordered set. An example of the first meaning is the six permutations (orderings) of the set : written as tuples, they are (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). Anagrams of a word whose letters are all different are also permutations: the letters are already ordered in the original word, and the anagram reorders them. The study of permutations of finite sets is an important topic in combinatorics and group theory. Permutations are used in almost every branch of mathematics and in many other fields of science. In computer science, they are used for analyzing sorting algorithms; in quantum physics, for describing states of particles; and in biology, for describing RNA sequences. The number of permutations of distinct objects is factorial, us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Independence
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes. Two events are independent, statistically independent, or stochastically independent if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds. Similarly, two random variables are independent if the realization of one does not affect the probability distribution of the other. When dealing with collections of more than two events, two notions of independence need to be distinguished. The events are called pairwise independent if any two events in the collection are independent of each other, while mutual independence (or collective independence) of events means, informally speaking, that each event is independent of any combination of other events in the collection. A similar notion exists for collections of random variables. Mutual independence implies pairwise independence ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
