title: Terry Serpico

text: Serpico was born in Fort Sill in Lawton, Oklahoma, the youngest of three children. He became interested in acting after graduating from high school. He attended Boston University before transferring to and graduating from the State University of New York at Purchase in 1989. He is of German and Italian descent.


title: Terry Serpico

text: Serpico began his career as a stunt performer. In 1997, he was cast in his first major acting role in "Donnie Brasco". In television, Serpico has guest-starred on such shows as "Law & Order", "", "", and "Person of Interest".


title: Terry Serpico

text: He played Mickey Mantle in the ESPN miniseries "The Bronx Is Burning". He has enjoyed a recurring role in "Rescue Me", and a starring role as Col. Frank Sherwood in "Army Wives".


title: Cauchy sequence

text: In mathematics, a Cauchy sequence (; ), named after Augustin-Louis Cauchy, is a sequence whose elements become arbitrarily close to each other as the sequence progresses. More precisely, given any small positive distance, all but a finite number of elements of the sequence are less than that given distance from each other.


title: Cauchy sequence

text: It is not sufficient for each term to become arbitrarily close to the term. For instance, in the sequence of square roots of natural numbers:


title: Cauchy sequence

text: However, with growing values of the index , the terms formula_3 become arbitrarily large. So, for any index and distance , there exists an index big enough such that formula_4 (Actually, any formula_5 suffices.) As a result, despite how far one goes, the remaining terms of the sequence never get close to ; hence the sequence is not Cauchy.


title: Cauchy sequence

text: The utility of Cauchy sequences lies in the fact that in a complete metric space (one where all such sequences are known to converge to a limit), the criterion for convergence depends only on the terms of the sequence itself, as opposed to the definition of convergence, which uses the limit value as well as the terms. This is often exploited in algorithms, both theoretical and applied, where an iterative process can be shown relatively easily to produce a Cauchy sequence, consisting of the iterates, thus fulfilling a logical condition, such as termination.


title: Cauchy sequence

text: Generalizations of Cauchy sequences in more abstract uniform spaces exist in the form of Cauchy filters and Cauchy nets.


title: Cauchy sequence

text: of real numbers is called a Cauchy sequence if for every positive real number formula_7 there is a positive integer "N" such that for all natural numbers formula_8


title: Cauchy sequence

text: where the vertical bars denote the absolute value. In a similar way one can define Cauchy sequences of rational or complex numbers. Cauchy formulated such a condition by requiring formula_10 to be infinitesimal for every pair of infinite "m", "n".


title: Cauchy sequence

text: For any real number "r", the sequence of truncated decimal expansions of "r" forms a Cauchy sequence. For example, when formula_11 this sequence is (3, 3.1, 3.14, 3.141, ...). The "m"th and "n"th terms differ by at most formula_12 when "m" < "n", and as "m" grows this becomes smaller than any fixed positive number formula_13


title: Cauchy sequence

text: If formula_14 is a sequence in the set formula_15 then a "modulus of Cauchy convergence" for the sequence is a function formula_16 from the set of natural numbers to itself, such that for all natural numbers formula_17 and natural numbers formula_18 formula_19


title: Cauchy sequence

text: Any sequence with a modulus of Cauchy convergence is a Cauchy sequence. The existence of a modulus for a Cauchy sequence follows from the well-ordering property of the natural numbers (let formula_20 be the smallest possible formula_21 in the definition of Cauchy sequence, taking formula_22 to be formula_23). The existence of a modulus also follows from the principle of dependent choice, which is a weak form of the axiom of choice, and it also follows from an even weaker condition called AC. "Regular Cauchy sequences" are sequences with a given modulus of Cauchy convergence (usually formula_24 or formula_25). Any Cauchy sequence with a modulus of Cauchy convergence is equivalent to a regular Cauchy sequence; this can be proven without using any form of the axiom of choice.


title: Cauchy sequence

text: Moduli of Cauchy convergence are used by constructive mathematicians who do not wish to use any form of choice. Using a modulus of Cauchy convergence can simplify both definitions and theorems in constructive analysis. Regular Cauchy sequences were used by and by in constructive mathematics textbooks.


title: Cauchy sequence

text: Since the definition of a Cauchy sequence only involves metric concepts, it is straightforward to generalize it to any metric space "X".


title: Cauchy sequence

text: To do so, the absolute value formula_26 is replaced by the distance formula_27 (where "d" denotes a metric) between formula_28 and formula_29


title: Cauchy sequence

text: is Cauchy, if for every positive real number formula_32 there is a positive integer formula_21 such that for all positive integers formula_8 the distance


title: Cauchy sequence

text: Roughly speaking, the terms of the sequence are getting closer and closer together in a way that suggests that the sequence ought to have a limit in "X".


title: Cauchy sequence

text: Nonetheless, such a limit does not always exist within "X": the property of a space that every Cauchy sequence converges in the space is called "completeness", and is detailed below.


title: Cauchy sequence

text: A metric space ("X", "d") in which every Cauchy sequence converges to an element of "X" is called complete.


title: Cauchy sequence

text: The real numbers are complete under the metric induced by the usual absolute value, and one of the standard constructions of the real numbers involves Cauchy sequences of rational numbers. In this construction, each equivalence class of Cauchy sequences of rational numbers with a certain tail behavior—that is, each class of sequences that get arbitrarily close to one another— is a real number.


title: Cauchy sequence

text: A rather different type of example is afforded by a metric space "X" which has the discrete metric (where any two distinct points are at distance 1 from each other). Any Cauchy sequence of elements of "X" must be constant beyond some fixed point, and converges to the eventually repeating term.


title: Cauchy sequence

text: There are sequences of rationals that converge (in formula_37) to irrational numbers; these are Cauchy sequences having no limit in formula_38 In fact, if a real number "x" is irrational, then the sequence ("x"), whose "n"-th term is the truncation to "n" decimal places of the decimal expansion of "x", gives a Cauchy sequence of rational numbers with irrational limit "x". Irrational numbers certainly exist in formula_39 for example:


title: Cauchy sequence

text: The open interval formula_46 in the set of real numbers with an ordinary distance in formula_37 is not a complete space: there is a sequence formula_48 in it, which is Cauchy (for arbitrarily small distance bound formula_49 all terms formula_50 of formula_51 fit in the formula_52 interval), however does not converge in formula_53 — its 'limit', number 0, does not belong to the space formula_54


title: Cauchy sequence

text: These last two properties, together with the Bolzano–Weierstrass theorem, yield one standard proof of the completeness of the real numbers, closely related to both the Bolzano–Weierstrass theorem and the Heine–Borel theorem. Every Cauchy sequence of real numbers is bounded, hence by Bolzano–Weierstrass has a convergent subsequence, hence is itself convergent. This proof of the completeness of the real numbers implicitly makes use of the least upper bound axiom. The alternative approach, mentioned above, of the real numbers as the completion of the rational numbers, makes the completeness of the real numbers tautological.


title: Cauchy sequence

text: One of the standard illustrations of the advantage of being able to work with Cauchy sequences and make use of completeness is provided by consideration of the summation of an infinite series of real numbers


title: Cauchy sequence

text: (or, more generally, of elements of any complete normed linear space, or Banach space). Such a series


title: Cauchy sequence

text: formula_62 is considered to be convergent if and only if the sequence of partial sums formula_63 is convergent, where formula_64 It is a routine matter to determine whether the sequence of partial sums is Cauchy or not, since for positive integers formula_65


title: Cauchy sequence

text: If formula_67 is a uniformly continuous map between the metric spaces "M" and "N" and ("x") is a Cauchy sequence in "M", then formula_68 is a Cauchy sequence in "N". If formula_69 and formula_70 are two Cauchy sequences in the rational, real or complex numbers, then the sum formula_71 and the product formula_72 are also Cauchy sequences.


title: Cauchy sequence

text: There is also a concept of Cauchy sequence for a topological vector space formula_53: Pick a local base formula_74 for formula_53 about 0; then (formula_76) is a Cauchy sequence if for each member formula_77 there is some number formula_21 such that whenever


title: Cauchy sequence

text: formula_79 is an element of formula_80 If the topology of formula_53 is compatible with a translation-invariant metric formula_82 the two definitions agree.


title: Cauchy sequence

text: Since the topological vector space definition of Cauchy sequence requires only that there be a continuous "subtraction" operation, it can just as well be stated in the context of a topological group: A sequence formula_83 in a topological group formula_84 is a Cauchy sequence if for every open neighbourhood formula_85 of the identity in formula_84 there exists some number formula_21 such that whenever formula_88 it follows that formula_89 As above, it is sufficient to check this for the neighbourhoods in any local base of the identity in formula_90


title: Cauchy sequence

text: As in the construction of the completion of a metric space, one can furthermore define the binary relation on Cauchy sequences in formula_84 that formula_83 and formula_93 are equivalent if for every open neighbourhood formula_85 of the identity in formula_84 there exists some number formula_21 such that whenever formula_88 it follows that formula_98 This relation is an equivalence relation: It is reflexive since the sequences are Cauchy sequences. It is symmetric since formula_99 which by continuity of the inverse is another open neighbourhood of the identity. It is transitive since formula_100 where formula_101 and formula_102 are open neighbourhoods of the identity such that formula_103; such pairs exist by the continuity of the group operation.


title: Cauchy sequence

text: Then a sequence formula_69 in formula_84 is said to be Cauchy (with respect to formula_109) if and only if for any formula_22 there is formula_21 such that for all formula_112


title: Cauchy sequence

text: Technically, this is the same thing as a topological group Cauchy sequence for a particular choice of topology on formula_113 namely that for which formula_109 is a local base.


title: Cauchy sequence

text: The set formula_115 of such Cauchy sequences forms a group (for the componentwise product), and the set formula_116 of null sequences (sequences such that formula_117) is a normal subgroup of formula_118 The factor group formula_119 is called the completion of formula_84 with respect to formula_121


title: Cauchy sequence

text: One can then show that this completion is isomorphic to the inverse limit of the sequence formula_122


title: Cauchy sequence

text: An example of this construction familiar in number theory and algebraic geometry is the construction of the formula_123-adic completion of the integers with respect to a prime formula_124 In this case, formula_84 is the integers under addition, and formula_126 is the additive subgroup consisting of integer multiples of formula_127


title: Cauchy sequence

text: If formula_109 is a cofinal sequence (that is, any normal subgroup of finite index contains some formula_126), then this completion is canonical in the sense that it is isomorphic to the inverse limit of formula_130 where formula_109 varies over normal subgroups of finite index. For further details, see Ch. I.10 in Lang's "Algebra".


title: Cauchy sequence

text: A real sequence formula_132 has a natural hyperreal extension, defined for hypernatural values "H" of the index "n" in addition to the usual natural "n". The sequence is Cauchy if and only if for every infinite "H" and "K", the values formula_133 and formula_134 are infinitely close, or adequal, that is,


title: Cauchy sequence

text: introduced a notion of Cauchy completion of a category. Applied to formula_36 (the category whose objects are rational numbers, and there is a morphism from "x" to "y" if and only if formula_137), this Cauchy completion yields formula_138 (again interpreted as a category using its natural ordering).


title: Sam Corlett

text: Corlett was born and raised on the Central Coast, New South Wales, Australia, with his parents being a Counsellor and a Tradesman. Corlett was a professional model before he became an actor, working for Viviens Models. Corlett also had a high level involvement in sport growing up.


title: Sam Corlett

text: In 2020, Corlett secured a recurring role as Caliban (Prince of Hell) for 14 episodes of "Chilling Adventures of Sabrina" opposite Kiernan Shipka, which was filmed in Vancouver, Canada.


title: Sam Corlett

text: Corlett plays the main role as Leif Eriksson in History's new "Vikings" sequel "" which was released on Netflix on 25 February 2022. Corlett teams up with Leo Suter who plays Harald Sigurdsson and Frida Gustavsson as Freydís Eiríksdóttir in the Viking saga, set in a time over a century after the Lothbrok era. Leif Eriksson was believed to be one of the first Europeans to explore North America. Whilst filming "" at Ashford Studios in Wicklow, Ireland, Corlett started his working day with meditation, followed by a seven-kilometre run, then a swim in the very cold Irish Sea and some weight training each evening.


title: Nadsat

text: Nadsat is a fictional register or argot used by the teenage gang members in Anthony Burgess's dystopian novel "A Clockwork Orange". Burgess was a linguist and he used this background to depict his characters as speaking a form of Russian-influenced English. The name comes from the Russian suffix equivalent of "-teen" as in "thirteen" (-надцать, "-nad·tsat"). Nadsat was also used in Stanley Kubrick's film adaptation of the book.


title: Nadsat

text: Nadsat is a mode of speech used by the "nadsat", members of the teen subculture in the novel "A Clockwork Orange". The narrator and protagonist of the book, Alex, uses it in first-person style to relate the story to the reader. He also uses it to communicate with other characters in the novel, such as his "droogs", parents, victims and any authority-figures with whom he comes in contact. As with many speakers of non-standard varieties of English, Alex is capable of speaking standard English when he wants to. It is not a written language: the sense that readers get is of a transcription of vernacular speech.


title: Nadsat

text: Nadsat is English with some borrowed words from Russian. It also contains influences from Cockney rhyming slang, the King James Bible, German, some words of unclear origin and some that Burgess invented. The word "nadsat" is the suffix of Russian numerals from 11 to 19 (-надцать). The suffix is an almost exact linguistic parallel to the English '-teen' and is derived from "на", meaning "on" and a shortened form of "десять", the number ten. "Droog" is Russian друг "close friend". Some of the words are almost childish plays on English words, such as ("egg") and ("apology"), as well as regular English slang "sod" and "snuff it". The word "like" and the expression "the old" are often used as fillers or discourse markers.


title: Nadsat

text: The original 1991 translation of Burgess's book into Russian solved the problem of how to illustrate the Nadsat words by using transliterated, slang English words in places where Burgess had used Russian onesfor example, "droogs" became "фрэнды" (). Borrowed English words with Russian inflection were widely used in Russian slang, especially among Russian hippies in the 1970s–1980s.


title: Nadsat

text: Burgess, a polyglot who loved language in all its forms, was aware that linguistic slang was of a constantly changing nature. He knew that if he used contemporary modes of speech, the novel would very quickly become dated. His use of Nadsat was pragmatic; he needed his narrator to have a unique voice that would remain ageless, while reinforcing Alex's indifference to his society's norms, and to suggest that youth subculture was independent from the rest of society. In "A Clockwork Orange", Alex's interrogators describe the source of his argot as "subliminal penetration".


title: Nadsat

text: Russian influences play the biggest role in Nadsat. Most of those Russian-influenced words are slightly anglicized loan-words, often maintaining the original Russian pronunciation. One example is the Russian word "Lyudi", which is anglicized to , meaning "people". Another Russian word is "Bábushka" which is anglicized to "baboochka", meaning "grandmother", "old woman". Some of the anglicised words are truncated, for example "pony" from "ponimát’", "to understand", or otherwise shortened, for example "veck" from "čelovék", "person", "man" (though the anglicized word "chelloveck" is also used in the book).


title: Nadsat

text: A further means of constructing Nadsat words is the employment of homophones (known as folk etymology). For example, one Nadsat term which may seem like an English composition, "horrorshow", actually stems from the Russian word for "good"; "khorosho", which sounds similar to "horrorshow". In this same manner many of the Russian loan-words become an English–Russian hybrid, with Russian origins, and English spellings and pronunciations. A further example is the Russian word for "head", "golová", which sounds similar to "Gulliver" known from "Gulliver’s Travels"; "Gulliver" became the Nadsat expression for the concept "head".


title: Nadsat

text: Many of Burgess's loanwords, such as "devotchka" ("girl") and "droog" ("friend") maintain both their relative spelling and meaning over the course of translation.


title: Nadsat

text: Additional words were borrowed from other languages: A (possibly Saudi-owned) hotel was named 'Al Idayyin, an Arabic-sounding variant on “Holiday Inn” Hotel chain, while also alluding to the name Aladdin.


title: Nadsat

text: Nadsat's English slang is constructed with common language-formation techniques. Some words are blended, others clipped or compounded. In Nadsat-language a "fit of laughter" becomes a "guff" (shortened version of "guffawing"); a "skeleton key" becomes a "polyclef" ("many keys"); and the "state jail" is blended to the "staja", which has the double entendre "stager", so that its prisoners got there by a staged act of corruption, as revenge by the state, an interpretation that would fit smoothly into the storyline. Many common English slang terms are simply shortened. A "cancer stick" which is (or was) a common English-slang expression for a "cigarette" is shortened to a "cancer".


title: Fast chess

text: Fast chess, also known as Speed chess, is a type of chess in which each player is given less time to consider their moves than normal tournament time controls allow. Fast chess is subdivided, by decreasing time controls, into rapid chess, blitz chess, and bullet chess. Armageddon chess is a particular variation of fast chess in which different rules apply for each of the two players.


title: Fast chess

text: The top ranked 2021 world rapid chess player is Magnus Carlsen from Norway, who is also the top ranked classical chess player. The top ranked blitz chess player at the beginning of 2022 is Hikaru Nakamura.


title: Fast chess

text: The top ranked 2021 women's rapid and blitz chess player is Hou Yifan from China, who is also the top ranked women's classical chess player.


title: Fast chess

text: The World Chess Federation (FIDE) divides time controls for chess into "classical" time controls, and the fast chess time controls. , for master-level players (with an Elo of 2200 or higher) the regulations state that at least 120 minutes per player (based on a 60-move game) must be allocated for a game to be rated on the "classical" list; for lower rated players this can be reduced to as little as 60 minutes. Games played faster than these time controls can be rated for rapid and blitz if they comply with the time controls for those categories.


title: Fast chess

text: Players of fast and blitz chess are exempt from the requirement to record their moves onto a scoresheet (A.2). The arbiter or their assistant is responsible for the recording in competitions (A.3.1.2, B.3.1.2). Electronic recording is preferred.


title: Fast chess

text: A fast chess game can be further divided into several categories, which are primarily distinguished by the selection of time controls. Games may be played with or without time increments per move.


title: Fast chess

text: Time controls for each player in a game of rapid chess are, according to FIDE, more than 10 minutes but less than 60 minutes. Rapid chess can be played with or without time increments for each move. When time increments are used, a player can automatically gain, for instance, ten more seconds on the clock after each move. When time increments are used, the total time per player for a 60-move game must be more than 10 minutes but less than 60 minutes. Rapid chess was called "active chess" by FIDE between 1987 and 1989.


title: Fast chess

text: For the FIDE World Rapid Championship, each player has 15 minutes plus 10 seconds additional time per move starting from move 1.


title: Fast chess

text: Time controls for each player in a game of blitz chess are, according to FIDE, 10 minutes or less per player. This can be played with or without an increment or delay per move, made possible by the adoption of digital clocks. Three minutes with a two-second increment is preferred. In the case of time increments, the total time per player for a 60-move game must be 10 minutes or less (hence averaging 10 seconds or less per move).


title: Fast chess

text: For the FIDE World Blitz Championship, each player has 3 minutes plus 2 additional seconds per move, starting from move 1.


title: Fast chess

text: A variant of blitz chess, bullet chess games have less than three minutes per player, based on a 40-move game; some chess servers rate one-minute-per-player games separately. Lower time controls are called 'hyperbullet' and 'ultrabullet' for 30-second-per-player and 15-second-per-player games, respectively. Other time control options for bullet games include 2 minutes with one-second increment or 1 minute with a two-second increment. The term "lightning" can also be applied to this variant.


title: Fast chess

text: Online bullet chess avoids practical problems associated with live bullet chess, particularly players accidentally knocking over the pieces. Playing online also allows premoving, or making a move before the opponent has taken their turn.


title: Fast chess

text: A variant of blitz chess where a drawn game is counted as a win for Black. This guarantees the game ends decisively, so it can be used as a final tie breaker game. It is used in tournaments such as Chess World Cup as a tie breaker.


title: Fast chess

text: To compensate for giving Black draw odds, White has more time on the clock. Common times are six minutes for White and five minutes for Black or five minutes for White and four minutes for Black. This can also be played with a small increment.


title: Fast chess

text: Some tournaments utilise a bidding system for individual players of each match to decide how little time they would be willing to play with as black. The player with the lowest bid for each match receives the black pieces with draw odds. This system minimises the perceived unfairness of Armageddon time controls that are decided in advance before a tournament with colours randomly allocated.


title: Fast chess

text: Before the advent of digital clocks, five minutes per side was the standard for blitz or speed chess. Before the introduction of chess clocks, chess club "rapid transit" tournaments had referees who called out every ten seconds. The Washington Divan (2445 15th St. NW) had regular weekly games and used a special clock that beeped every ten seconds to indicate the time to move. Players had to use their full ten seconds and move on the bell.


title: Fast chess

text: In 1988, Walter Browne formed the World Blitz Chess Association and its magazine "Blitz Chess", which folded in 2003.


title: Fast chess

text: In some chess tournaments and matches, the final standings of the contestants are decided by a series of games with ever-shortening control times as tie breaks. In this case, two games may be played with each time control, as playing with black or white pieces is not equally liked among players. The short time controls in fast chess reduce the amount of time available to consider each move, and may result in a frantic game, especially as time runs out. A player whose time runs out automatically loses, unless the opposing player has insufficient material to checkmate, in which case the game is a draw. "Losing on time" is possible at even the longer, traditional time controls, but is more common in blitz and rapid versions.


title: Fast chess

text: Play is governed by the FIDE Laws of Chess, except as modified by a specific tournament. However, in case of a dispute during a tournament, either player may stop the clock and call the arbiter to make a final and binding judgment.


title: Fast chess

text: Chess boxing uses a fast version for the chess component of the sport, granting 9 minutes for each side with no increment.


title: Fast chess

text: With the USCF, a game with more than 10 minutes affects the Quick rating, and the upper bounds for this rating is capped at 65 minutes per player. As 30-minute to 65-minute-per-player time controls are also under the Regular rating system, these games affect both the Quick and Regular ratings and are known as "dual-rated" games. However, the K factor (a statistic used for ratings) is reduced by comparison, meaning that players will either lose or gain (or rarely both) fewer rating points compared to a solely Quick or Regular game. Any time control over 65 minutes counts under the Regular rating only. All of these time controls include the delay added to the time control, such as a 60-minute game with a 5-second delay, which is still considered to be a 60-minute game, not a 65-minute game.


title: Fast chess

text: As of March 2013, the USCF has also added a separate Blitz class rating for any time control between 5 and 10 minutes per player. It is not possible for a game to be dual rated as both Blitz and Quick. Unlike Quick chess, 5 minutes can also mean game 3+2 (three minutes with a two-second increment).


title: Fast chess

text: Both official and unofficial FIDE-sponsored world championships for fast chess have been held since the 1970s.


title: Fast chess

text: In 1987, Garry Kasparov (the World Champion of classical chess at the time) and Nigel Short played a 6-game exhibition Rapid match ("Speed Chess Challenge") at the London Hippodrome, won by Kasparov 4–2.


title: Fast chess

text: The 1988 victory by Anatoly Karpov in Mazatlan was officially called the "World Active Championship", but FIDE changed the word 'active' to 'rapid' soon after.


title: Fast chess

text: In 1992, FIDE held the Women's World Rapid and Blitz Championship in Budapest, Hungary. Both Rapid and Blitz Championships were won by Susan Polgar.


title: Fast chess

text: The 2001 victory by Garry Kasparov in the FIDE World Cup of Rapid Chess (organized by the French Chess Federation in Cannes) was held contemporaneously to the Melody Amber rapids (thus splitting the top players between the two events), and it is sometimes considered to be official, although it was never named as a "championship" but rather a "world cup".


title: Fast chess

text: Viswanathan Anand won the official FIDE 2003 Rapid Championship at the 6th Cap d'Agde event. After no bids in 2004, FIDE optioned the 2005 Rapid to Cap d'Agde, but it was not held. Teimour Radjabov won the 2006 "7th Cap d’Agde Rapid Chess Tournament", but this had no FIDE status.


title: Fast chess

text: The yearly Frankfurt or Mainz events hosted by the "Chess Tigers" (2001–2010) were considered as the traditional rapid chess championship, and it often received world championship billing in the absence of an annual FIDE-recognized championship. In its last two years, the 2009 "Grenkeleasing World Rapid Chess Championship" in Mainz was won by Levon Aronian, and the 2010 "Open GRENKE Rapid World Championship" in Mainz was won by Gata Kamsky. The Association of Chess Professionals (ACP) also held a World Rapid Cup in some of these years, and the annual Amber chess tournament (1992 to 2011) also had a rapid segment. There was also occasionally a Eurotel Trophy or Intel Grand Prix event, each of which would be of high stature.


title: Fast chess

text: The first unofficial "Speed Chess Championship of the World" (or World Blitz Championship) was held in Herceg Novi on 8 April 1970. This was shortly after the first USSR versus the rest of the world match (in Belgrade), in which ten of these players also competed. Eleven Grandmasters and one International Master played a double round-robin tournament. Bobby Fischer won first place, with a score of 19 points out of a possible 22. Fischer scored seventeen wins, four draws, and one loss (to Viktor Korchnoi). Mikhail Tal was a distant second, 4½ points behind. Fischer won both games against each of Tal, Tigran Petrosian, and Vasily Smyslov; all of them were past World Champions.


title: Fast chess

text: By 1971, the Russian and Moscow five-minute championships had been going several years, with Tal, Bronstein, and Petrosian all having success. That year, Fischer played in a blitz tournament organised by the Manhattan Chess Club, and scored 21½/22. There were also strong tournaments in Bugojno (in 1978), which was won by Karpov; and Nikšić (in 1983), which was won by Kasparov.


title: Fast chess

text: In 1987, the S.W.I.F.T. super-tournament was held in Brussels, Belgium; first prize was shared by Garry Kasparov and Ljubomir Ljubojević. The first FIDE-sponsored World Blitz Championship was won by Mikhail Tal in 1988.


title: Fast chess

text: In 2000, Anand won the "Plus GSM World Blitz Chess Cup," which has since been referred to as a world championship, albeit inconsistently.


title: Fast chess

text: The second FIDE-recognized World Blitz Championship was won by Alexander Grischuk in 2006 in Rishon Lezion, Israel; the third World Blitz Championship was won by Vassily Ivanchuk in 2007. The 4th World Blitz Championship was held in Almaty in 2008, and it was won by Leinier Dominguez Pérez of Cuba.


title: Fast chess

text: In 2009 and 2010, there was an event called the "World Blitz Championship", held after the Tal Memorial in Moscow in November. It was won by Magnus Carlsen (in 2009) and Levon Aronian (in 2010), with the Women's Championship being won by Kateryna Lagno (in 2010). There is no record of a 2009 blitz event in the FIDE Calendar for that year; however, the October 2009 FIDE Congress discussed whether it should be a "proper" Championship (given the qualification scheme), and it left the decision to the corresponding internal Commission. For 2010, it was organized in conjunction with FIDE from the beginning. However, in neither case was an arbiter's report presented to the next FIDE Congress or General Assembly, as would be expected for a World Championship, and indeed occurred previously with the 2008 Blitz Championship. The 2012 Arbiter's report refers to "7th World Blitz Championship" thus seeming to imply that 2009 and 2010 events were indeed Championships; although this report can be faulted for referring to the rapid championship of 2012 as being the "1st World Rapid Championship", which at the very least forgets Anand's official Rapid Championship in 2003. The balance of the evidence favors these Blitz Championships as being counted as official.


title: Fast chess

text: In 2011, there was no official blitz championship held, but FIDE was involved with the Sport Accord Mind Games blitz won by Maxime Vachier-Lagrave, with Hou Yifan winning the women's division.


title: Fast chess

text: Since 2012 FIDE have held joint World Rapid and Blitz Championships most years, with some years Women's World Rapid and Blitz Championships also being held.


title: Fast chess

text: In 2012 the World Rapid and Blitz Championships were held at Batumi, Georgia and Astana, Kazakhstan (Women's Championships) Sergey Karjakin won the Rapid Championship. Alexander Grischuk won the Blitz Championship. Antoaneta Stefanova won the Women's Rapid Championship. Valentina Gunina won the Women's Blitz Championship.


title: Fast chess

text: In 2013 the World Rapid and Blitz Championships were held at Khanty-Mansiysk, Russia. Shakhriyar Mamedyarov won the Rapid Championship. Lê Quang Liêm won the Blitz Championship.


title: Fast chess

text: In 2014 the World Rapid and Blitz Championships were held at Dubai, UAE and Khanty-Mansiysk, Russia (Women's Championships). Magnus Carlsen won both Rapid and Blitz Championships. Kateryna Lagno won the Women's Rapid Championship. Anna Muzychuk won the Women's Blitz Championship.


title: Fast chess

text: In 2015 the World Rapid and Blitz Championships were held in Berlin, Germany. Magnus Carlsen won the Rapid Championship. He also received the privilege of playing at a dedicated Board 1 the whole time, not having to move while others did. The given reason was that Norwegian television was sponsoring the event, and moving the heavy cameras around would be too much hassle. After his first-round draw, he should not have been on Board 1 until Round 8 when he caught the leaders. Carlsen himself later called this "weird" that Board 1 would be reserved for him. Alexander Grischuk won the Blitz Championship.


title: Fast chess

text: In 2015, FIDE did not receive the expected 80,000 euros from Agon's organization of the event, causing a budget shortfall of 55,000 euros. It was later announced that approximately 200,000 euros were lost on the event.


title: Fast chess

text: In 2016, the World Rapid Championships were held at the Ali Bin Hamad Al Attiya Arena in Doha, Qatar. Vassily Ivanchuk of Ukraine won the 2016 World Rapid Championship, while Carlsen, after defending his title with difficulty in 2015, came in third place. In the Blitz Championship, Sergey Karjakin of Russia and contender in the recently held World Chess Championship 2016 won the championship title albeit due to a better tiebreak over the second place Carlsen. Karjakin defeated Carlsen in their individual encounter. Carlsen was once again reserved board 1 for both championships. Anna Muzychuk also from Ukraine, won both the 2016 Women World Rapid and Blitz Championshipship.


title: Fast chess

text: At the FIDE Presidential Board meeting at the end of March 2016, they gave Agon six months to find an organizer for the 2017 event. At the Baku General Assembly in September, it was announced they had extended this deadline until the end of 2016. The issue of the non-payment of the players for the IMSA Mind Games was also brought up.


title: Fast chess

text: Many top chess players do not take rapid, blitz, and bullet chess as seriously as chess with standard time controls. Some quotes from top chess players may serve to illustrate this:


title: Group dynamics

text: Group dynamics is a system of behaviors and psychological processes occurring within a social group ("intra"group dynamics), or between social groups ("inter"group dynamics). The study of group dynamics can be useful in understanding decision-making behaviour, tracking the spread of diseases in society, creating effective therapy techniques, and following the emergence and popularity of new ideas and technologies. These applications of the field are studied in psychology, sociology, anthropology, political science, epidemiology, education, social work, leadership studies, business and managerial studies, as well as communication studies.


title: Group dynamics

text: The history of group dynamics (or group processes) has a consistent, underlying premise: 'the whole is greater than the sum of its parts.' A social group is an entity that has qualities which cannot be understood just by studying the individuals that make up the group. In 1924, Gestalt psychologist Max Wertheimer proposed ‘There are entities where the behaviour of the whole cannot be derived from its individual elements nor from the way these elements fit together; rather the opposite is true: the properties of any of the parts are determined by the intrinsic structural laws of the whole’ (Wertheimer 1924, p. 7). (The proposition remains questionable, since modern biologists and game theorists do look to explain the 'structural laws of the whole' in terms of 'the way the elements fit together'.)


title: Group dynamics

text: As a field of study, group dynamics has roots in both psychology and sociology. Wilhelm Wundt (1832–1920), credited as the founder of experimental psychology, had a particular interest in the psychology of communities, which he believed possessed phenomena (human language, customs, and religion) that could not be described through a study of the individual. On the sociological side, Émile Durkheim (1858–1917), who was influenced by Wundt, also recognized collective phenomena, such as public knowledge. Other key theorists include Gustave Le Bon (1841–1931) who believed that crowds possessed a 'racial unconscious' with primitive, aggressive, and antisocial instincts, and William McDougall (psychologist), who believed in a 'group mind,' which had a distinct existence born from the interaction of individuals. (The concept of a collective consciousness is not essential to group dynamics.)


title: Group dynamics

text: Eventually, the social psychologist Kurt Lewin (1890–1947) coined the term "group dynamics" to describe the positive and negative forces within groups of people. In 1945, he established "The Group Dynamics Research Center" at the Massachusetts Institute of Technology, the first institute devoted explicitly to the study of group dynamics. Throughout his career, Lewin was focused on how the study of group dynamics could be applied to real-world, social issues.


title: Group dynamics

text: Increasingly, research has applied evolutionary psychology principles to group dynamics. As humans social environments became more complex, they acquired adaptations by way of group dynamics that enhance survival. Examples include mechanisms for dealing with status, reciprocity, identifying cheaters, ostracism, altruism, group decision, leadership, and intergroup relations. Also, a combination of evolution and game theory has been used to explain the development and maintenance of cooperative behavior between individuals in a group.


title: Group dynamics

text: Gustave Le Bon was a French social psychologist whose seminal study, "" (1896) led to the development of group psychology.


title: Group dynamics

text: The British psychologist William McDougall in his work "The Group Mind" (1920) researched the dynamics of groups of various sizes and degrees of organization.


title: Group dynamics

text: In "Group Psychology and the Analysis of the Ego," (1922), Sigmund Freud based his preliminary description of group psychology on Le Bon's work, but went on to develop his own, original theory, related to what he had begun to elaborate in "Totem and Taboo." Theodor Adorno reprised Freud's essay in 1951 with his "Freudian Theory and the Pattern of Fascist Propaganda", and said that "It is not an overstatement if we say that Freud, though he was hardly interested in the political phase of the problem, clearly foresaw the rise and nature of fascist mass movements in purely psychological categories."


title: Group dynamics

text: Jacob L. Moreno was a psychiatrist, dramatist, philosopher and theoretician who coined the term "group psychotherapy" in the early 1930s and was highly influential at the time.


title: Group dynamics

text: Kurt Lewin (1943, 1948, 1951) is commonly identified as the founder of the movement to study groups scientifically. He coined the term "group dynamics" to describe the way groups and individuals act and react to changing circumstances.


title: Group dynamics

text: William Schutz (1958, 1966) looked at interpersonal relations as stage-developmental, inclusion (am I included?), control (who is top dog here?), and affection (do I belong here?). Schutz sees groups resolving each issue in turn in order to be able to progress to the next stage.


title: Group dynamics

text: Conversely, a struggling group can devolve to an earlier stage, if unable to resolve outstanding issues at its present stage.


title: Group dynamics

text: Schutz referred to these group dynamics as "the interpersonal underworld," group processes which are largely unseen and un-acknowledged, as opposed to "content" issues, which are nominally the agenda of group meetings.


title: Group dynamics

text: Wilfred Bion (1961) studied group dynamics from a psychoanalytic perspective, and stated that he was much influenced by Wilfred Trotter for whom he worked at University College Hospital London, as did another key figure in the Psychoanalytic movement, Ernest Jones. He discovered several mass group processes which involved the group as a whole adopting an orientation which, in his opinion, interfered with the ability of a group to accomplish the work it was nominally engaged in. Bion's experiences are reported in his published books, especially "Experiences in Groups." The Tavistock Institute has further developed and applied the theory and practices developed by Bion.


title: Group dynamics

text: Bruce Tuckman (1965) proposed the four-stage model called Tuckman's Stages for a group. Tuckman's model states that the ideal group decision-making process should occur in four stages:


title: Group dynamics

text: Tuckman later added a fifth stage for the dissolution of a group called "adjourning". ("Adjourning" may also be referred to as "mourning", i.e. mourning the adjournment of the group). This model refers to the overall pattern of the group, but of course individuals within a group work in different ways. If distrust persists, a group may never even get to the norming stage.


title: Group dynamics

text: M. Scott Peck developed stages for larger-scale groups (i.e., communities) which are similar to Tuckman's stages of group development. Peck describes the stages of a community as:


title: Group dynamics

text: Communities may be distinguished from other types of groups, in Peck's view, by the need for members to eliminate barriers to communication in order to be able to form true community. Examples of common barriers are: expectations and preconceptions; prejudices; ideology, counterproductive norms, theology and solutions; the need to heal, convert, fix or solve and the need to control. A community is born when its members reach a stage of "emptiness" or peace.


title: Group dynamics

text: Richard Hackman developed a synthetic, research-based model for designing and managing work groups. Hackman suggested that groups are successful when they satisfy internal and external clients, develop capabilities to perform in the future, and when members find meaning and satisfaction in the group. Hackman proposed five conditions that increase the chance that groups will be successful. These include:


title: Group dynamics

text: "Intragroup dynamics" (also referred to as ingroup-, within-group, or commonly just ‘group dynamics’) are the underlying processes that give rise to a set of norms, roles, relations, and common goals that characterize a particular social group. Examples of groups include religious, political, military, and environmental groups, sports teams, work groups, and therapy groups. Amongst the members of a group, there is a state of interdependence, through which the behaviours, attitudes, opinions, and experiences of each member are collectively influenced by the other group members. In many fields of research, there is an interest in understanding how group dynamics influence individual behaviour, attitudes, and opinions.


title: Group dynamics

text: The dynamics of a particular group depend on how one defines the "boundaries" of the group. Often, there are distinct "subgroups" within a more broadly defined group. For example, one could define U.S. residents (‘Americans’) as a group, but could also define a more specific set of U.S. residents (for example, 'Americans in the South'). For each of these groups, there are distinct dynamics that can be discussed. Notably, on this very broad level, the study of group dynamics is similar to the study of "culture". For example, there are group dynamics in the U.S. South that sustain a "culture of honor", which is associated with norms of toughness, honour-related violence, and self-defence.


title: Group dynamics

text: Group formation starts with a psychological bond between individuals. The "social cohesion approach" suggests that group formation comes out of bonds of interpersonal attraction. In contrast, the "social identity approach" suggests that a group starts when a collection of individuals perceive that they share some social category (‘smokers’, ‘nurses,’ ‘students,’ ‘hockey players’), and that interpersonal attraction only secondarily enhances the connection between individuals. Additionally, from the social identity approach, group formation involves both identifying with some individuals and explicitly "not" identifying with others. So to say, a level of psychological "distinctiveness" is necessary for group formation. Through interaction, individuals begin to develop group norms, roles, and attitudes which define the group, and are internalized to influence behaviour.


title: Group dynamics

text: "Emergent groups" arise from a relatively spontaneous process of group formation. For example, in response to a natural disaster, an "emergent response group" may form. These groups are characterized as having no preexisting structure (e.g. group membership, allocated roles) or prior experience working together. Yet, these groups still express high levels of interdependence and coordinate knowledge, resources, and tasks.


title: Group dynamics

text: Joining a group is determined by a number of different factors, including an individual's personal traits; gender; social motives such as need for affiliation, need for power, and need for intimacy; attachment style; and prior group experiences. Groups can offer some advantages to its members that would not be possible if an individual decided to remain alone, including gaining social support in the forms of emotional support, instrumental support, and informational support. It also offers friendship, potential new interests, learning new skills, and enhancing self esteem. However, joining a group may also cost an individual time, effort, and personal resources as they may conform to social pressures and strive to reap the benefits that may be offered by the group.


title: Group dynamics

text: The Minimax Principle is a part of social exchange theory that states that people will join and remain in a group that can provide them with the maximum amount of valuable rewards while at the same time, ensuring the minimum amount of costs to themselves. However, this does not necessarily mean that a person will join a group simply because the reward/cost ratio seems attractive. According to Howard Kelley and John Thibaut, a group may be attractive to us in terms of costs and benefits, but that attractiveness alone does not determine whether or not we will join the group. Instead, our decision is based on two factors: our comparison level, and our comparison level for alternatives.


title: Group dynamics

text: In John Thibaut and Harold Kelley's social exchange theory, comparison level is the standard by which an individual will evaluate the desirability of becoming a member of the group and forming new social relationships within the group. This comparison level is influenced by previous relationships and membership in different groups. Those individuals who have experienced positive rewards with few costs in previous relationships and groups will have a higher comparison level than a person who experienced more negative costs and fewer rewards in previous relationships and group memberships. According to the social exchange theory, group membership will be more satisfying to a new prospective member if the group's outcomes, in terms of costs and rewards, are above the individual's comparison level. As well, group membership will be unsatisfying to a new member if the outcomes are below the individual's comparison level.


title: Group dynamics

text: Comparison level only predicts how satisfied a new member will be with the social relationships within the group. To determine whether people will actually join or leave a group, the value of other, alternative groups needs to be taken into account. This is called the comparison level for alternatives. This comparison level for alternatives is the standard by which an individual will evaluate the quality of the group in comparison to other groups the individual has the opportunity to join. Thiabaut and Kelley stated that the "comparison level for alternatives can be defined informally as the lowest level of outcomes a member will accept in the light of available alternative opportunities.”


title: Group dynamics

text: Joining and leaving groups is ultimately dependent on the comparison level for alternatives, whereas member satisfaction within a group depends on the comparison level. To summarize, if membership in the group is above the comparison level for alternatives and above the comparison level, the membership within the group will be satisfying and an individual will be more likely to join the group. If membership in the group is above the comparison level for alternatives but below the comparison level, membership will be not be satisfactory; however, the individual will likely join the group since no other desirable options are available. When group membership is below the comparison level for alternatives but above the comparison level, membership is satisfying but an individual will be unlikely to join. If group membership is below both the comparison and alternative comparison levels, membership will be dissatisfying and the individual will be less likely to join the group.


title: Group dynamics

text: Groups can vary drastically from one another. For example, three best friends who interact every day as well as a collection of people watching a movie in a theater both constitute a group. Past research has identified four basic types of groups which include, but are not limited to: primary groups, social groups, collective groups, and categories. It is important to define these four types of groups because they are intuitive to most lay people. For example, in an experiment, participants were asked to sort a number of groups into categories based on their own criteria. Examples of groups to be sorted were a sports team, a family, people at a bus stop and women. It was found that participants consistently sorted groups into four categories: intimacy groups, task groups, loose associations, and social categories. These categories are conceptually similar to the four basic types to be discussed. Therefore, it seems that individuals intuitively define aggregations of individuals in this way.


title: Group dynamics

text: Primary groups are characterized by relatively small, long-lasting groups of individuals who share personally meaningful relationships. Since these groups often interact face-to-face, they know each other very well and are unified. Individuals that are a part of primary groups consider the group to be an important part of their lives. Consequently, members strongly identify with their group, even without regular meetings. Cooley believed that primary groups were essential for integrating individuals into their society since this is often their first experience with a group. For example, individuals are born into a primary group, their family, which creates a foundation for them to base their future relationships. Individuals can be born into a primary group; however, primary groups can also form when individuals interact for extended periods of time in meaningful ways. Examples of primary groups include family, close friends, and gangs.


title: Group dynamics

text: A social group is characterized by a formally organized group of individuals who are not as emotionally involved with each other as those in a primary group. These groups tend to be larger, with shorter memberships compared to primary groups. Further, social groups do not have as stable memberships, since members are able to leave their social group and join new groups. The goals of social groups are often task-oriented as opposed to relationship-oriented. Examples of social groups include coworkers, clubs, and sports teams.


title: Group dynamics

text: Collectives are characterized by large groups of individuals who display similar actions or outlooks. They are loosely formed, spontaneous, and brief. Examples of collectives include a flash mob, an audience at a movie, and a crowd watching a building burn.


title: Group dynamics

text: Categories are characterized by a collection of individuals who are similar in some way. Categories become groups when their similarities have social implications. For example, when people treat others differently because of certain aspects of their appearance or heritage, for example, this creates groups of different races. For this reason, categories can appear to be higher in entitativity and essentialism than primary, social, and collective groups. Entitativity is defined by Campbell as the extent to which collections of individuals are perceived to be a group. The degree of entitativity that a group has is influenced by whether a collection of individuals experience the same fate, display similarities, and are close in proximity. If individuals believe that a group is high in entitativity, then they are likely to believe that the group has unchanging characteristics that are essential to the group, known as essentialism. Examples of categories are New Yorkers, gamblers, and women.


title: Group dynamics

text: The social group is a critical source of information about individual identity. We naturally make comparisons between our own group and other groups, but we do not necessarily make objective comparisons. Instead, we make evaluations that are self-enhancing, emphasizing the positive qualities of our own group (see ingroup bias). In this way, these comparisons give us a distinct and valued social identity that benefits our self-esteem. Our social identity and group membership also satisfies a need to belong. Of course, individuals belong to multiple groups. Therefore, one's social identity can have several, qualitatively distinct parts (for example, one's ethnic identity, religious identity, and political identity).


title: Group dynamics

text: Optimal distinctiveness theory suggests that individuals have a desire to be similar to others, but also a desire to differentiate themselves, ultimately seeking some balance of these two desires (to obtain "optimal distinctiveness"). For example, one might imagine a young teenager in the United States who tries to balance these desires, not wanting to be ‘just like everyone else,’ but also wanting to ‘fit in’ and be similar to others. One's collective self may offer a balance between these two desires. That is, to be similar to others (those who you share group membership with), but also to be different from others (those who are outside of your group).


title: Group dynamics

text: In the social sciences, group cohesion refers to the processes that keep members of a social group connected. Terms such as attraction, solidarity, and morale are often used to describe group cohesion. It is thought to be one of the most important characteristics of a group, and has been linked to group performance, intergroup conflict and therapeutic change.


title: Group dynamics

text: Group cohesion, as a scientifically studied property of groups, is commonly associated with Kurt Lewin and his student, Leon Festinger. Lewin defined group cohesion as the willingness of individuals to stick together, and believed that without cohesiveness a group could not exist. As an extension of Lewin's work, Festinger (along with Stanley Schachter and Kurt Back) described cohesion as, “the total field of forces which act on members to remain in the group” (Festinger, Schachter, & Back, 1950, p. 37). Later, this definition was modified to describe the forces acting on individual members to remain in the group, termed "attraction to the group". Since then, several models for understanding the concept of group cohesion have been developed, including Albert Carron's hierarchical model and several bi-dimensional models (vertical v. horizontal cohesion, task v. social cohesion, belongingness and morale, and personal v. social attraction). Before Lewin and Festinger, there were, of course, descriptions of a very similar group property. For example, Emile Durkheim described two forms of solidarity (mechanical and organic), which created a sense of collective conscious and an emotion-based sense of community.


title: Group dynamics

text: Beliefs within the ingroup are based on how individuals in the group see their other members. Individuals tend to upgrade likeable in-group members and deviate from unlikeable group members, making them a separate outgroup. This is called the black sheep effect. The way a person judges socially desirable and socially undesirable individuals depends upon whether they are part of the ingroup or outgroup.


title: Group dynamics

text: This phenomenon has been later accounted for by subjective group dynamics theory. According to this theory, people derogate socially undesirable (deviant) ingroup members relative to outgroup members, because they give a bad image of the ingroup and jeopardize people's social identity.


title: Group dynamics

text: In more recent studies, Marques and colleagues have shown that this occurs more strongly with regard to ingroup full members than other members. Whereas "new members" of a group must prove themselves to the full members to become accepted, full members have undergone socialization and are already accepted within the group. They have more privilege than newcomers but more responsibility to help the group achieve its goals. "Marginal members" were once full members but lost membership because they failed to live up to the group's expectations. They can rejoin the group if they go through re-socialization. Therefore, full members' behavior is paramount to define the ingroup's image.


title: Group dynamics

text: Bogart and Ryan surveyed the development of new members' stereotypes about in-groups and out-groups during socialization. Results showed that the new members judged themselves as consistent with the stereotypes of their in-groups, even when they had recently committed to join those groups or existed as marginal members. They also tended to judge the group as a whole in an increasingly less positive manner after they became full members. However, there is no evidence that this affects the way they are judged by other members. Nevertheless, depending on the self-esteem of an individual, members of the in-group may experience different private beliefs about the group's activities but will publicly express the opposite—that they actually share these beliefs. One member may not personally agree with something the group does, but to avoid the black sheep effect, they will publicly agree with the group and keep the private beliefs to themselves. If the person is privately self-aware, he or she is more likely to comply with the group even if they possibly have their own beliefs about the situation.


title: Group dynamics

text: In situations of hazing within fraternities and sororities on college campuses, pledges may encounter this type of situation and may outwardly comply with the tasks they are forced to do regardless of their personal feelings about the Greek institution they are joining. This is done in an effort to avoid becoming an outcast of the group. Outcasts who behave in a way that might jeopardize the group tend to be treated more harshly than the likeable ones in a group, creating a black sheep effect. Full members of a fraternity might treat the incoming new members harshly, causing the pledges to decide if they approve of the situation and if they will voice their disagreeing opinions about it.


title: Group dynamics

text: Individual behaviour is influenced by the presence of others. For example, studies have found that individuals work harder and faster when others are present (see social facilitation), and that an individual's performance is reduced when others in the situation create distraction or conflict. Groups also influence individual's decision-making processes. These include decisions related to ingroup bias, persuasion (see Asch conformity experiments), obedience (see Milgram Experiment), and groupthink. There are both positive and negative implications of group influence on individual behaviour. This type of influence is often useful in the context of work settings, team sports, and political activism. However, the influence of groups on the individual can also generate extremely negative behaviours, evident in Nazi Germany, the My Lai Massacre, and in the Abu Ghraib prison (also see Abu Ghraib torture and prisoner abuse).


title: Group dynamics

text: A group's structure is the internal framework that defines members' relations to one another over time. Frequently studied elements of group structure include roles, norms, values, communication patterns, and status differentials. Group structure has also been defined as the underlying pattern of roles, norms, and networks of relations among members that define and organize the group.


title: Group dynamics

text: Roles can be defined as a tendency to behave, contribute and interrelate with others in a particular way. Roles may be assigned formally, but more often are defined through the process of role differentiation. Role differentiation is the degree to which different group members have specialized functions. A group with a high level of role differentiation would be categorized as having many different roles that are specialized and narrowly defined. A key role in a group is the leader, but there are other important roles as well, including task roles, relationship roles, and individual roles. Functional (task) roles are generally defined in relation to the tasks the team is expected to perform. Individuals engaged in task roles focus on the goals of the group and on enabling the work that members do; examples of task roles include coordinator, recorder, critic, or technician. A group member engaged in a relationship role (or socioemotional role) is focused on maintaining the interpersonal and emotional needs of the groups' members; examples of relationship role include encourager, harmonizer, or compromiser.


title: Group dynamics

text: Norms are the informal rules that groups adopt to regulate members' behaviour. Norms refer to what should be done and represent value judgments about appropriate behaviour in social situations. Although they are infrequently written down or even discussed, norms have powerful influence on group behaviour. They are a fundamental aspect of group structure as they provide direction and motivation, and organize the social interactions of members. Norms are said to be emergent, as they develop gradually throughout interactions between group members. While many norms are widespread throughout society, groups may develop their own norms that members must learn when they join the group. There are various types of norms, including: prescriptive, proscriptive, descriptive, and injunctive.


title: Group dynamics

text: Intermember Relations are the connections among the members of a group, or the social network within a group. Group members are linked to one another at varying levels. Examining the intermember relations of a group can highlight a group's density (how many members are linked to one another), or the degree centrality of members (number of ties between members). Analysing the intermember relations aspect of a group can highlight the degree centrality of each member in the group, which can lead to a better understanding of the roles of certain group (e.g. an individual who is a 'go-between' in a group will have closer ties to numerous group members which can aid in communication, etc.).


title: Group dynamics

text: Values are goals or ideas that serve as guiding principles for the group. Like norms, values may be communicated either explicitly or on an ad hoc basis. Values can serve as a rallying point for the team. However, some values (such as conformity) can also be dysfunction and lead to poor decisions by the team.


title: Group dynamics

text: Communication patterns describe the flow of information within the group and they are typically described as either centralized or decentralized. With a centralized pattern, communications tend to flow from one source to all group members. Centralized communications allow standardization of information, but may restrict the free flow of information. Decentralized communications make it easy to share information directly between group members. When decentralized, communications tend to flow more freely, but the delivery of information may not be as fast or accurate as with centralized communications. Another potential downside of decentralized communications is the sheer volume of information that can be generated, particularly with electronic media.


title: Group dynamics

text: Status differentials are the relative differences in status among group members. When a group is first formed the members may all be on an equal level, but over time certain members may acquire status and authority within the group; this can create what is known as a "pecking order" within a group. Status can be determined by a variety of factors and characteristics, including specific status characteristics (e.g. task-specific behavioural and personal characteristics, such as experience) or diffuse status characteristics (e.g. age, race, ethnicity). It is important that other group members perceive an individual's status to be warranted and deserved, as otherwise they may not have authority within the group. Status differentials may affect the relative amount of pay among group members and they may also affect the group's tolerance to violation of group norms (e.g. people with higher status may be given more freedom to violate group norms).


title: Group dynamics

text: Forsyth suggests that while many daily tasks undertaken by individuals could be performed in isolation, the preference is to perform with other people.


title: Group dynamics

text: In a study of dynamogenic stimulation for the purpose of explaining pacemaking and competition in 1898, Norman Triplett theorized that "the bodily presence of another rider is a stimulus to the racer in arousing the competitive instinct...". This dynamogenic factor is believed to have laid the groundwork for what is now known as social facilitation—an "improvement in task performance that occurs when people work in the presence of other people".


title: Group dynamics

text: Further to Triplett's observation, in 1920, Floyd Allport found that although people in groups were more productive than individuals, the quality of their product/effort was inferior.


title: Group dynamics

text: In 1965, Robert Zajonc expanded the study of arousal response (originated by Triplett) with further research in the area of social facilitation. In his study, Zajonc considered two experimental paradigms. In the first—audience effects—Zajonc observed behaviour in the presence of passive spectators, and the second—co-action effects—he examined behaviour in the presence of another individual engaged in the same activity.


title: Group dynamics

text: Zajonc observed two categories of behaviours—dominant responses to tasks that are easier to learn and which dominate other potential responses and nondominant responses to tasks that are less likely to be performed. In his Theory of Social Facilitation, Zajonc concluded that in the presence of others, when action is required, depending on the task requirement, either social facilitation or social interference will impact the outcome of the task. If social facilitation occurs, the task will have required a dominant response from the individual resulting in better performance in the presence of others, whereas if social interference occurs the task will have elicited a nondominant response from the individual resulting in subpar performance of the task.


title: Group dynamics

text: Several theories analysing performance gains in groups via drive, motivational, cognitive and personality processes, explain why social facilitation occurs.


title: Group dynamics

text: Zajonc hypothesized that compresence (the state of responding in the presence of others) elevates an individual's drive level which in turn triggers social facilitation when tasks are simple and easy to execute, but impedes performance when tasks are challenging.


title: Group dynamics

text: Nickolas Cottrell, 1972, proposed the evaluation apprehension model whereby he suggested people associate social situations with an evaluative process. Cottrell argued this situation is met with apprehension and it is this motivational response, not arousal/elevated drive, that is responsible for increased productivity on simple tasks and decreased productivity on complex tasks in the presence of others.


title: Group dynamics

text: In The Presentation of Self in Everyday Life (1959), Erving Goffman assumes that individuals can control how they are perceived by others. He suggests that people fear being perceived as having negative, undesirable qualities and characteristics by other people, and that it is this fear that compels individuals to portray a positive self-presentation/social image of themselves. In relation to performance gains, Goffman's self-presentation theory predicts, in situations where they may be evaluated, individuals will consequently increase their efforts in order to project/preserve/maintain a positive image.


title: Group dynamics

text: Distraction-conflict theory contends that when a person is working in the presence of other people, an interference effect occurs splitting the individual's attention between the task and the other person. On simple tasks, where the individual is not challenged by the task, the interference effect is negligible and performance, therefore, is facilitated. On more complex tasks, where drive is not strong enough to effectively compete against the effects of distraction, there is no performance gain. The Stroop task (Stroop effect) demonstrated that, by narrowing a person's focus of attention on certain tasks, distractions can improve performance.


title: Group dynamics

text: Social orientation theory considers the way a person approaches social situations. It predicts that self-confident individuals with a positive outlook will show performance gains through social facilitation, whereas a self-conscious individual approaching social situations with apprehension is less likely to perform well due to social interference effects.


title: Group dynamics

text: "Intergroup dynamics" (or intergroup relations) refers to the behavioural and psychological relationship between two or more groups. This includes perceptions, attitudes, opinions, and behaviours towards one's own group, as well as those towards another group. In some cases, intergroup dynamics is prosocial, positive, and beneficial (for example, when multiple research teams work together to accomplish a task or goal). In other cases, intergroup dynamics can create conflict. For example, Fischer & Ferlie found initially positive dynamics between a clinical institution and its external authorities dramatically changed to a 'hot' and intractable conflict when authorities interfered with its embedded clinical model. Similarly, underlying the 1999 Columbine High School shooting in Littleton, Colorado, United States, intergroup dynamics played a significant role in Eric Harris’ and Dylan Klebold’s decision to kill a teacher and 14 students (including themselves).


title: Group dynamics

text: According to social identity theory, intergroup conflict starts with a process of comparison between individuals in one group (the ingroup) to those of another group (the outgroup). This comparison process is not unbiased and objective. Instead, it is a mechanism for enhancing one's self-esteem. In the process of such comparisons, an individual tends to:


title: Group dynamics

text: Even without any intergroup interaction (as in the minimal group paradigm), individuals begin to show favouritism towards their own group, and negative reactions towards the outgroup. This conflict can result in prejudice, stereotypes, and discrimination. Intergroup conflict can be highly competitive, especially for social groups with a long history of conflict (for example, the 1994 Rwandan genocide, rooted in group conflict between the ethnic Hutu and Tutsi). In contrast, intergroup competition can sometimes be relatively harmless, particularly in situations where there is little history of conflict (for example, between students of different universities) leading to relatively harmless generalizations and mild competitive behaviours. Intergroup conflict is commonly recognized amidst racial, ethnic, religious, and political groups.


title: Group dynamics

text: The formation of intergroup conflict was investigated in a popular series of studies by Muzafer Sherif and colleagues in 1961, called the Robbers Cave Experiment. The Robbers Cave Experiment was later used to support realistic conflict theory. Other prominent theories relating to intergroup conflict include social dominance theory, and social-/self-categorization theory.


title: Group dynamics

text: There have been several strategies developed for reducing the tension, bias, prejudice, and conflict between social groups. These include the "contact hypothesis", the "jigsaw classroom", and several categorization-based strategies.


title: Group dynamics

text: In 1954, Gordon Allport suggested that by promoting contact between groups, prejudice can be reduced. Further, he suggested four optimal conditions for contact: equal status between the groups in the situation; common goals; intergroup cooperation; and the support of authorities, law, or customs. Since then, over 500 studies have been done on prejudice reduction under variations of the contact hypothesis, and a meta-analytic review suggests overall support for its efficacy. In some cases, even without the four optimal conditions outlined by Allport, prejudice between groups can be reduced.


title: Group dynamics

text: Under the contact hypothesis, several models have been developed. A number of these models utilize a "superordinate identity" to reduce prejudice. That is, a more broadly defined, ‘umbrella’ group/identity that includes the groups that are in conflict. By emphasizing this superordinate identity, individuals in both subgroups can share a common social identity. For example, if there is conflict between White, Black, and Latino students in a high school, one might try to emphasize the ‘high school’ group/identity that students share to reduce conflict between the groups. Models utilizing superordinate identities include the common ingroup identity model, the ingroup projection model, the mutual intergroup differentiation model, and the ingroup identity model. Similarly, "recategorization" is a broader term used by Gaertner et al. to describe the strategies aforementioned.


title: Group dynamics

text: There are also techniques for reducing prejudice that utilize interdependence between two or more groups. That is, members across groups have to rely on one another to accomplish some goal or task. In the Robbers Cave Experiment, Sherif used this strategy to reduce conflict between groups. Elliot Aronson’s Jigsaw Classroom also uses this strategy of interdependence. In 1971, thick racial tensions were abounding in Austin, Texas. Aronson was brought in to examine the nature of this tension within schools, and to devise a strategy for reducing it (so to improve the process of school integration, mandated under Brown v. Board of Education in 1954). Despite strong evidence for the effectiveness of the "jigsaw classroom," the strategy was not widely used (arguably because of strong attitudes existing outside of the schools, which still resisted the notion that racial and ethnic minority groups are equal to Whites and, similarly, should be integrated into schools).


title: Forza Horizon 3

text: Forza Horizon 3 is a 2016 racing video game developed by Playground Games and published by Microsoft Studios for the Xbox One and Windows. It is the ninth instalment in the "Forza" series and the third instalment in its spinoff "Forza Horizon". The game is set in a fictionalised Australia, where the player is the leader of the titular Horizon car festival and has to expand the festival by completing events to earn fans. Like previous "Forza Horizon" games, it features an open world environment where players can freely roam the map.


title: Forza Horizon 3

text: "Forza Horizon 3" began development in 2014 after the release of "Forza Horizon 2". Turn 10 Studios assisted with the game's development, as they did with other "Forza Horizon" games. Over the course of development, Playground Games tested different technological concepts for the game, while also trying to improve more features over the previous title. The Australian setting was chosen for its variety of regions, and a team was sent to Australia to conduct research for the game.


title: Forza Horizon 3

text: "Forza Horizon 3" was released in September 2016. At release, critics praised the map design, graphics, and amount of content, while most criticism was directed towards the monotony of races. The game won and was nominated for multiple awards and sold over 2.5 million copies in 2017. Downloadable content had also been released periodically, including two expansion packs. The game was followed by "Forza Horizon 4", released in 2018.


title: Forza Horizon 3

text: "Forza Horizon 3" is a racing video game set in an open world environment based in a fictional representation of Australia. The gameplay world is about twice the size of "Forza Horizon 2", and the game contains locales and regions based upon their real-life Australian counterparts. While previous "Forza Horizon" games have depicted the player as being one of the racers of the Horizon Festival, the player is now the director of the festival, and their role is to expand it throughout Australia by completing races, challenges, and stunts to earn fans. If enough fans are earned at a certain threshold, the player can set up new festival locations and unlock more events.


title: Forza Horizon 3

text: Three types of racing modes are available in the game: Exhibition, Championship, and Rivals. Exhibition is a single race at one location, whereas Championship contains multiple races dispersed throughout the gameplay world. Rivals is a versus race against the player and an AI opponent, where the player has to compete in a time trial to beat the time set by the opponent. Added in "Forza Horizon 2", the player can also participate in Bucket List Challenges, where they are given a task to complete with a specific vehicle. The newly introduced Horizon Blueprint feature lets the player customise races and Bucket List Challenges.


title: Forza Horizon 3

text: Apart from races and Bucket List Challenges, the player can engage in several other activities. Breakable boards called "bonus boards" can be discovered around the gameplay world, and when driven over, they award the player with experience points or a discount on fast travelling. As the player progresses through the game, they can receive rumours of barn finds to uncover and restore. When performing stunts with a vehicle, the player is awarded "skill points". If enough skill points are acquired, they can be used to purchase perks that may award cars, experience points, in-game currency, and driving advantages, among other benefits. The player may participate in Forzathon competitions, which provide weekly challenges and give awards once completed.


title: Forza Horizon 3

text: Returning from previous "Forza" games, "Forza Horizon 3" features a vehicle AI called Drivatars, which learns and mimics the driving abilities of "Forza" players. Drivatars are found throughout the gameplay world, and they appear in races as opponents, where they can be adjusted by game difficulty via the player. Apart from standard races, Drivatars can be challenged to a head-to-head race. If the player wins the race, they will be able to recruit that Drivatar onto their racing team, which allows the player to earn additional experience points, fans, and in-game currency. The player can also recruit Drivatars in a car convoy. When in a car convoy, Drivatars will follow the player, and they can be upgraded by skill points to perform certain tasks throughout the game.


title: Forza Horizon 3

text: The player can upgrade and tune individual parts of their vehicles, with body kits being available as well. Additionally, the game includes a vehicle cutsomisation option called "Upgrade Heroes", which utilises both tuning and body kits to alter both a vehicle's performance and appearance, although the cutomisation preset is limited to a certain number of vehicles. The colour of vehicles and their collective parts can changed, and the player can also design liveries for vehicles. These liveries can be sold through the in-game shop, which further includes an auction system to bid on cars from other players. A total of 350 vehicles were available at the game's launch.


title: Forza Horizon 3

text: "Forza Horizon 3" offers open world multiplayer modes including an online cooperative mode for up to four players and a competitive mode for up to twelve, where players can compete in races and minigames with their vehicles. As from previous "Forza" games, the player can join clubs, where they have the ability to compete against players of other clubs in races and minigames.


title: Forza Horizon 3

text: "Forza Horizon 3" was developed by UK-based Playground Games, the creators behind previous "Forza Horizon" titles. Additional work was provided by Turn 10 Studios, who made the "Forza Motorsport" series. The game was designed using the ForzaTech game engine, which is used for most other "Forza" games. The development team started conceptualizing the creation of "Forza Horizon 3" in 2014 initially after "Forza Horizon 2" was released. The team desired to give players more freedom in "Forza Horizon 3" compared to its predecessor. They also aimed for the game to be of better quality, therefore they sought to optimise more gameplay and graphical aspects over the previous title. One of these changes was minimizing the amount of loading screen time, as it could damage the game's impression of being persistently high quality. Creative director Ralph Fulton felt that "Forza Horizon 3" was a "generational leap" over its predecessor because of the work the development team put in to better improve the game.


title: Forza Horizon 3

text: Playground Games started with a broad range of locations for "Forza Horizon 3", narrowing the list of locations with more research. Because of Australia's largely diverse environment, the development team ultimately made the decision to have the game set there, as they also considered the country to be a possible setting for future "Forza Horizon" games. Mike Brown, a game designer at Playground Games, thought that the team made the correct decision to select Australia as the setting, describing the country's diverse scenery as "perfect".


title: Forza Horizon 3

text: To help create a convincing gameplay world, a team was sent to Australia to take reference photos to aid in the game design. These photos consisted of plants, rocks, and road details, among others. A significant amount of work was put into simulating landmarks of the country, such as the Twelve Apostles. Minor details were also implemented into the game, like the colours of Australian phone boxes and garbage bins, as well as including native wildlife. Playground Games stated that they explored and represented every ecologically distinct part of the country in "Forza Horizon 3"; the gameplay world consists of six distinct regions. However, the world is somewhat geographically inaccurate, with locations in real life existing in different geographic areas in the game. According to Brown, the explanation for this inconsistency was to create a better gameplay experience for the player.


title: Forza Horizon 3

text: Ralph Fulton explained that Playground Games desired to help celebrate Australian car culture and familiarise the culture to people in other parts of the world, thus multiple Australian car models were incorporated into the game. He added, "[Australia's] culture of Ford vs Holden, and V8s and Utes isn’t immediately familiar to everybody north of the equator, but we did feel it was really interesting and colourful and would add to the game."


title: Forza Horizon 3

text: High-dynamic-range (HDR) played a key role in the visuals of "Forza Horizon 3". Originally, there was not any thought of incorporating HDR into the game during development, but due to the development team discovering the HDR output of the Xbox One S, it was decided to start programming the feature. ForzaTech was found to be a good match for HDR, as the light rendering of the game engine was adequately set up the incorporate the brightness gamut of HDR. Multiple televisions were then bought for investigation of the feature. The development team later discovered that the televisions displayed HDR variously, which added more difficulty to the process of adding the feature to the game.


title: Forza Horizon 3

text: Over the course of development, the team talked about and tested new technology prototypes for several months to help enhance the visuals for the game. Among these prototypes was an HDR sky system. As an idea, the team thought of pointing a high-resolution camera at the sky for hours as a time-lapse. A test was then conducted in Leamington Spa, England. Lighting artist Jamie Wood admitted that during the test, there was more variety in shooting a camera at a sky than the sky design system that was used in "Forza Horizon 2". Three teams of two were then sent to Braidwood, New South Wales to capture Australia's more distinguishing skies, clouds, and weather patterns. For a few months, the teams performed the shooting process using HDR cameras. The cameras took thousands of photos with frame interpolation over 24 hour periods, alongside the lenses and light sensors needing to be cleaned regularly. Videos of the sky were also taken, with the footage being about 30 days long overall. The shooting process took place through various weather conditions and times of day to resemble a "dynamic weather system" in the game. This further meant that camera exposures and filters had to be changed frequently to adjust to each time of day. The footage of the sky was then imported into the game. Because of the sky footage, days were longer in "Forza Horizon 3" than its predecessor, and clouds also correlate with weather systems in-game.


title: Forza Horizon 3

text: The lighting effects in "Forza Horizon 3" are calculated with real-time computing, which helps simulate a realistic sun in the game. Shadows are generated based on how light is distributed and occluded depending on the locations of surrounding objects and substances. Real-time computing is also used in the game's voxel-based global illumination system to calculate the bouncing of light. The sky, other sources of light, and occlusion data is used to determine surfaces light bounces onto. This helps light accurately blend into areas that have varying degrees of brightness.


title: Forza Horizon 3

text: Playground Games wanted the beach to be an important racing area in the game, therefore much effort was put into allowing the sea to realistically interact with the beach to make the location look lifelike. To help assist in developing the sea, Playground Games contacted game developer Rare, who was working on "Sea of Thieves" at the time. As both developers were working on creating the sea in their games, they decided to share computer code, which both developers improved on.


title: Forza Horizon 3

text: Car models were mainly designed with CAD data exchange between the developers and the car manufacturer. However, for cars that didn't support CAD data exchange, especially rarer and older cars, designers had to track them down for modelling details, sometimes taking upwards of weeks to locate some of them. As with the Lamborghini Centenario, the cover car of the game, a photographer was sent to Italy to take photos and measurements of the car. Since the Centenario was made of hundreds of different types of materials, Playground Games desired to simulate the car at the "sub-pixel level". Using data from the images and measurements, a mesh of the car was modelled with 3D Studio Max, while designers had to figure out where materials needed to be simulated in the mesh.


title: Forza Horizon 3

text: Ralph Fulton explained that "humans form their first impressions incredibly quickly", elaborating that the first few minutes of playing a video game can drastically change how a player thinks of it. Playground Games later conducting a study of first impressions before developing "Forza Horizon 3". Two groups of test subjects both played the same "Forza" game for the same amount of time, except one group played in a sports car and the other played in a regular car. When asked about their experiences playing the game, the group that played in the sports car rated the game generally better. As a result, Playground Games spent a large part of their development cycle (about eighteen months) developing and curating the first few scenes of the game. In February 2015, it was decided that the first few scenes would be split between the opening drive and the first of the game's events, with the decided route for the opening drive being finalizsed a month later. By June 2015, the route was being tested and concept art was drawn for the scenery that the player would see during the opening drive, although some concepts had to be adjusted or removed, such as the rainforest being made less dense. Problems also emerged with the car that the player would be driving in during the opening sequence, the Centenario. The Centenario resulted in being too fast for the player to observe the scenery as intended, requiring changes in the route and terrain. As the opening drive also went off-road, a cutscene had to be instituted to switch the Centenario to a buggy to accompany the harsher terrain. Additionally, the first event after the opening drive had to be pushed back for further improvement, prompting modifications to be made to the opponent vehicle.


title: Forza Horizon 3

text: During the development process of the four-player cooperative campaign, the goal was to enable all players to play with "as little friction as possible", with the development team then generating a list of goals for an organised campaign. After assessing the campaign layout, the team created a list of problems that could negatively influence the gameplay and came to the conclusion that there four major issues that could affect gameplay the most. With each issue, the team brainstormed a list of possible solutions, picking the solution that produced the least conflict between players. The first issue, where players could be hours apart in campaign progress, made a screen appear that informs the player of how many fans they earned, and the festivals they can upgrade or open whenever they leave a cooperative session. If players also completed races in a cooperative session that have not yet been unlocked in their single-player session, the race will appear as "completed" on the user interface in single-player. The second issue was that races could have specific requirements for cars based on the restrictions the session leader has set, players with fewer cars may not reach those specifications. The solution was considered more straightforward, which introduced a rental feature that allowed players to borrow the session leader's car during a race. For the third issue, where players with less skill may finish races in lower positions, every race was converted into a team race between the players and the AI opponents. A point system was then added for every opponent beaten. This created a structure that let inexperienced players to contribute to the campaign even if they beat only one opponent. Although the fourth issue wasn't part of the team's original goals, it did come up often during testing phases, which was that the leader of the session had to guide other players through the game, even if there was not any sort of communication between players. To resolve the problem, a feature was implemented that notified the session leader's actions to all other players whenever the leader did something, such as starting an event.


title: Forza Horizon 3

text: "Forza Horizon 3" was announced on 13 June 2016 during Microsoft's E3 press conference, where Ralph Fulton displayed a gameplay demo during the briefing. The game was released on 27 September 2016. Players were able to purchase three different editions of the game: the Standard, Deluxe, or Ultimate editions. The Deluxe and Ultimate editions gave players several downloadable content car packs and other exclusive content, while players that pre-ordered the Ultimate Edition were also able to earn early access to the game on 23 September. "Forza Horizon 3" supports cross-platform play and is part of the Xbox Play Anywhere program, allowing the game to be playable both on Xbox and Windows if purchased digitally.


title: Forza Horizon 3

text: Initially after the game was released, there were various in-game performance problems that occurred concerning the game's compatibility with Windows. An issue also arose involving the game's wheelspin feature, an award system that offers the chance for players to earn a new car or a certain amount of in-game currency, which may sometimes give players the maximum amount of currency that could be acquired in the game. These issues were later addressed and promptly fixed by Playground Games. Some players had also claimed that they were falsely banned after Playground Games issued bans to players using hacking clients. A Microsoft spokesperson later stated that players who felt that they were falsely punished can email them for investigation and removal of the bans. In January 2017, an update had the potential to corrupt the game for Windows users. The corrupted update was later removed by Playground Games.


title: Forza Horizon 3

text: In January 2018, "Forza Horizon 3" was ported to the Xbox One X, enabling the graphics of the game to be changed on the console, including adding 4K resolution, higher polygon models, increasing sample quality, and enhancing other graphical features. The game made use of Groove Music to play custom soundtracks, however, the ability to stream music to the game was stopped on 31 March 2019, after Groove Music was discontinued, limiting players to the in-game soundtrack as with the other "Forza Horizon" games. On 27 September 2020, the game and all its downloadable content were removed from the Microsoft Store after reaching end-of-life status.


title: Forza Horizon 3

text: Several downloadable content (DLC) car packs were released periodically. While most packs featured a small collection of cars, some packs had themes, such as being type specific or manufacturer specific. Examples include the "Motorsport All-Stars Pack", which includes several racing cars, and the "Porsche Car Pack", consisting of cars made by vehicle manufacturer Porsche. In addition, the "Hoonigan Car Pack" includes in-game versions of cars that were used by the Hoonigan Racing Division.


title: Forza Horizon 3

text: On 13 December 2016, the expansion pack "Blizzard Mountain" was released. The pack added a new location to the game, characterised by a mountainous landscape and having harsh, snowy weather conditions. The severe weather conditions added a challenging feature to driving, as aspects like icy roads and whiteout affected the ability of the player to control the vehicle. Instead of accumulating fans, as is synonymous in the Australian location, players had the goal of collecting stars instead. Similar to earning fans, acquiring certain amounts of stars unlocks more events around the region. Additionally, three racing game modes were added to the DLC, and players received a rally/off-road car pack that is able to be customisable with snow tires with the purchase of "Blizzard Mountain".


title: Forza Horizon 3

text: On 9 May 2017, in collaboration with Mattel's Hot Wheels, Playground Games released a second expansion pack titled "Forza Horizon 3: Hot Wheels". Like "Blizzard Mountain", the pack added a new area to the game, portrayed as an archipelago connected by real-world scale Hot Wheels stunt track pieces instead of regular roads. The game's track acts similarly to an actual Hot Wheels course, illustrated by different kinds of stunt sections, such as vertical loops and half-pipes. Races can be customised with the Horizon Blueprint feature, where individual pieces of track are able to be swapped with other pieces. Continuing from "Blizzard Mountain", stars have to be earned in races to unlock more events, and players were given a car pack with the purchase of the expansion, of which some of the vehicles are life-scale Hot Wheels cars.