Editing Chess (section)

==Connections to other fields==

===Arts and humanities===
{{Main|Chess in the arts}}
In the [[Middle Ages]] and during the [[Renaissance]], chess was a part of [[nobility|noble]] culture; it was used to teach war strategy and was dubbed the "[[Chess or the King's Game|King's Game]]".<ref>{{harvp|Vale|2001|pp=170–199}}</ref> Gentlemen are "to be meanly seene in the play at Chestes", says the overview at the beginning of [[Baldassare Castiglione]]'s ''[[The Book of the Courtier]]'' (1528, English 1561 by Sir Thomas Hoby), but chess should not be a gentleman's main passion. Castiglione explains it further:
[[File:Meister der Manessischen Liederhandschrift 004.jpg|thumb|Noble chess players, Germany, {{circa|1320}}]]
{{blockquote|And what say you to the game at chestes? It is {{sic|truely|hide=y}} an honest kynde of enterteynmente and wittie, quoth Syr Friderick. But me think it hath a fault, whiche is, that a man may be to couning at it, for who ever will be excellent in the playe of chestes, I beleave he must beestowe much tyme about it, and applie it with so much study, that a man may assoone learne some noble scyence, or compase any other matter of importaunce, and yet in the ende in beestowing all that laboure, he knoweth no more but a game. Therfore in this I beleave there happeneth a very rare thing, namely, that the meane is more commendable, then the excellency.<ref>{{cite book |url=http://darkwing.uoregon.edu/~rbear/courtier/courtier2.html |archive-url=https://web.archive.org/web/20000818234955/http://darkwing.uoregon.edu/~rbear/courtier/courtier2.html |url-status=dead |archive-date=18 August 2000 |title=The Second Book of the Courtier |author=Count Bladessar Castilio |translator=Sir Thomas Hoby |editor=Walter Raleigh |publisher=David Nutt |location=London |date=1900 |access-date=7 May 2010 |orig-year=1561}}</ref>}}

Some of the elaborate chess sets used by the aristocracy at least partially survive, such as the [[Lewis chessmen]].

Chess was often used as a basis of sermons on [[morality]]. An example is ''Liber de moribus hominum et officiis nobilium sive super ludo scacchorum'' ('Book of the customs of men and the duties of nobles or the Book of Chess'), written by an Italian [[Order of Preachers|Dominican]] friar [[Jacobus de Cessolis]] {{circa|1300}}. This book was one of the most popular of the Middle Ages.<ref>{{harvp|Olmert|1996|p=127}}</ref> The work was translated into many other languages (the first printed edition was published at Utrecht in 1473) and was the basis for [[William Caxton]]'s ''The Game and Playe of the Chesse'' (1474), one of the first books printed in English.<ref>{{Cite book|chapter=§3. The first book printed in English — "The Recuyell of the Histories of Troy" | title= XIII. The Introduction of Printing into England and the Early Work of the Press. | volume= 2. The End of the Middle Ages | publisher= The Cambridge History of English and American Literature: An Encyclopedia in Eighteen Volumes. 1907–21|chapter-url=https://www.bartleby.com/212/1303.html|access-date=2022-12-29|via= Bartleby|archive-date=15 August 2022|archive-url=https://web.archive.org/web/20220815001313/https://www.bartleby.com/212/1303.html|url-status=live | author = E. Gordon Duff | date= 1907}}</ref> Different chess pieces were used as metaphors for different classes of people, and human duties were derived from the rules of the game or from visual properties of the chess pieces:<ref>{{harvp|Adams|2006}}</ref>

{{blockquote|The knyght ought to be made alle armed upon an hors in suche wyse that he haue an helme on his heed and a spere in his ryght hande/ and coueryd wyth his sheld/ a swerde and a mace on his lyft syde/ Cladd wyth an hawberk and plates to fore his breste/ legge harnoys on his legges/ Spores on his heelis on his handes his gauntelettes/ his hors well broken and taught and apte to bataylle and couerid with his armes/ whan the knyghtes ben maad they ben bayned or bathed/ that is the signe that they shold lede a newe lyf and newe maners/ also they wake alle the nyght in prayers and orysons vnto god that he wylle gyue hem grace that they may gete that thynge that they may not gete by nature/ The kynge or prynce gyrdeth a boute them a swerde in signe/ that they shold abyde and kepe hym of whom they take theyr dispenses and dignyte.<ref>{{Cite book |author1-last=Caxton | author1-first= William 
| author2-last=Jacobus |author2-first=de Cessolis
|editor= William Edward Armytage Axon | orig-date= 1474
|url=http://www.gutenberg.org/ebooks/10672 |title=The Game and Playe of the Chesse |publisher=Project Gutenberg |access-date=20 May 2010 |date=January 2004 |archive-url=https://web.archive.org/web/20090924213005/http://www.gutenberg.org/etext/10672 |archive-date=24 September 2009 |url-status=live}}</ref>}}

Known in the circles of clerics, students, and merchants, chess entered into the popular culture of the Middle Ages. An example is the 209th song of [[Carmina Burana]] from the 13th&nbsp;century, which starts with the names of chess pieces, ''Roch, pedites, regina...''<ref>{{cite web |url=http://www.fh-augsburg.de/~harsch/Chronologia/Lspost13/CarminaBurana/bur_cpo2.html |title=Carmina potoria |publisher=Bibliotheca Augustana |access-date=26 November 2008 |url-status=live |archive-url=https://web.archive.org/web/20071229151500/http://www.fh-augsburg.de/~harsch/Chronologia/Lspost13/CarminaBurana/bur_cpo2.html |archive-date=29 December 2007}}</ref> The game of chess, at times, has been discouraged by various religious authorities in Middle Ages: Jewish,<ref>{{Cite encyclopedia|title=Chess | author1 = Joseph Jacobs | author2= A. Porter |url=https://www.jewishencyclopedia.com/articles/4314-chess|access-date=2022-12-29|encyclopedia =[[The Jewish Encyclopedia]]|archive-date=29 December 2022|archive-url=https://web.archive.org/web/20221229064440/https://www.jewishencyclopedia.com/articles/4314-chess|url-status=live}}</ref> Catholic and [[Eastern Orthodox Church|Orthodox]].<ref>{{harvp|Murray|1985|pp=166–167, 410}}</ref> Some Muslim authorities prohibited it even recently, for example [[Ruhollah Khomeini]] in 1979 and [[Abdul-Aziz ibn Abdullah Al ash-Sheikh|Abdul-Aziz ash-Sheikh]] even later.<ref name="Forbidden">{{cite news |url=https://www.theguardian.com/world/2016/jan/21/chess-forbidden-in-islam-rules-saudi-arabia-grand-mufti|last1=Shaheen|first1=Kareem|title=Chess forbidden in Islam, rules Saudi mufti, but issue not black and white |work=The Guardian |date=21 January 2016|access-date=1 April 2019 |archive-url=https://web.archive.org/web/20160213200335/http://www.theguardian.com/world/2016/jan/21/chess-forbidden-in-islam-rules-saudi-arabia-grand-mufti |archive-date=13 February 2016 |url-status=live}}</ref>

During the [[Age of Enlightenment]], chess was viewed as a means of self-improvement. [[Benjamin Franklin]], in his article "[[The Morals of Chess]]" (1786), wrote:
{{blockquote|
The Game of Chess is not merely an idle amusement; several very valuable qualities of the mind, useful in the course of human life, are to be acquired and strengthened by it, so as to become habits ready on all occasions; for life is a kind of Chess, in which we have often points to gain, and competitors or adversaries to contend with, and in which there is a vast variety of good and ill events, that are, in some degree, the effect of prudence, or the want of it. By playing at Chess then, we may learn:

'''I. Foresight''', which looks a little into futurity, and considers the consequences that may attend an action ...

'''II. Circumspection''', which surveys the whole Chess-board, or scene of action: – the relation of the several Pieces, and their situations ...

'''III. Caution''', not to make our moves too hastily ...<ref>{{harvp|Franklin|2003}} [1786], p. 289</ref>
}}

[[File:Red King sleeping.jpg|thumb|right|upright 1.1|''[[Through the Looking-Glass]]'': the Red King is snoring. Illustration by Sir [[John Tenniel]].]]
Chess was occasionally criticized in the 19th century as a waste of time.<ref>{{cite web |website=Medium|url=https://medium.com/message/why-chess-will-destroy-your-mind-78ad1034521f |title=Why Chess Will Destroy Your Mind |first=Clive |last=Thompson |date=22 May 2014 |url-status=live |archive-url=https://web.archive.org/web/20170901152810/https://medium.com/message/why-chess-will-destroy-your-mind-78ad1034521f |archive-date=1 September 2017}}</ref><ref>{{cite web |url=https://www.techdirt.com/articles/20140613/08020527566/that-time-when-people-thought-playing-chess-would-make-you-violent.shtml |title=That Time When People Thought Playing Chess Would Make You Violent |website=TechDirt|last1=Geigner|first1=Timothy|date=20 June 2014 |url-status=live |archive-url=https://web.archive.org/web/20170324191000/https://www.techdirt.com/articles/20140613/08020527566/that-time-when-people-thought-playing-chess-would-make-you-violent.shtml |archive-date=24 March 2017}}</ref>

Chess is taught to children in schools around the world today. Many schools host chess clubs, and there are many scholastic tournaments specifically for children. Tournaments are held regularly in many countries, hosted by organizations such as the [[United States Chess Federation]] and the National Scholastic Chess Foundation.<ref>{{cite web |url=http://www.nscfchess.org/nscfmiss.html |archive-url=https://web.archive.org/web/20091230140133/http://www.nscfchess.org/nscfmiss.html |archive-date=30 December 2009 |title=National Scholastic Chess Foundation |access-date=30 December 2009}}</ref>

Chess is many times depicted in [[Chess in the arts and literature|the arts]]; significant works where chess plays a key role range from Thomas Middleton's ''[[A Game at Chess]]'' to ''[[Through the Looking-Glass]]'' by Lewis Carroll, to Vladimir Nabokov's ''[[The Defense]]'', to ''[[The Royal Game]]'' by Stefan Zweig. Chess has also featured in film classics such as [[Ingmar Bergman]]'s ''[[The Seventh Seal]]'', [[Satyajit Ray]]'s ''[[Shatranj Ke Khilari|The Chess Players]]'', and [[Powell and Pressburger]]'s ''[[A Matter of Life and Death (film)|A Matter of Life and Death]]''.

Chess is also present in contemporary popular culture. For example, the characters in ''[[Star Trek]]'' play a futuristic version of the game called "[[Federation (Star Trek)|Federation]] [[Tri-Dimensional Chess]]",<ref>{{Cite journal|last=Kraaijeveld|date=2000|title=Origin of chess–a phylogenetic perspective|url=http://ex.ludicum.org/publicacoes/bgsj/3.pdf#page=38|journal=Board Games Studies|volume=3|pages=39–50|via=|access-date=16 January 2021|archive-date=29 September 2020|archive-url=https://web.archive.org/web/20200929011559/http://ex.ludicum.org/publicacoes/bgsj/3.pdf#page=38|url-status=live}}</ref> and "[[Wizard's Chess]]" is played in J.K. Rowling's ''[[Harry Potter]]''.<ref name="Mayes-Elma2006">{{cite book|author=Ruthann Mayes-Elma|url=https://books.google.com/books?id=LiWrXUHgnL8C&pg=PA95|title=Females and Harry Potter: Not All that Empowering|publisher=Rowman & Littlefield|year=2006|isbn=978-0-7425-3779-8|pages=95–|access-date=16 January 2021|archive-date=13 August 2021|archive-url=https://web.archive.org/web/20210813113441/https://books.google.com/books?id=LiWrXUHgnL8C&pg=PA95|url-status=live}}</ref>

===Mathematics===
{{See also|Mathematical chess problem|Solving chess}}
The game structure and nature of chess are related to several branches of mathematics. Many [[combinatorics|combinatorical]] and [[topology|topological]] problems connected to chess, such as the [[knight's tour]] and the [[eight queens puzzle]], have been known for hundreds of years.

[[File:Knight's tour.svg|thumb|upright 0.8|Mathematicians [[Euler]], [[Adrien-Marie Legendre|Legendre]], [[de Moivre]], and [[Vandermonde]] studied the [[knight's tour]].]]
The number of legal positions in chess is estimated to be {{thinspace|(4.59|±|0.38)|×|10<sup>44</sup>}} with a 95% confidence level,<ref>{{cite web |title=Chess Position Ranking |author=John Tromp |website=[[GitHub]] | year=2021 | url=https://github.com/tromp/ChessPositionRanking | url-status=live|archive-url=https://web.archive.org/web/20210808152713/https://github.com/tromp/ChessPositionRanking |archive-date=8 August 2021 }}</ref> with a [[game-tree complexity]] of approximately 10<sup>123</sup>. The game-tree complexity of chess was first calculated by [[Claude Shannon]] as 10<sup>120</sup>, a number known as the [[Shannon number]].<ref>{{cite web|title=Evolution of the Chess Robot: Brute force Wins|first=Jonathan|last=Babb|publisher=Massachusetts Institute of Technology|date=January 10, 1996|url=http://groups.csail.mit.edu/cag/pub/papers/jbabb-area.ps.Z|access-date=21 February 2023|archive-date=21 February 2023|archive-url=https://web.archive.org/web/20230221064724/http://groups.csail.mit.edu/cag/pub/papers/jbabb-area.ps.Z|url-status=live}}</ref> An average position typically has thirty to forty possible moves, but there may be as few as zero (in the case of checkmate or stalemate) or (in a constructed position) as many as 218.<ref>{{cite web |url=http://www.chessbox.de/Compu/schachzahl2_e.html |archive-url=https://web.archive.org/web/20070613072827/http://www.chessbox.de/Compu/schachzahl2_e.html |archive-date=13 June 2007 |publisher=ChessBox.de |title=The biggest Number of simultaneous possible legal Moves |url-status=dead}}</ref>

In 1913, [[Ernst Zermelo]] used chess as a basis for his theory of game strategies, which is considered one of the predecessors of [[game theory]].<ref>Zermelo, Ernst (1913), Uber eine Anwendung der Mengenlehre auf die Theorie des Schachspiels, Proceedings of the Fifth International Congress of Mathematicians 2, 501–04. Cited from Eichhorn, Christoph: Der Beginn der Formalen Spieltheorie: Zermelo (1913), [http://www.mathematik.uni-muenchen.de/~spielth/artikel/Zermelo.pdf Uni-Muenchen.de] {{webarchive|url=https://web.archive.org/web/20070612134609/http://www.mathematik.uni-muenchen.de/~spielth/artikel/Zermelo.pdf |date=12 June 2007 }}. Retrieved 23 March 2007.</ref> [[Zermelo's theorem (game theory)|Zermelo's theorem]] states that it is possible to [[Solving chess|solve chess]], i.e. to determine with certainty the outcome of a perfectly played game (either White can force a win, or Black can force a win, or both sides can force at least a draw).<ref>{{cite web |url=http://www.gap-system.org/~history/Projects/MacQuarrie/Chapters/Ch4.html |title=Fundamentals |work=gap-system.org |url-status=dead |archive-url=https://web.archive.org/web/20110607183513/http://www.gap-system.org/~history/Projects/MacQuarrie/Chapters/Ch4.html |archive-date=7 June 2011}}</ref> With 10<sup>43</sup> legal positions in chess, however, it will take an impossibly long time to compute a perfect strategy with any feasible technology.<ref>{{cite book |title=Encyclopedia of Computer Science and Technology: Volume 8 |chapter=Games |page=394 |isbn=978-0-8247-2258-6 |publisher=CRC Press |year=1977}}</ref>

====Applied mathematics====
A novel methodology in [[steganography]] explores the use of chess-based covers (such as puzzles, chess problems, game reports, training documents, news articles, etc.) for concealing data within a selection of {{Chessgloss|move|moves}}, each hiding some [[bit]]s.<ref>{{cite journal |last1=Desoky |first1=Abdelrahman |last2=Younis |first2=Mohamed |title=Chestega: chess steganography methodology |journal=Security and Communication Networks |date=November 2009 |volume=2 |issue=6 |pages=555–566 |doi=10.1002/sec.99 |doi-access=free }}</ref><ref>{{cite journal |last1=Hernandez-Castro |first1=Julio C. |last2=Blasco-Lopez |first2=Ignacio |last3=Estevez-Tapiador |first3=Juan M. |last4=Ribagorda-Garnacho |first4=Arturo |title=Steganography in games: A general methodology and its application to the game of Go |journal=Computers & Security |date=February 2006 |volume=25 |issue=1 |pages=64–71 |doi=10.1016/j.cose.2005.12.001 }}</ref> Several proof-of-concept projects have been developed that convert text or files into [[binary code]], which is then converted into a series of legal chess moves, that can then be [[Decryption|decrypted]] and downloaded.<ref>{{Cite web |last=Mukherjee |first=Nayanika |date=15 September 2024 |title='I turned Lichess into Google Drive': 18yo shows how to store files, secret messages in a game of chess |url=https://indianexpress.com/article/puzzles-and-games/info/chess-games-cloud-storage-creative-coding-cryptography-brainteasers-9567020/ |access-date=28 January 2025 |newspaper=[[The Indian Express]]}}</ref>

[[Correspondence chess]] has been historically suspected of being a potential steganographic medium. [[Melville Davisson Post]] documented a [[chess problem]] that was used to create a pictorial [[cipher]] during [[World War I]].<ref>{{Cite magazine |last=Post |first=Melville Davisson |author-link=Melville Davisson Post |date=January 1918 |title=German War Ciphers |hdl=2027/uiug.30112077173703?urlappend=%3Bseq=626%3Bownerid=13510798903194481-672 |hdl-access=free |magazine=[[Everybody's Magazine]] |volume=38 |number=1 |pages=28–34 }}</ref><ref>{{Cite magazine |last=Oberhaus |first=Daniel |date=25 March 2017 |title=The Spy Who Checkmated Me: Why Postal Chess Was Banned During Wartime |url=https://www.vice.com/en/article/the-spy-who-checkmated-me-why-postal-chess-was-banned-during-wartime/ |access-date=28 January 2025 |magazine=[[Vice (magazine)|Vice]]}}</ref> During [[World War II]], extensive [[postal censorship]] was imposed on [[military personnel]] from the United States and Canada that made playing correspondence chess impossible, arising from suspicion that chess could be used to send secret messages to the enemies.<ref>{{Cite magazine |last=Dubois |first=Joan |date=September 1991 |title=Golden Knights in Review |url=https://uscf1-nyc1.aodhosting.com/CL-AND-CR-ALL/CL-ALL/1991/1991_09.pdf#page=40 |magazine=[[Chess Life]] |pages=40–45 |via=[[US Chess Federation]] |volume=46 |number=9}}</ref>

===Psychology===
There is an extensive scientific literature on chess psychology.{{refn|Chess is even called the "[[drosophila]]" of [[cognitive psychology]] and [[artificial intelligence]] (AI) studies, because it represents the domain in which expert performance has been most intensively studied and measured.<ref>{{harvp|Grabner|Stern|Neubauer|2007|pp=398–420}}</ref>|group=note}}<ref>{{harvp|de Groot|Gobet|1996}}</ref><ref>{{harvp|Gobet|de Voogt|Retschitzki|2004}}</ref><ref>{{harvp|Holding|1985}}</ref><ref>{{harvp|Saariluoma|1995}}</ref> [[Alfred Binet]] and others showed that [[knowledge]] and verbal, rather than visuospatial, ability lies at the core of expertise.<ref>{{harvp|Binet|1894}}</ref><ref>{{harvp|Robbins|Anderson|Barker|Bradley|Fearnyhough|Henson|Hudson|Baddeley|1996|pp=83–93}}</ref> In his doctoral thesis, [[Adriaan de Groot]] showed that chess masters can rapidly perceive the key features of a position.<ref>{{harvp|de Groot|1965}}</ref> According to de Groot, this [[perception]], made possible by years of practice and study, is more important than the sheer ability to anticipate moves. De Groot showed that chess masters can memorize positions shown for a few seconds almost perfectly. The ability to memorize does not alone account for chess-playing skill, since masters and novices, when faced with random arrangements of chess pieces, had equivalent recall (about six positions in each case). Rather, it is the ability to recognize patterns, which are then memorized, which distinguished the skilled players from the novices. When the positions of the pieces were taken from an actual game, the masters had almost total positional recall.<ref>Richards J. Heuer Jr. ''Psychology of Intelligence Analysis'' Center for the Study of Intelligence, Central Intelligence Agency 1999 (see [https://www.cia.gov/library/center-for-the-study-of-intelligence/csi-publications/books-and-monographs/psychology-of-intelligence-analysis/art6.html Chapter 3] {{webarchive|url=https://web.archive.org/web/20070912045710/https://www.cia.gov/library/center-for-the-study-of-intelligence/csi-publications/books-and-monographs/psychology-of-intelligence-analysis/art6.html |date=12 September 2007 }}).</ref>

More recent research has focused on [[chess as mental training]]; the respective roles of knowledge and look-ahead search; [[brain imaging]] studies of chess masters and novices; [[blindfold chess]]; the role of [[Personality psychology|personality]] and [[intelligence]] in chess skill; gender differences; and computational models of chess expertise. The role of practice and talent in the development of chess and other domains of expertise has led to much empirical investigation. Ericsson and colleagues have argued that deliberate practice is sufficient for reaching high levels of expertise in chess.<ref>{{ cite journal
| last1= Ericsson | first1= K.A.
| last2= Krampe | first2= R. Th.
| last3= Tesch-Römer | first3= C. 
| date= 1993
|url=http://www.freakonomics.com/pdf/DeliberatePractice%28PsychologicalReview%29.pdf |archive-url=https://web.archive.org/web/20060512183911/http://www.freakonomics.com/pdf/DeliberatePractice%28PsychologicalReview%29.pdf |url-status=dead |archive-date=12 May 2006 |title=The role of deliberate practice in the acquisition of expert performance | journal=Psychological Review | volume= 100 | issue= 3
| pages= 363–406| doi= 10.1037/0033-295X.100.3.363
| s2cid= 11187529
}}</ref> Recent research, however, fails to replicate their results and indicates that factors other than practice are also important.<ref>{{Cite journal |last1=Macnamara |first1=Brooke N. |last2=Maitra |first2=Megha |date=21 August 2019 |title=The role of deliberate practice in expert performance: revisiting Ericsson, Krampe & Tesch-Römer (1993) |journal=Royal Society Open Science|volume=6 |issue=8 |page=190327 |doi=10.1177/0963721411421922|pmid=31598236 |pmc=6731745 |s2cid=190327 }}</ref><ref name="Gobet-Fernand2011">Gobet, F. & Chassy, P. (in press). {{cite web |url=http://bura.brunel.ac.uk/bitstream/2438/736/1/Seasonality%20and%20chess.pdf |title=Season of birth and chess expertise. |url-status=live |archive-url=https://web.archive.org/web/20110718172434/http://bura.brunel.ac.uk/bitstream/2438/736/1/Seasonality%20and%20chess.pdf |archive-date=18 July 2011}}&nbsp;{{small|(65.8&nbsp;KB)}} ''Journal of Biosocial Science''. <br/> Gobet, F. & Campitelli, G. (2007). {{cite web |url=http://bura.brunel.ac.uk/bitstream/2438/611/1/Gobet_DevPsyc_Final.pdf |title=The role of domain-specific practice, handedness and starting age in chess. |url-status=live |archive-url=https://web.archive.org/web/20070808073144/http://bura.brunel.ac.uk/bitstream/2438/611/1/Gobet_DevPsyc_Final.pdf |archive-date=8 August 2007 |df=dmy-all}}&nbsp;{{small|(196&nbsp;KB)}} ''Developmental Psychology'', 43, 159–72. Both retrieved 2007-07-15.</ref>
For example, [[Fernand Gobet]] and colleagues have shown that stronger players started playing chess at a young age and that experts born in the Northern Hemisphere are more likely to have been born in late winter and early spring. Compared to the general population, chess players are more likely to be non-right-handed, though they found no correlation between handedness and skill.<ref name="Gobet-Fernand2011" />

A relationship between chess skill and intelligence has long been discussed in scientific literature as well as in popular culture. Academic studies that investigate the relationship date back at least to 1927.<ref>Djakow, I. N., Petrowski, N. W., & Rudik, P. A. (1927).

Psychologie des schachspiels.</ref> Although one meta-analysis and most children studies find a positive correlation between general cognitive ability and chess skill, adult studies show mixed results.<ref>{{Cite journal |date=1 November 2016 |title=The relationship between cognitive ability and chess skill: A comprehensive meta-analysis |journal=Intelligence |language=en |volume=59 |pages=72–83 |doi=10.1016/j.intell.2016.08.002 |issn=0160-2896 |last1=Burgoyne |first1=Alexander P. |last2=Sala |first2=Giovanni |last3=Gobet |first3=Fernand |last4=MacNamara |first4=Brooke N. |last5=Campitelli |first5=Guillermo |last6=Hambrick |first6=David Z. |url=http://eprints.lse.ac.uk/102241/1/INTELL_2016_117_The_Relationship_between_Cognitive_Ability_and_Chess_Skill_a_Comprehensive_Meta_Analysis.pdf |access-date=26 February 2020 |archive-date=6 May 2020 |archive-url=https://web.archive.org/web/20200506054933/http://eprints.lse.ac.uk/102241/1/INTELL_2016_117_The_Relationship_between_Cognitive_Ability_and_Chess_Skill_a_Comprehensive_Meta_Analysis.pdf |url-status=live }}</ref><ref>{{Cite journal |last1=Campitelli |first1=Guillermo |last2=Gobet |first2=Fernand |date=5 October 2011 |title=Deliberate Practice: Necessary But Not Sufficient |journal=Current Directions in Psychological Science |volume=20 |issue=5 |pages=280–285 |doi=10.1177/0963721411421922|s2cid=145572294 }}</ref>