Editing Tetris (section)

==Research==
=== Psychological research ===
{{See also|Tetris effect}}
The psychological and addictive effects of ''Tetris'' were first scientifically recognized by Soviet clinical psychologist [[Vladimir Pokhilko]] {{circa}} 1985.{{sfn|Ackerman|2016|p=73}}<ref name="MarkWolf2012">{{cite book |first=Mark J. P. |last=Wolf | title=Encyclopedia of Video Games: The Culture, Technology, and Art of Gaming |chapter=Tetris |chapter-url=https://archive.org/details/isbn_9780313379369_2/page/640/mode/2up | date=August 31, 2012 |location=Santa Barbara, CA| publisher=[[Greenwood Press]] | isbn=978-0-313-37936-9 | pages=640–642 | chapter-url-access=registration |via=[[Internet Archive]] }}</ref> Pokhilko was a recipient of the IBM version of ''Tetris'' in [[Moscow]]. Interested in its potential psychological effects based on his experiences playing the game, Pokhilko distributed copies of ''Tetris'' to his colleagues at the Moscow Medical Center. Pokhilko regretted his decision after constant gameplay impaired medical research so he proceeded to destroy the distributed copies. After new copies were reintroduced to his facility, Pokhilko used ''Tetris'' while testing patients.{{sfn|Ackerman|2016|pp=69–70}} 

Starting with the research of American psychologist [[Richard J. Haier]] in 1992,<ref>{{cite journal|vauthors=Haier RJ, Siegel BV, MacLachlan A, Soderling E, Lottenberg S, Buchsbaum MS|title=Regional glucose metabolic changes after learning a complex visuospatial/motor task: a positron emission tomographic study|journal=Brain Res.|volume=570|issue=1–2|pages=134–43|date=January 1992|pmid=1617405|doi=10.1016/0006-8993(92)90573-R|s2cid=21725897}}</ref>{{sfn|Ackerman|2016|pp=81–82}}<ref>{{cite journal |last1=Latham |first1=Andrew J. |last2=Patson |first2=Lucy L. M. |last3=Tippette |first3=Lynette J. |title=The virtual brain: 30 years of video-game play and cognitive abilities |journal=[[Frontiers in Psychology]] |date=September 13, 2013 |volume=4 |page=629 |doi=10.3389/fpsyg.2013.00629|doi-access=free |pmid=24062712 |pmc=3772618 }}</ref> ''Tetris'' has been frequently used as a form of cognitive assessment and neuroimaging.<ref name=currentpsychology-2021>{{cite journal |last1=Agren |first1=Thomas |last2=Hoppe |first2=Johanna M. |last3=Singh |first3=Laura |last4=Holmes |first4=Emily A. |last5=Rosén |first5=Jörgen |title=The neural basis of Tetris gameplay: implicating the role of visuospatial processing |journal=Current Psychology |date=August 2, 2021 |volume=42 |issue=10 |pages=8156–8163 |doi=10.1007/s12144-021-02081-z |doi-access=free }}</ref><ref>{{cite journal |url=https://link.springer.com/article/10.3758/s13428-014-0547-y#Fn3 |last1=Lindstedt |first1=John K. |last2=Gray |first2=Wayne D. |title=Meta-T: TetrisⓇ as an experimental paradigm for cognitive skills research |journal=[[Behavior Research Methods]] |date=March 12, 2015 |volume=47 |issue=4 |pages=945–965 |doi=10.3758/s13428-014-0547-y |pmid=25761389 |access-date=November 14, 2024 |archive-date=January 22, 2022 |archive-url=https://web.archive.org/web/20220122090625/https://link.springer.com/article/10.3758%2Fs13428-014-0547-y#Fn3 |url-status=live }}</ref> Furthermore, ''Tetris'' has been studied as a potential form of psychological intervention such as for [[PTSD]] and [[wikt:craving|cravings]] with promising results.<ref name=currentpsychology-2021/>{{sfn|Plank|2022|p=271}} The "[[Tetris effect|''Tetris'' effect]]" refers to the phenomena of perceiving certain patterns in dreams and mental images following engagement in a repetitive activity such as playing ''Tetris.''{{sfn|Ackerman|2016|p=73}}<ref name=time-movie>{{cite magazine |url=https://time.com/6266810/tetris-movie-apple-tv-true-story/ |last=McCluskey |first=Megan |title=The Complicated True Story Behind Apple TV+'s Tetris Movie |magazine=[[Time (magazine)|Time]] |date=March 31, 2023 |access-date=November 12, 2024 |archive-date=February 27, 2024 |archive-url=https://web.archive.org/web/20240227090730/https://time.com/6266810/tetris-movie-apple-tv-true-story/ |url-status=live }}</ref> The term was coined by Jeffrey Goldsmith in a 1994 article for ''[[Wired (magazine)|Wired]]'',<ref name="wired/1994/05/tetris">{{cite magazine |last1=Goldsmith |first1=Jeffrey |date=1994-05-01 |title=This Is Your Brain on Tetris |url=https://www.wired.com/1994/05/tetris-2/ |url-status=live |archive-url=https://web.archive.org/web/20221122022558/https://www.wired.com/1994/05/tetris-2/ |archive-date=November 22, 2022 |access-date=22 November 2022 |magazine=Wired}}</ref> in which he compared ''Tetris'' to an "electronic drug".{{sfn|Ackerman|2016|p=77–78}}

=== Computer science research ===
In 1992, John Brzustowski at the [[University of British Columbia]] wrote a thesis on the question of whether or not one could theoretically play ''Tetris'' forever.<ref>{{Cite thesis |last=Brzustowski |first=John |title=Can you win at Tetris? |date=March 1992 |degree=Master of Science |publisher=[[University of British Columbia]] |url=https://open.library.ubc.ca/media/stream/pdf/831/1.0079748 |format=PDF |archive-url=https://web.archive.org/web/20220318064558/https://open.library.ubc.ca/media/stream/pdf/831/1.0079748 |archive-date=March 18, 2022 |access-date=October 16, 2013 |url-status=live}} [https://archive.org/details/20220318_20220318_0433 Alt URL]</ref> He reached the conclusion that ''Tetris'' is statistically doomed to end. If a player receives a sufficiently large sequence of alternating S and Z tetrominoes, the naïve gravity used by the standard game eventually forces the player to leave holes on the board. The holes will necessarily stack to the top and end the game. If the pieces are distributed randomly, this sequence will eventually occur. Thus, if a game with, for example, an ideal, uniform, uncorrelated [[Random number generation|random number generator]] is played long enough, any player will [[almost surely]] top out.<ref>{{Cite web |last=Burgiel |first=Heidi |date=January 7, 1996 |title=Discussion of the Tetris Applet |url=http://www.math.uic.edu/~burgiel/Tetris/explanation.html |url-status=dead |archive-url=https://web.archive.org/web/20061209110731/http://www.math.uic.edu/~burgiel/Tetris/explanation.html |archive-date=December 9, 2006 |access-date=February 25, 2007 |website=Tetris Research Page}}</ref><ref>Heidi Burgiel. [http://www.geom.umn.edu/%7Eburgiel/Tetris/tetris.PS How to Lose at Tetris] {{webarchive|url=https://web.archive.org/web/20030513033006/http://www.geom.umn.edu/~burgiel/Tetris/tetris.PS |date=May 13, 2003 }}, Mathematical Gazette, vol. 81, pp. 194–200 1997</ref>

In [[computer science]], it is common to analyze the [[Computational complexity theory|computational complexity]] of problems, including real-life problems and games. In 2001, a group of [[MIT]] researchers proved that for the "offline" version of ''Tetris'' (the player knows the complete sequence of pieces that will be dropped, i.e. there is no hidden information) the following objectives are [[NP-complete]]:
# Maximizing the number of rows cleared while playing the given piece sequence.
# Maximizing the number of pieces placed before a loss occurs.
# Maximizing the number of simultaneous clearing of four rows.
# Minimizing the height of the highest filled grid square over the course of the sequence.

Also, it is [[Hardness of approximation|difficult to even approximately solve]] the first, second, and fourth problem. It is [[NP-hard]], given an initial field and a sequence of ''p'' pieces, to approximate the first two problems to within a factor of {{nowrap|''p''<sup>1 − ''ε''</sup>}} for any constant {{nowrap|''ε'' > 0}}. It is NP-hard to approximate the last problem within a factor of {{nowrap|2 − ''ε''}} for any constant {{nowrap|''ε'' > 0}}. To prove NP-completeness, it was shown that there is a polynomial [[Reduction (complexity)|reduction]] between the [[3-partition problem]], which is also NP-complete, and the ''Tetris'' problem.<ref>{{cite conference|url=http://erikdemaine.org/papers/Tetris_COCOON2003/paper.pdf|title=Tetris is Hard, Even to Approximate|last1=Demaine|first1=Erik D.|last2=Hohenberger|first2=Susan|last3=Liben-Nowell|first3=David|date=July 25–28, 2003|conference=Proceedings of the 9th International Computing and Combinatorics Conference (COCOON 2003)|conference-url=https://web.archive.org/web/20120105042734/http://www.cs.montana.edu/bhz/cocoon03.html|location=Big Sky, Montana|access-date=December 18, 2009|archive-url=https://web.archive.org/web/20100613201613/http://erikdemaine.org/papers/Tetris_COCOON2003/paper.pdf|archive-date=June 13, 2010|url-status=live}}</ref><ref>{{cite book |url=https://archive.org/details/powerupunlocking0000lane/ |last=Lane |first=Matthew |title=Power-up: Unlocking the Hidden Mathematics in Video Games |publisher=[[Princeton University Press]] |date=2017 |pages=165–166 |isbn=9780691161518 |via=[[Internet Archive]] |url-access=registration}}</ref>