Game complexity (English Wikipedia)

Bonnet, Edouard; Jamain, Florian; Saffidine, Abdallah (2013). "On the complexity of trick-taking card games". In Rossi, Francesca (ed.). IJCAI 2013, Proceedings of the 23rd International Joint Conference on Artificial Intelligence, Beijing, China, August 3-9, 2013. IJCAI/AAAI. pp. 482–488.

adsabs.harvard.edu (Global: 14^th place; English: 9^th place)

ui.adsabs.harvard.edu

Jonathan Schaeffer; et al. (July 6, 2007). "Checkers is Solved". Science. 317 (5844): 1518–1522. Bibcode:2007Sci...317.1518S. doi:10.1126/science.1144079. PMID 17641166. S2CID 10274228.
Bell, George I. (2009). "The Shortest Game of Chinese Checkers and Related Problems". Integers. 9. arXiv:0803.1245. Bibcode:2008arXiv0803.1245B. doi:10.1515/INTEG.2009.003. S2CID 17141575.

ams.org (Global: 434^th place; English: 249^th place)

mathscinet.ams.org

Orman, Hilarie K. (1996). "Pentominoes: a first player win" (PDF). In Nowakowski, Richard J. (ed.). Games of No Chance: Papers from the Combinatorial Games Workshop held in Berkeley, CA, July 11–21, 1994. Mathematical Sciences Research Institute Publications. Vol. 29. Cambridge University Press. pp. 339–344. ISBN 0-521-57411-0. MR 1427975.
Lachmann, Michael; Moore, Cristopher; Rapaport, Ivan (2002). "Who wins Domineering on rectangular boards?". In Nowakowski, Richard (ed.). More Games of No Chance: Proceedings of the 2nd Combinatorial Games Theory Workshop held in Berkeley, CA, July 24–28, 2000. Mathematical Sciences Research Institute Publications. Vol. 42. Cambridge University Press. pp. 307–315. ISBN 0-521-80832-4. MR 1973019.
Kasai, Takumi; Adachi, Akeo; Iwata, Shigeki (1979). "Classes of pebble games and complete problems". SIAM Journal on Computing. 8 (4): 574–586. doi:10.1137/0208046. MR 0573848. Proves completeness of the generalization to arbitrary graphs.
Iwata, Shigeki; Kasai, Takumi (1994). "The Othello game on an $n\times n$ board is PSPACE-complete". Theoretical Computer Science. 123 (2): 329–340. doi:10.1016/0304-3975(94)90131-7. MR 1256205.
Fraenkel, Aviezri S.; Lichtenstein, David (1981). "Computing a perfect strategy for $n\times n$ chess requires time exponential in $n$ ". Journal of Combinatorial Theory, Series A. 31 (2): 199–214. doi:10.1016/0097-3165(81)90016-9. MR 0629595.

arxiv.org (Global: 49^th place; English: 31^st place)

Bell, George I. (2009). "The Shortest Game of Chinese Checkers and Related Problems". Integers. 9. arXiv:0803.1245. Bibcode:2008arXiv0803.1245B. doi:10.1515/INTEG.2009.003. S2CID 17141575.
Gualà, Luciano; Leucci, Stefano; Natale, Emanuele (2014). "Bejeweled, Candy Crush and other match-three games are (NP-)hard". 2014 IEEE Conference on Computational Intelligence and Games, CIG 2014, Dortmund, Germany, August 26-29, 2014. IEEE. pp. 1–8. arXiv:1403.5830. doi:10.1109/CIG.2014.6932866. ISBN 978-1-4799-3547-5.
Donghwi Park (2015). "Space-state complexity of Korean chess and Chinese chess". arXiv:1507.06401 [math.GM].
E. Bonnet; F. Jamain; A. Saffidine (March 25, 2014). "Havannah and TwixT are PSPACE-complete". arXiv:1403.6518 [cs.CC].
R. A. Hearn (February 2, 2005). "Amazons is PSPACE-complete". arXiv:cs.CC/0502013.
CDA Evans and Joel David Hamkins (2014). "Transfinite game values in infinite chess". arXiv:1302.4377 [math.LO].
Stefan Reisch, Joel David Hamkins, and Phillipp Schlicht (2012). "The mate-in-n problem of infinite chess is decidable". Conference on Computability in Europe: 78–88. arXiv:1201.5597.{{cite journal}}: CS1 maint: multiple names: authors list (link)
Alex Churchill, Stella Biderman, and Austin Herrick (2020). "Magic: the Gathering is Turing Complete". arXiv:1904.09828 [cs.AI].{{cite arXiv}}: CS1 maint: multiple names: authors list (link)
Stella Biderman (2020). "Magic: the Gathering is as Hard as Arithmetic". arXiv:2003.05119 [cs.AI].
Lokshtanov, Daniel; Subercaseaux, Bernardo (May 14, 2022). "Wordle is NP-hard". arXiv:2203.16713 [cs.CC].

computerhistory.org (Global: 2,702^nd place; English: 1,789^th place)

archive.computerhistory.org

The size of the state space and game tree for chess were first estimated in Shannon, Claude (1950). "Programming a Computer for Playing Chess" (PDF). Philosophical Magazine. 41 (314). Archived from the original (PDF) on 2010-07-06. Shannon gave estimates of 10⁴³ and 10¹²⁰ respectively, smaller than the upper bound in the table, which is detailed in Shannon number.

cwi.nl (Global: low place; English: low place)

homepages.cwi.nl

"Statistics on the length of a go game".

doi.org (Global: 2^nd place; English: 2^nd place)

Stefan Reisch (1980). "Gobang ist PSPACE-vollständig (Gobang is PSPACE-complete)". Acta Informatica. 13 (1): 59–66. doi:10.1007/bf00288536. S2CID 21455572.
Slany, Wolfgang (2000). "The complexity of graph Ramsey games". In Marsland, T. Anthony; Frank, Ian (eds.). Computers and Games, Second International Conference, CG 2000, Hamamatsu, Japan, October 26-28, 2000, Revised Papers. Lecture Notes in Computer Science. Vol. 2063. Springer. pp. 186–203. doi:10.1007/3-540-45579-5_12. ISBN 978-3-540-43080-3.
H. J. van den Herik; J. W. H. M. Uiterwijk; J. van Rijswijck (2002). "Games solved: Now and in the future". Artificial Intelligence. 134 (1–2): 277–311. doi:10.1016/S0004-3702(01)00152-7.
Edelkamp, Stefan, and Peter Kissmann. “Symbolic Classification of General Two-Player Games.” KI 2008: Advances in Artificial Intelligence, edited by Andreas R. Dengel et al., vol. 5243, Springer Berlin Heidelberg, 2008, pp. 185–92. DOI.org (Crossref), https://doi.org/10.1007/978-3-540-85845-4_23.
Jonathan Schaeffer; et al. (July 6, 2007). "Checkers is Solved". Science. 317 (5844): 1518–1522. Bibcode:2007Sci...317.1518S. doi:10.1126/science.1144079. PMID 17641166. S2CID 10274228.
Schaeffer, Jonathan (2007). "Game over: Black to play and draw in checkers" (PDF). ICGA Journal. 30 (4): 187–197. doi:10.3233/ICG-2007-30402. Archived from the original (PDF) on 2016-04-03.
J. M. Robson (1984). "N by N checkers is Exptime complete". SIAM Journal on Computing. 13 (2): 252–267. doi:10.1137/0213018.
M.P.D. Schadd; M.H.M. Winands; J.W.H.M. Uiterwijk; H.J. van den Herik; M.H.J. Bergsma (2008). "Best Play in Fanorona leads to Draw" (PDF). New Mathematics and Natural Computation. 4 (3): 369–387. doi:10.1142/S1793005708001124.
Bell, George I. (2009). "The Shortest Game of Chinese Checkers and Related Problems". Integers. 9. arXiv:0803.1245. Bibcode:2008arXiv0803.1245B. doi:10.1515/INTEG.2009.003. S2CID 17141575.
Kasai, Takumi; Adachi, Akeo; Iwata, Shigeki (1979). "Classes of pebble games and complete problems". SIAM Journal on Computing. 8 (4): 574–586. doi:10.1137/0208046. MR 0573848. Proves completeness of the generalization to arbitrary graphs.
Iwata, Shigeki; Kasai, Takumi (1994). "The Othello game on an $n\times n$ board is PSPACE-complete". Theoretical Computer Science. 123 (2): 329–340. doi:10.1016/0304-3975(94)90131-7. MR 1256205.
Fraenkel, Aviezri S.; Lichtenstein, David (1981). "Computing a perfect strategy for $n\times n$ chess requires time exponential in $n$ ". Journal of Combinatorial Theory, Series A. 31 (2): 199–214. doi:10.1016/0097-3165(81)90016-9. MR 0629595.
Gualà, Luciano; Leucci, Stefano; Natale, Emanuele (2014). "Bejeweled, Candy Crush and other match-three games are (NP-)hard". 2014 IEEE Conference on Computational Intelligence and Games, CIG 2014, Dortmund, Germany, August 26-29, 2014. IEEE. pp. 1–8. arXiv:1403.5830. doi:10.1109/CIG.2014.6932866. ISBN 978-1-4799-3547-5.
Chang-Ming Xu; Ma, Z.M.; Jun-Jie Tao; Xin-He Xu (2009). "Enhancements of proof number search in connect6". 2009 Chinese Control and Decision Conference. p. 4525. doi:10.1109/CCDC.2009.5191963. ISBN 978-1-4244-2722-2. S2CID 20960281.
Hsieh, Ming Yu; Tsai, Shi-Chun (October 1, 2007). "On the fairness and complexity of generalized k -in-a-row games". Theoretical Computer Science. 385 (1–3): 88–100. doi:10.1016/j.tcs.2007.05.031.
Tesauro, Gerald (May 1, 1992). "Practical issues in temporal difference learning". Machine Learning. 8 (3–4): 257–277. doi:10.1007/BF00992697.
Witter, R.T. (2021). Backgammon Is Hard. In: Du, DZ., Du, D., Wu, C., Xu, D. (eds) Combinatorial Optimization and Applications. COCOA 2021. Lecture Notes in Computer Science(), vol 13135. Springer, Cham. https://doi.org/10.1007/978-3-030-92681-6_38
Shi-Jim Yen, Jr-Chang Chen; Tai-Ning Yang; Shun-Chin Hsu (March 2004). "Computer Chinese Chess" (PDF). International Computer Games Association Journal. 27 (1): 3–18. doi:10.3233/ICG-2004-27102. S2CID 10336286. Archived from the original (PDF) on 2007-06-14.
Iida, Hiroyuki; Sakuta, Makoto; Rollason, Jeff (January 2002). "Computer shogi". Artificial Intelligence. 134 (1–2): 121–144. doi:10.1016/S0004-3702(01)00157-6.

draftsim.com (Global: low place; English: low place)

"Infinite Combos in MTG: 39 Awesome Combos to Try".

github.com (Global: 380^th place; English: 337^th place)

T, Brian (October 20, 2018). "Btsan/generate_tictactoe". GitHub. Retrieved 2020-04-08.

icosahedral.net (Global: low place; English: low place)

David Jian Wu (2011). "Move Ranking and Evaluation in the Game of Arimaa" (PDF).

janzert.com (Global: low place; English: low place)

arimaa.janzert.com

Brian Haskin (2006). "A Look at the Arimaa Branching Factor".

maastrichtuniversity.nl (Global: low place; English: low place)

project.dke.maastrichtuniversity.nl

Victor Allis (1994). Searching for Solutions in Games and Artificial Intelligence (PDF) (Ph.D. thesis). University of Limburg, Maastricht, The Netherlands. ISBN 90-900748-8-0.
Robert Briesemeister (2009). Analysis and Implementation of the Game OnTop (PDF) (Thesis). Maastricht University, Dept of Knowledge Engineering.
Diederik Wentink (2001). Analysis and Implementation of the game Gipf (PDF) (Thesis). Maastricht University.
Chorus, Pascal. "Implementing a Computer Player for Abalone Using Alpha-Beta and Monte-Carlo Search" (PDF). Dept of Knowledge Engineering, Maastricht University. Retrieved 2012-03-29.
Joosten, B. "Creating a Havannah Playing Agent" (PDF). Retrieved 2012-03-29.
Kevin Moesker (2009). Txixt: Theory, Analysis, and Implementation (PDF) (Thesis). Faculty of Humanities and Sciences of Maastricht University.
Cathleen Heyden (2009). Implementing a Computer Player for Carcassonne (PDF) (Thesis). Maastricht University, Dept of Knowledge Engineering.
Hensgens, P. P. L. M. (2001). "A Knowledge-Based Approach of the Game of Amazons" (PDF). Universiteit Maastricht, Institute for Knowledge and Agent Technology.
F.C. Schadd (2009). Monte-Carlo Search Techniques in the Modern Board Game Thurn and Taxis (PDF) (Thesis). Maastricht University. Archived from the original (PDF) on 2021-01-14.
Christ-Jan Cox (2006). "Analysis and Implementation of the Game Arimaa" (PDF).
A.F.C. Arts (2010). Competitive Play in Stratego (PDF) (Thesis). Maastricht.

dke.maastrichtuniversity.nl

M.P.D. Schadd; M.H.M. Winands; J.W.H.M. Uiterwijk; H.J. van den Herik; M.H.J. Bergsma (2008). "Best Play in Fanorona leads to Draw" (PDF). New Mathematics and Natural Computation. 4 (3): 369–387. doi:10.1142/S1793005708001124.
Mark H.M. Winands (2004). Informed Search in Complex Games (PDF) (Ph.D. thesis). Maastricht University, Maastricht, The Netherlands. ISBN 90-5278-429-9.

msri.org (Global: low place; English: low place)

Orman, Hilarie K. (1996). "Pentominoes: a first player win" (PDF). In Nowakowski, Richard J. (ed.). Games of No Chance: Papers from the Combinatorial Games Workshop held in Berkeley, CA, July 11–21, 1994. Mathematical Sciences Research Institute Publications. Vol. 29. Cambridge University Press. pp. 339–344. ISBN 0-521-57411-0. MR 1427975.

ndhu.edu.tw (Global: low place; English: low place)

csie.ndhu.edu.tw

Shi-Jim Yen, Jr-Chang Chen; Tai-Ning Yang; Shun-Chin Hsu (March 2004). "Computer Chinese Chess" (PDF). International Computer Games Association Journal. 27 (1): 3–18. doi:10.3233/ICG-2004-27102. S2CID 10336286. Archived from the original (PDF) on 2007-06-14.

nih.gov (Global: 5^th place; English: 5^th place)

pubmed.ncbi.nlm.nih.gov

Jonathan Schaeffer; et al. (July 6, 2007). "Checkers is Solved". Science. 317 (5844): 1518–1522. Bibcode:2007Sci...317.1518S. doi:10.1126/science.1144079. PMID 17641166. S2CID 10274228.

parisdescartes.fr (Global: 6,447^th place; English: low place)

helios2.mi.parisdescartes.fr

Kloetzer, Julien; Iida, Hiroyuki; Bouzy, Bruno (2007). "The Monte-Carlo approach in Amazons" (PDF). Computer Games Workshop, Amsterdam, the Netherlands, 15-17 June 2007. pp. 185–192.

semanticscholar.org (Global: 15^th place; English: 8^th place)

api.semanticscholar.org

Stefan Reisch (1980). "Gobang ist PSPACE-vollständig (Gobang is PSPACE-complete)". Acta Informatica. 13 (1): 59–66. doi:10.1007/bf00288536. S2CID 21455572.
Jonathan Schaeffer; et al. (July 6, 2007). "Checkers is Solved". Science. 317 (5844): 1518–1522. Bibcode:2007Sci...317.1518S. doi:10.1126/science.1144079. PMID 17641166. S2CID 10274228.
Bell, George I. (2009). "The Shortest Game of Chinese Checkers and Related Problems". Integers. 9. arXiv:0803.1245. Bibcode:2008arXiv0803.1245B. doi:10.1515/INTEG.2009.003. S2CID 17141575.
Chang-Ming Xu; Ma, Z.M.; Jun-Jie Tao; Xin-He Xu (2009). "Enhancements of proof number search in connect6". 2009 Chinese Control and Decision Conference. p. 4525. doi:10.1109/CCDC.2009.5191963. ISBN 978-1-4244-2722-2. S2CID 20960281.
Shi-Jim Yen, Jr-Chang Chen; Tai-Ning Yang; Shun-Chin Hsu (March 2004). "Computer Chinese Chess" (PDF). International Computer Games Association Journal. 27 (1): 3–18. doi:10.3233/ICG-2004-27102. S2CID 10336286. Archived from the original (PDF) on 2007-06-14.

stackexchange.com (Global: 4,114^th place; English: 3,027^th place)

math.stackexchange.com

"combinatorics - TicTacToe State Space Choose Calculation". Mathematics Stack Exchange. Retrieved 2020-04-08.

tromp.github.io (Global: low place; English: low place)

John Tromp (2010). "John's Connect Four Playground".
John Tromp; Gunnar Farnebäck (2007). "Combinatorics of Go". This paper derives the bounds 48<log(log(N))<171 on the number of possible games N.
Tromp, John (2016). "Number of legal Go positions".

unibo.it (Global: 3,746^th place; English: 5,990^th place)

ai.unibo.it

Galassi, Andrea (2018). "An Upper Bound on the Complexity of Tablut".

uvt.nl (Global: low place; English: low place)

ticc.uvt.nl

Schaeffer, Jonathan (2007). "Game over: Black to play and draw in checkers" (PDF). ICGA Journal. 30 (4): 187–197. doi:10.3233/ICG-2007-30402. Archived from the original (PDF) on 2016-04-03.

washington.edu (Global: 1,171^st place; English: 736^th place)

hyperion.cs.washington.edu

Glendenning, Lisa (May 2005). Mastering Quoridor (PDF). Computer Science (B.Sc. thesis). University of New Mexico. Archived from the original (PDF) on 2012-03-15.

web.archive.org (Global: 1^st place; English: 1^st place)

Schaeffer, Jonathan (2007). "Game over: Black to play and draw in checkers" (PDF). ICGA Journal. 30 (4): 187–197. doi:10.3233/ICG-2007-30402. Archived from the original (PDF) on 2016-04-03.
The size of the state space and game tree for chess were first estimated in Shannon, Claude (1950). "Programming a Computer for Playing Chess" (PDF). Philosophical Magazine. 41 (314). Archived from the original (PDF) on 2010-07-06. Shannon gave estimates of 10⁴³ and 10¹²⁰ respectively, smaller than the upper bound in the table, which is detailed in Shannon number.
Shi-Jim Yen, Jr-Chang Chen; Tai-Ning Yang; Shun-Chin Hsu (March 2004). "Computer Chinese Chess" (PDF). International Computer Games Association Journal. 27 (1): 3–18. doi:10.3233/ICG-2004-27102. S2CID 10336286. Archived from the original (PDF) on 2007-06-14.
Glendenning, Lisa (May 2005). Mastering Quoridor (PDF). Computer Science (B.Sc. thesis). University of New Mexico. Archived from the original (PDF) on 2012-03-15.
F.C. Schadd (2009). Monte-Carlo Search Techniques in the Modern Board Game Thurn and Taxis (PDF) (Thesis). Maastricht University. Archived from the original (PDF) on 2021-01-14.

Game complexity (English Wikipedia)

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