Editing Solved game (section)

==Solved games==
; [[Oware|Awari]] (a game of the [[Mancala]] family)
: The variant of [[Oware]] allowing game ending "grand slams" was strongly solved by [[Henri Bal]] and John Romein at the [[Vrije Universiteit]] in [[Amsterdam]], Netherlands (2002). Either player can force the game into a draw.
; [[Chopsticks (hand game)|Chopsticks]]
: Strongly solved. If two players both play perfectly, the game will go on indefinitely.{{cn|date=July 2018}}
; [[Connect Four]]
: [[File:Connect Four.jpg|thumb|The game of Connect Four has been solved]] Solved first by James D. Allen on October 1, 1988, and independently by [[Victor Allis]] on October 16, 1988.<ref name="autogenerated1">{{cite web|url=https://tromp.github.io/c4/c4.html|title=John's Connect Four Playground|website=tromp.github.io}}</ref> The first player can force a win. Strongly solved by John Tromp's 8-ply database<ref>{{cite web |url=https://archive.ics.uci.edu/ml/datasets/Connect-4 |title=UCI Machine Learning Repository: Connect-4 Data Set |website=archive.ics.uci.edu}}</ref> (Feb 4, 1995). Weakly solved for all boardsizes where width+height is at most 15 (as well as 8×8 in late 2015)<ref name="autogenerated1" /> (Feb 18, 2006). Solved for all boardsizes where width+height equals 16 on May 22, 2024.<ref>{{cite web|url=https://github.com/ChristopheSteininger/c4|title=ChristopheSteininger/c4|website=github.com}}</ref>
; Free [[gomoku]]
: Solved by [[Victor Allis]] (1993). The first player can force a win without opening rules.<ref name="Allis" />
; [[Ghost (game)|Ghost]]
: Solved by Alan Frank using the ''[[Official Scrabble Players Dictionary]]'' in 1987.<ref>{{Cite journal |last=Frank |first=Alan |date=1987-08-01 |title=Ghostbusters |url=https://digitalcommons.butler.edu/wordways/vol20/iss4/4 |journal=Word Ways |volume=20 |issue=4}}</ref>
; [[Hexapawn]]
:3×3 variant solved as a win for black, several other larger variants also solved.<ref>{{cite web|url=http://www.chessvariants.com/small.dir/hexapawn.html|title=Hexapawn|first=Robert|last=Price|website=www.chessvariants.com}}</ref>
; [[Kalah]]
: Most variants solved by Geoffrey Irving, Jeroen Donkers and Jos Uiterwijk (2000) except Kalah (6/6). The (6/6) variant was solved by Anders Carstensen (2011). Strong first-player advantage was proven in most cases.<ref>[http://graphics.stanford.edu/~irving/papers/irving2000_kalah.pdf Solving Kalah] by Geoffrey Irving, Jeroen Donkers and Jos Uiterwijk.</ref><ref>[http://kalaha.krus.dk/ Solving (6,6)-Kalaha] by Anders Carstensen.</ref>
; [[L game]]
: Easily solvable. Either player can force the game into a draw.
; [[Maharajah and the Sepoys]]
: This asymmetrical game is a win for the sepoys player with correct play.{{Cn|date=November 2022}}
; [[Nim]]
: Strongly solved.<ref>{{citation | last = Bouton | first = C. L. | author-link = Charles L. Bouton | doi = 10.2307/1967631 | issue = 14 | journal = [[Annals of Mathematics]] | pages = 35–39 | title = Nim, ''a game with a complete mathematical theory'' | volume = 3 | year = 1901–1902| jstor = 1967631 }}</ref>
; [[Nine men's morris]]
: Solved by Ralph Gasser (1993). Either player can force the game into a draw.<ref>{{Cite book|last=Gasser|first=Ralph|url=http://library.msri.org/books/Book29/files/gasser.pdf|title=Games of No Chance|publisher=Cambridge University Press|year=1996|isbn=9780521574112|editor-last=Nowakowski|editor-first=Richard|volume=29|location=Cambridge|pages=101–113|language=en|chapter=Solving Nine Men’s Morris|access-date=2022-01-03|archive-date=2015-07-24|archive-url=https://web.archive.org/web/20150724080747/http://library.msri.org/books/Book29/files/gasser.pdf|url-status=dead}}</ref><ref>[http://www.ics.uci.edu/~eppstein/cgt/morris.html Nine Men's Morris is a Draw] by Ralph Gasser</ref>
; [[Order and Chaos]]
: Order (First player) wins.<ref>{{cite web|url=https://boardgamegeek.com/thread/1579397/solved-order-wins|title=solved: Order wins - Order and Chaos}}</ref>
; [[Congkak|Ohvalhu]]
: Weakly solved by humans, but proven by computers.{{Cn|date=November 2022}} (Dakon is, however, not identical to Ohvalhu, the game which actually had been observed by de Voogt){{Cn|date=November 2022}}
;[[Cinc camins#Variants|Pangki]]
:Strongly solved by Jason Doucette (2001).<ref>[http://www.jasondoucette.com/ai.html#Pangki Pangki is strongly solved as a draw] by Jason Doucette</ref>  The game is a draw.  There are only two unique first moves if you discard mirrored positions. One forces the draw, and the other gives the opponent a forced win in 15 moves.
;[[Pentago]]
: Strongly solved by Geoffrey Irving with use of a supercomputer at [[NERSC]]. The first player wins.
; [[Quarto (board game)|Quarto]]
: Solved by Luc Goossens (1998). Two perfect players will always draw.<ref>{{cite web|title=Quarto|website=wouterkoolen.info|access-date=29 February 2024|url=https://wouterkoolen.info/Talks/quarto.pdf}}</ref><ref>{{cite web | url=https://www.mathpages.com/home/kmath352.htm | title=414298141056 Quarto Draws Suffice! }}</ref><ref>{{cite web | url=http://ssel.vub.ac.be/Members/LucGoossens/quarto/quartotext.htm | archive-url=https://web.archive.org/web/20041012023358/http://ssel.vub.ac.be/Members/LucGoossens/quarto/quartotext.htm | archive-date=2004-10-12 | title=Quarto }}</ref>
; [[Renju]]-like game without opening rules involved
: Claimed to be solved by János Wagner and István Virág (2001).<ref>{{Cite web |last=Wágner |first=János |last2=Virág |first2=István |name-list-style=amp |date=March 2001 |title=Solving Renju |url=http://www.sze.hu/~gtakacs/download/wagnervirag_2001.pdf |url-status=live |archive-url=https://web.archive.org/web/20240424130418/http://www.sze.hu/~gtakacs/download/wagnervirag_2001.pdf |archive-date=24 April 2024 |archive-format=PDF |access-date=24 April 2024 |website=Széchenyi Egyetem - University of Győr |page=30 |language=en |format=PDF}}</ref> A first-player win.
; [[Teeko]]
: Solved by [[Guy L. Steele, Jr.|Guy Steele]] (1998). Depending on the variant either a first-player win or a draw.<ref>[http://mathworld.wolfram.com/Teeko.html Teeko], by E. Weisstein</ref>
; [[Three men's morris]]
: Trivially solvable. Either player can force the game into a draw.{{Cn|date=November 2022}}
; [[Three musketeers (game)|Three musketeers]]
: Strongly solved by Johannes Laire in 2009, and weakly solved by Ali Elabridi in 2017.<ref>{{Cite web|url=http://www.aui.ma/sse-capstone-repository/pdf/fall2017/WEAKLY%20SOLVING%20THE%20THREE%20MUSKETEERS%20GAME%20USING%20ARTIFICIAL%20INTELLIGENCE%20AND%20GAME%20THEORY%20Ali%20Elabridi.pdf|title=Weakly Solving the Three Musketeers Game Using Artificial Intelligence and Game Theory |last=Elabridi|first=Ali}}</ref> It is a win for the blue pieces (Cardinal Richelieu's men, or, the enemy).<ref>[https://github.com/jlaire/3M/tree/master/src Three Musketeers], by J. Lemaire</ref>
; [[Tic-tac-toe]]
: Extremely trivially strongly solvable because of the small game tree.<ref>[https://xkcd.com/832/ Tic-Tac-Toe], by R. Munroe</ref>  The game is a draw if no mistakes are made, with no mistake possible on the opening move.
; [[Wythoff's game]]
: Strongly solved by [[Willem Abraham Wythoff| W. A. Wythoff]] in 1907.<ref>{{citation | last = Wythoff | first = W. A. | author-link = Willem Abraham Wythoff | issue = 2 | journal = Nieuw Archief voor Wiskunde | pages = 199–202 | title = A modification of the game of nim | url = https://archive.org/details/nieuwarchiefvoo02genogoog/page/n219/mode/2up | volume = 7 | year = 1907}}</ref>