Editing Solved game (section)

==Partially solved games==

; [[Chess]]
:{{main|Solving chess}}
: Fully solving chess remains elusive, and it is speculated that the complexity of the game may preclude it ever being solved. Through [[retrograde analysis|retrograde computer analysis]] and [[endgame tablebase]]s, strong solutions have been found for all three- to seven-piece [[Chess endgame|endgames]], counting the two [[King (chess)|kings]] as pieces.
: Some [[Minichess|variants of chess on a smaller board with reduced numbers of pieces]] have been solved. Some other popular variants have also been solved; for example, a weak solution to [[Maharajah and the Sepoys]] is an easily memorable series of moves that guarantees victory to the "sepoys" player.
; [[Go (game)|Go]]
: The 5×5 board was weakly solved for all opening moves in 2002.<ref name=":3">[http://erikvanderwerf.tengen.nl/5x5/5x5solved.html 5×5 Go is solved] by Erik van der Werf</ref> The 7×7 board was weakly solved in 2015.<ref name=":4">{{cite web|url=http://blog.sina.com.cn/s/blog_53a2e03d0102vyt5.html|title=首期喆理围棋沙龙举行 李喆7路盘最优解具有里程碑意义_下棋想赢怕输_新浪博客|website=blog.sina.com.cn}} (which says the 7x7 solution is only weakly solved and it's still under research, 1. the correct komi is 9 (4.5 stone); 2. there are multiple optimal trees - the first 3 moves are unique - but within the first 7 moves there are 5 optimal trees; 3. There are many ways to play that don't affect the result)</ref> Humans usually play on a 19×19 board, which is over 145 [[Order of magnitude|orders of magnitude]] more complex than 7×7.<ref name=":2">[http://homepages.cwi.nl/~tromp/go/legal.html Counting legal positions in Go] {{webarchive|url=https://web.archive.org/web/20070930044508/http://homepages.cwi.nl/~tromp/go/legal.html |date=2007-09-30 }}, Tromp and Farnebäck, accessed 2007-08-24.</ref>
; [[Hex (board game)|Hex]]
: A [[strategy-stealing argument]] (as used by [[John Forbes Nash, Jr.|John Nash]]) shows that all square board sizes cannot be lost by the first player. Combined with a proof of the impossibility of a draw, this shows that the game is a first player win (so it is ultra-weak solved).{{cn|date=September 2022}}  On particular board sizes, more is known: it is strongly solved by several computers for board sizes up to 6×6.{{cn|date=September 2022}}  Weak solutions are known for board sizes 7×7 (using a [[pie rule|swapping strategy]]), 8×8, and 9×9;{{cn|date=September 2022}} in the 8×8 case, a weak solution is known for all opening moves.<ref>P. Henderson, B. Arneson, and R. Hayward, [webdocs.cs.ualberta.ca/~hayward/papers/solve8.pdf Solving 8×8 Hex ], Proc. IJCAI-09 505-510 (2009) Retrieved 29 June 2010.</ref>  Strongly solving Hex on an ''N''×''N'' board is unlikely as the problem has been shown to be [[PSPACE-complete]].{{cn|date=September 2022}} If Hex is played on an ''N''×(''N'' + 1) board then the player who has the shorter distance to connect can always win by a simple pairing strategy, even with the disadvantage of playing second.{{cn|date=September 2022}}

; [[International draughts]]
: All endgame positions with two through seven pieces were solved, as well as positions with 4×4 and 5×3 pieces where each side had one king or fewer, positions with five men versus four men, positions with five men versus three men and one king, and positions with four men and one king versus four men. The endgame positions were solved in 2007 by Ed Gilbert of the United States. Computer analysis showed that it was highly likely to end in a draw if both players played perfectly.<ref>[http://edgilbert.org/Checkers/KingsRow.htm Some of the nine-piece endgame tablebase] by Ed Gilbert</ref>{{better source|date=December 2019}}
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; [[Morabaraba]]
: Strongly solved by Gábor E. Gévay (2015). The first player wins in optimal play.<ref>{{Cite journal |last=Gevay |first=Gabor E. |last2=Danner |first2=Gabor |date=September 2016 |title=Calculating Ultrastrong and Extended Solutions for Nine Men’s Morris, Morabaraba, and Lasker Morris |url=https://ieeexplore.ieee.org/document/7080922/ |journal=IEEE Transactions on Computational Intelligence and AI in Games |volume=8 |issue=3 |pages=256–267 |doi=10.1109/TCIAIG.2015.2420191 |issn=1943-068X}}</ref> 
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; [[m,n,k-game|''m'',''n'',''k''-game]]
: It is trivial to show that the second player can never win; see [[strategy-stealing argument]]. Almost all cases have been solved weakly for ''k'' ≤ 4. Some results are known for ''k'' = 5. The games are drawn for ''k'' ≥ 8.{{Cn|date=November 2022}}