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<div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Finding an optimal algorithm for playing chess</div> <p><b>Solving chess</b> consists of finding an optimal strategy for the game of <a href="/wiki/Chess" title="Chess">chess</a>; that is, one by which one of the players (<a href="/wiki/White_and_Black_in_chess" title="White and Black in chess">White or Black</a>) can always force a victory, or either can force a draw (see <a href="/wiki/Solved_game" title="Solved game">solved game</a>). It is also related to more generally solving <i>chess-like</i> games (i.e. <a href="/wiki/Game_theory#Combinatorial_games" title="Game theory">combinatorial games</a> of <a href="/wiki/Perfect_information" title="Perfect information">perfect information</a>) such as <a href="/wiki/Capablanca_chess" title="Capablanca chess">Capablanca chess</a> and <a href="/wiki/Infinite_chess" title="Infinite chess">infinite chess</a>. In a weaker sense, <i>solving chess</i> may refer to proving which one of the three possible outcomes (White wins; Black wins; draw) is the result of two perfect players, without necessarily revealing the optimal strategy itself (see <a href="/wiki/Indirect_proof" class="mw-redirect" title="Indirect proof">indirect proof</a>).<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>No complete solution for chess in either of the two senses <a href="/wiki/Solved_game#Partially_solved_games" title="Solved game">is known</a>, nor is it expected that chess will be solved in the near future (if ever). Progress to date is extremely limited; there are <a href="/wiki/Endgame_tablebase" title="Endgame tablebase">tablebases</a> of perfect endgame play with a small number of pieces (up to seven), and some <a href="/wiki/Chess_variant" title="Chess variant">chess variants</a> have been solved at least weakly. Calculated estimates of <a href="/wiki/Game_complexity" title="Game complexity">game-tree complexity</a> and state-space complexity of chess exist which provide a bird's eye view of the computational effort that might be required to solve the game. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Partial_results">Partial results</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Solving_chess&action=edit&section=1" title="Edit section: Partial results"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Endgame_tablebases">Endgame tablebases</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Solving_chess&action=edit&section=2" title="Edit section: Endgame tablebases"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="thumb noviewer tright"><div class="center" style="line-height:130%;margin:0 auto;max-width:254px"> </div><div class="thumbinner" style="width:246px"><table cellpadding="0" cellspacing="0" style="font-size:88%;border:1px #c8ccd1 solid;padding:0;margin:auto"><tbody><tr style="vertical-align:middle"><td style="vertical-align:inherit;padding:0"></td><td style="padding:0;vertical-align:inherit;text-align:center;height:18px;width:26px">a</td><td style="padding:0;vertical-align:inherit;text-align:center;height:18px;width:26px">b</td><td style="padding:0;vertical-align:inherit;text-align:center;height:18px;width:26px">c</td><td style="padding:0;vertical-align:inherit;text-align:center;height:18px;width:26px">d</td><td style="padding:0;vertical-align:inherit;text-align:center;height:18px;width:26px">e</td><td style="padding:0;vertical-align:inherit;text-align:center;height:18px;width:26px">f</td><td style="padding:0;vertical-align:inherit;text-align:center;height:18px;width:26px">g</td><td style="padding:0;vertical-align:inherit;text-align:center;height:18px;width:26px">h</td><td style="vertical-align:inherit;padding:0"></td></tr><tr style="vertical-align:middle"><td style="padding:0;vertical-align:inherit;text-align:center;width:18px;height:26px">8</td><td colspan="8" rowspan="8" style="padding:0;vertical-align:inherit"><div class="chess-board notheme" style="position:relative"><span class="notpageimage" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Chessboard480.svg/208px-Chessboard480.svg.png" decoding="async" width="208" height="208" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Chessboard480.svg/312px-Chessboard480.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Chessboard480.svg/416px-Chessboard480.svg.png 2x" data-file-width="480" data-file-height="480" /></span></span><div style="position:absolute;z-index:3;top:26px;left:0px;width:26px;height:26px"><span class="mw-valign-top notpageimage" typeof="mw:File"><span title="a7 black rook"><img alt="a7 black rook" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Chess_rdt45.svg/26px-Chess_rdt45.svg.png" decoding="async" width="26" height="26" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Chess_rdt45.svg/39px-Chess_rdt45.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Chess_rdt45.svg/52px-Chess_rdt45.svg.png 2x" data-file-width="45" data-file-height="45" /></span></span></div><div style="position:absolute;z-index:3;top:26px;left:182px;width:26px;height:26px"><span class="mw-valign-top notpageimage" typeof="mw:File"><span title="h7 black knight"><img alt="h7 black knight" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Chess_ndt45.svg/26px-Chess_ndt45.svg.png" decoding="async" width="26" height="26" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Chess_ndt45.svg/39px-Chess_ndt45.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Chess_ndt45.svg/52px-Chess_ndt45.svg.png 2x" data-file-width="45" data-file-height="45" /></span></span></div><div style="position:absolute;z-index:3;top:52px;left:52px;width:26px;height:26px"><span class="mw-valign-top notpageimage" typeof="mw:File"><span title="c6 white queen"><img alt="c6 white queen" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Chess_qlt45.svg/26px-Chess_qlt45.svg.png" decoding="async" width="26" height="26" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Chess_qlt45.svg/39px-Chess_qlt45.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/15/Chess_qlt45.svg/52px-Chess_qlt45.svg.png 2x" data-file-width="45" data-file-height="45" /></span></span></div><div style="position:absolute;z-index:3;top:104px;left:130px;width:26px;height:26px"><span class="mw-valign-top notpageimage" typeof="mw:File"><span title="f4 black king"><img alt="f4 black king" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Chess_kdt45.svg/26px-Chess_kdt45.svg.png" decoding="async" width="26" height="26" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Chess_kdt45.svg/39px-Chess_kdt45.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Chess_kdt45.svg/52px-Chess_kdt45.svg.png 2x" data-file-width="45" data-file-height="45" /></span></span></div><div style="position:absolute;z-index:3;top:130px;left:78px;width:26px;height:26px"><span class="mw-valign-top notpageimage" typeof="mw:File"><span title="d3 white king"><img alt="d3 white king" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/Chess_klt45.svg/26px-Chess_klt45.svg.png" decoding="async" width="26" height="26" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/Chess_klt45.svg/39px-Chess_klt45.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/42/Chess_klt45.svg/52px-Chess_klt45.svg.png 2x" data-file-width="45" data-file-height="45" /></span></span></div><div style="position:absolute;z-index:3;top:156px;left:182px;width:26px;height:26px"><span class="mw-valign-top notpageimage" typeof="mw:File"><span title="h2 white knight"><img alt="h2 white knight" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/70/Chess_nlt45.svg/26px-Chess_nlt45.svg.png" decoding="async" width="26" height="26" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/70/Chess_nlt45.svg/39px-Chess_nlt45.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/70/Chess_nlt45.svg/52px-Chess_nlt45.svg.png 2x" data-file-width="45" data-file-height="45" /></span></span></div><div style="position:absolute;z-index:3;top:182px;left:78px;width:26px;height:26px"><span class="mw-valign-top notpageimage" typeof="mw:File"><span title="d1 black bishop"><img alt="d1 black bishop" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Chess_bdt45.svg/26px-Chess_bdt45.svg.png" decoding="async" width="26" height="26" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Chess_bdt45.svg/39px-Chess_bdt45.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/98/Chess_bdt45.svg/52px-Chess_bdt45.svg.png 2x" data-file-width="45" data-file-height="45" /></span></span></div><div style="position:absolute;z-index:3;top:182px;left:182px;width:26px;height:26px"><span class="mw-valign-top notpageimage" typeof="mw:File"><span title="h1 black queen"><img alt="h1 black queen" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Chess_qdt45.svg/26px-Chess_qdt45.svg.png" decoding="async" width="26" height="26" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Chess_qdt45.svg/39px-Chess_qdt45.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/47/Chess_qdt45.svg/52px-Chess_qdt45.svg.png 2x" data-file-width="45" data-file-height="45" /></span></span></div></div></td><td style="padding:0;vertical-align:inherit;text-align:center;width:18px;height:26px">8</td></tr><tr style="vertical-align:middle"><td style="padding:0;vertical-align:inherit;text-align:center;height:26px">7</td><td style="padding:0;vertical-align:inherit;text-align:center;height:26px">7</td></tr><tr style="vertical-align:middle"><td style="padding:0;vertical-align:inherit;text-align:center;height:26px">6</td><td style="padding:0;vertical-align:inherit;text-align:center;height:26px">6</td></tr><tr style="vertical-align:middle"><td style="padding:0;vertical-align:inherit;text-align:center;height:26px">5</td><td style="padding:0;vertical-align:inherit;text-align:center;height:26px">5</td></tr><tr style="vertical-align:middle"><td style="padding:0;vertical-align:inherit;text-align:center;height:26px">4</td><td style="padding:0;vertical-align:inherit;text-align:center;height:26px">4</td></tr><tr style="vertical-align:middle"><td style="padding:0;vertical-align:inherit;text-align:center;height:26px">3</td><td style="padding:0;vertical-align:inherit;text-align:center;height:26px">3</td></tr><tr style="vertical-align:middle"><td style="padding:0;vertical-align:inherit;text-align:center;height:26px">2</td><td style="padding:0;vertical-align:inherit;text-align:center;height:26px">2</td></tr><tr style="vertical-align:middle"><td style="padding:0;vertical-align:inherit;text-align:center;height:26px">1</td><td style="padding:0;vertical-align:inherit;text-align:center;height:26px">1</td></tr><tr style="vertical-align:middle"><td style="vertical-align:inherit;padding:0"></td><td style="padding:0;vertical-align:inherit;text-align:center;height:18px;width:26px">a</td><td style="padding:0;vertical-align:inherit;text-align:center;height:18px;width:26px">b</td><td style="padding:0;vertical-align:inherit;text-align:center;height:18px;width:26px">c</td><td style="padding:0;vertical-align:inherit;text-align:center;height:18px;width:26px">d</td><td style="padding:0;vertical-align:inherit;text-align:center;height:18px;width:26px">e</td><td style="padding:0;vertical-align:inherit;text-align:center;height:18px;width:26px">f</td><td style="padding:0;vertical-align:inherit;text-align:center;height:18px;width:26px">g</td><td style="padding:0;vertical-align:inherit;text-align:center;height:18px;width:26px">h</td><td style="vertical-align:inherit;padding:0"></td></tr></tbody></table><div class="thumbcaption"> A <b>mate-in-546</b> position found in the Lomonosov 7-piece tablebase. White to move. (In this example an 8th piece is added with a trivial first-move capture.) </div></div></div> <p><a href="/wiki/Endgame_tablebase" title="Endgame tablebase">Endgame tablebases</a> are computerized databases that contain precalculated exhaustive analyses of positions with small numbers of pieces remaining on the board. Tablebases have solved chess to a limited degree, determining perfect play in a number of <a href="/wiki/Chess_endgame" title="Chess endgame">endgames</a>, including all non-trivial endgames with no more than seven pieces or pawns (including the two kings).<sup id="cite_ref-Lomonosov_Tablebases_2-0" class="reference"><a href="#cite_note-Lomonosov_Tablebases-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>One consequence of developing the seven-piece endgame tablebase is that many interesting theoretical chess endings have been found. The longest seven-piece example is a mate-in-549 position discovered in the Lomonosov tablebase by Guy Haworth, ignoring the <a href="/wiki/50-move_rule" class="mw-redirect" title="50-move rule">50-move rule</a>.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Such a position is beyond the ability of any human to solve, and no chess engine plays it correctly, either, without access to the tablebase, which initially (in 2014) required 140 TB of storage space and the use of a supercomputer but was later reduced down to 18.4 TB through the Syzygy tablebase. As of January 2023, the longest known forced mating sequence for the eight-piece tablebase (also ignoring the 50-move rule) was 584 moves. This was discovered in mid-2022 by <a href="/w/index.php?title=Marc_Bourzutschky&action=edit&redlink=1" class="new" title="Marc Bourzutschky (page does not exist)">Marc Bourzutschky</a>.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> The eight-piece tablebase is currently incomplete, though, so it is not guaranteed that this is the absolute limit for the eight-piece tablebase. </p> <div class="mw-heading mw-heading3"><h3 id="Chess_variants">Chess variants</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Solving_chess&action=edit&section=3" title="Edit section: Chess variants"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A variant first described by Shannon provides an argument about the game-theoretic value of chess: he proposes allowing the move of “pass”. In this variant, it is provable with a <a href="/wiki/Strategy_stealing_argument" class="mw-redirect" title="Strategy stealing argument">strategy stealing argument</a> that the first player has at least a draw thus: if the first player has a winning move in the initial position, let him play it, else pass. The second player now faces the same situation owing to the mirror symmetry of the initial position: if the first player had no winning move in the first instance, the second player has none now. Therefore, the second player can at best draw, and the first player can at least draw, so a perfect game results in the first player winning or drawing.<sup id="cite_ref-CSpaper_6-0" class="reference"><a href="#cite_note-CSpaper-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>Some <a href="/wiki/Chess_Variant" class="mw-redirect" title="Chess Variant">chess variants</a> which are simpler than chess have been solved. A winning strategy for Black in <a href="/wiki/Maharajah_and_the_Sepoys" title="Maharajah and the Sepoys">Maharajah and the Sepoys</a> can be easily memorised. The 5×5 <a href="/wiki/Minichess#5×5_chess" title="Minichess">Gardner's Minichess</a> variant has been <a href="/wiki/Solved_game" title="Solved game">weakly solved</a> as a draw.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Although <a href="/wiki/Losing_Chess" class="mw-redirect" title="Losing Chess">losing chess</a> is played on an 8×8 board, its forced capture rule greatly limits its complexity, and a computational analysis managed to weakly solve this variant as a win for White.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>The prospect of solving individual, specific, chess-like games becomes more difficult as the board-size is increased, such as in large chess variants, and <a href="/wiki/Infinite_chess" title="Infinite chess">infinite chess</a>.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="The_complexity_of_chess">The complexity of chess</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Solving_chess&action=edit&section=4" title="Edit section: The complexity of chess"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Information_theory" title="Information theory">Information theorist</a> <a href="/wiki/Claude_Shannon" title="Claude Shannon">Claude Shannon</a> in 1950 outlined a theoretical procedure for playing a perfect game (i.e. solving chess): <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style></p><blockquote class="templatequote"><p>"With chess it is possible, in principle, to play a perfect game or construct a machine to do so as follows: One considers in a given position all possible moves, then all moves for the opponent, etc., to the end of the game (in each variation). The end must occur, by the rules of the games after a finite number of moves (remembering the <a href="/wiki/Fifty-move_rule" title="Fifty-move rule">50 move drawing rule</a>). Each of these variations ends in win, loss or draw. By working backward from the end one can determine whether there is a forced win, the position is a draw or is lost."</p></blockquote> <p>Shannon then went on to estimate that solving chess according to that procedure would require comparing some 10<sup>120</sup> possible game variations, or having a "dictionary" denoting an optimal move for each of the approximately 10<sup>43</sup> possible board positions (currently known to be about 5x10<sup>44</sup>).<sup id="cite_ref-CSpaper_6-1" class="reference"><a href="#cite_note-CSpaper-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> The number of mathematical operations required to solve chess, however, may be significantly different than the number of operations required to produce the entire <a href="/wiki/Game_tree" title="Game tree">game-tree</a> of chess. In particular, if White has a forced win, only a subset of the game-tree would require evaluation to confirm that a forced-win exists (i.e. with no refutations from Black). Furthermore, Shannon's calculation for the complexity of chess assumes an average game length of 40 moves, but there is no mathematical basis to say that a forced win by either side would have any relation to this game length. Indeed, some expertly played games (grandmaster-level play) have been as short as 16 moves. For these reasons, mathematicians and game theorists have been reluctant to categorically state that solving chess is an intractable problem.<sup id="cite_ref-CSpaper_6-2" class="reference"><a href="#cite_note-CSpaper-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Predictions_on_when_or_if_chess_will_be_solved">Predictions on when or if chess will be solved</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Solving_chess&action=edit&section=5" title="Edit section: Predictions on when or if chess will be solved"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1950, Shannon calculated, based on a game tree complexity of 10<sup>120</sup> and a computer operating at one megahertz (a big stretch at that time: the UNIVAC 1 introduced in 1951 could perform ~2000 operations per second or 2 kilohertz) that could evaluate a terminal node in 1 microsecond would take 10<sup>90</sup> years to make its first move. Even allowing for technological advances, solving chess within a practical time frame would therefore seem beyond any conceivable technology. </p><p><a href="/wiki/Hans-Joachim_Bremermann" title="Hans-Joachim Bremermann">Hans-Joachim Bremermann</a>, a professor of <a href="/wiki/Mathematics" title="Mathematics">mathematics</a> and <a href="/wiki/Biophysics" title="Biophysics">biophysics</a> at the <a href="/wiki/University_of_California_at_Berkeley" class="mw-redirect" title="University of California at Berkeley">University of California at Berkeley</a>, further argued in a 1965 paper that the "speed, memory, and processing capacity of any possible future computer equipment are limited by specific physical barriers: the <i><a href="/wiki/Speed_of_light" title="Speed of light">light barrier</a></i>, the <i>quantum barrier</i>, and the <i>thermodynamical barrier</i>. These limitations imply, for example, that no computer, however constructed, will ever be able to examine the entire tree of possible move sequences of the game of chess." Nonetheless, Bremermann did not foreclose the possibility that a computer would someday be able to solve chess. He wrote, "In order to have a computer play a perfect or nearly perfect game, it will be necessary either to analyze the game completely ... or to analyze the game in an approximate way and combine this with a limited amount of tree searching. ... A theoretical understanding of such heuristic programming, however, is still very much wanting."<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>Recent scientific advances have not significantly changed these assessments. The game of <a href="/wiki/English_draughts" title="English draughts">checkers</a> was (weakly) solved in 2007,<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> but it has roughly the square root of the number of positions in chess. <a href="/wiki/Jonathan_Schaeffer" title="Jonathan Schaeffer">Jonathan Schaeffer</a>, the scientist who led the effort, said a breakthrough such as <a href="/wiki/Quantum_computing" title="Quantum computing">quantum computing</a> would be needed before solving chess could even be attempted, but he does not rule out the possibility, saying that the one thing he learned from his 16-year effort of solving checkers "is to never underestimate the advances in technology".<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Solving_chess&action=edit&section=6" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Shannon_number" title="Shannon number">Shannon number</a> (a calculation of the lower bound of the game-tree complexity of chess)</li> <li><a href="/wiki/First-move_advantage_in_chess" title="First-move advantage in chess">First-move advantage in chess</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Solving_chess&action=edit&section=7" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"> <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output 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Retrieved <span class="nowrap">2009-03-21</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Checkers%2C+Solved%21&rft.pub=IEEE&rft.aulast=Sreedhar&rft.aufirst=Suhas&rft_id=http%3A%2F%2Fwww.spectrum.ieee.org%2Fprint%2F5379&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASolving+chess" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Solving_chess&action=edit&section=8" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=PN-I6u-AxMg">"Infinite Chess, PBS Infinite Series"</a> Infinite Chess, PBS Infinite Series.</li></ul> <div class="navbox-styles"><style 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abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Chess" title="Template:Chess"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Chess" title="Template talk:Chess"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Chess" title="Special:EditPage/Template:Chess"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Chess" style="font-size:114%;margin:0 4em"><a href="/wiki/Chess" title="Chess">Chess</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Outline_of_chess" title="Outline of chess">Outline</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chess_theory" title="Chess theory">Chess theory</a></li> <li><a href="/wiki/Chess_title" title="Chess title">Chess titles</a> <ul><li><a href="/wiki/Grandmaster_(chess)" title="Grandmaster (chess)">Grandmaster</a></li></ul></li> <li><a href="/wiki/Computer_chess" title="Computer chess">Computer chess</a> <ul><li><a href="/wiki/Glossary_of_computer_chess_terms" title="Glossary of computer chess terms">glossary</a></li> <li><a href="/wiki/Human%E2%80%93computer_chess_matches" title="Human–computer chess matches">matches</a></li> <li><a href="/wiki/Chess_engine" title="Chess engine">engines</a></li> <li><a href="/wiki/List_of_chess_software" title="List of chess software">software</a></li></ul></li> <li><a href="/wiki/Correspondence_chess" title="Correspondence chess">Correspondence chess</a></li> <li><a href="/wiki/FIDE" title="FIDE">FIDE</a></li> <li><a href="/wiki/Glossary_of_chess" title="Glossary of chess">Glossary</a></li> <li><a href="/wiki/Online_chess" title="Online chess">Online chess</a> <ul><li><a href="/wiki/Premove" title="Premove">Premove</a></li> <li><a href="/wiki/Internet_chess_server" title="Internet chess server">Internet chess server</a> <ul><li><a href="/wiki/List_of_Internet_chess_servers" title="List of Internet chess servers">list</a></li></ul></li></ul></li> <li><a href="/wiki/Chess_rating_system" title="Chess rating system">Rating system</a> <ul><li><a href="/wiki/FIDE_world_rankings" class="mw-redirect" title="FIDE world rankings">world rankings</a></li> <li><a href="/wiki/Norm_(chess)" title="Norm (chess)">norms</a></li></ul></li> <li><a href="/wiki/Chess_variant" title="Chess variant">Variants</a> <ul><li><a href="/wiki/List_of_chess_variants" title="List of chess variants">List</a></li></ul></li> <li><a href="/wiki/List_of_world_records_in_chess" title="List of world records in chess">World records</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Chess_equipment" title="Chess equipment">Equipment</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chess_set" title="Chess set">Chess set</a> <ul><li><a href="/wiki/Chessboard" title="Chessboard">chessboard</a></li> <li><a href="/wiki/Dubrovnik_chess_set" title="Dubrovnik chess set">Dubrovnik chess set</a></li> <li><a href="/wiki/Staunton_chess_set" title="Staunton chess set">Staunton chess set</a></li></ul></li> <li><a href="/wiki/Chess_piece" title="Chess piece">Chess pieces</a> <ul><li><a href="/wiki/King_(chess)" title="King (chess)">King</a></li> <li><a href="/wiki/Queen_(chess)" title="Queen (chess)">Queen</a></li> <li><a href="/wiki/Rook_(chess)" title="Rook (chess)">Rook</a></li> <li><a href="/wiki/Bishop_(chess)" title="Bishop (chess)">Bishop</a></li> <li><a href="/wiki/Knight_(chess)" title="Knight (chess)">Knight</a></li> <li><a href="/wiki/Pawn_(chess)" title="Pawn (chess)">Pawn</a></li> <li><a href="/wiki/Fairy_chess_piece" title="Fairy chess piece">Fairy</a></li></ul></li> <li><a href="/wiki/Chess_clock" title="Chess clock">Chess clock</a></li> <li><a href="/wiki/Chess_table" title="Chess table">Chess table</a></li> <li><dfn><a href="/wiki/Glossary_of_chess#score_sheets" title="Glossary of chess"><span title="See entry at: Glossary of chess § Score sheets" style="color:inherit;" class="glossary-link">Score sheets</span></a></dfn></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/History_of_chess" title="History of chess">History</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Timeline_of_chess" title="Timeline of chess">Timeline</a> <ul><li><i><a href="/wiki/Versus_de_scachis" title="Versus de scachis">Versus de scachis</a></i></li> <li><i><a href="/wiki/G%C3%B6ttingen_manuscript" title="Göttingen manuscript">Göttingen manuscript</a></i></li> <li><a href="/wiki/Charlemagne_chessmen" title="Charlemagne chessmen">Charlemagne chessmen</a></li> <li><a href="/wiki/Lewis_chessmen" title="Lewis chessmen">Lewis chessmen</a></li> <li><a href="/wiki/Romantic_chess" title="Romantic chess">Romantic chess</a></li> <li><a href="/wiki/Hypermodernism_(chess)" title="Hypermodernism (chess)">Hypermodernism</a></li> <li><a href="/wiki/Soviet_chess_school" title="Soviet chess school">Soviet chess school</a></li> <li><a href="/wiki/Comparison_of_top_chess_players_throughout_history" title="Comparison of top chess players throughout history">Top player comparison</a></li></ul></li> <li><a href="/wiki/Geography_of_chess" title="Geography of chess">Geography of chess</a> <ul><li><a href="/wiki/Chess_in_Africa" title="Chess in Africa">Africa</a> <ul><li><a href="/wiki/Chess_in_South_Africa" title="Chess in South Africa">South Africa</a></li></ul></li> <li><a href="/wiki/Chess_in_China" title="Chess in China">China</a></li> <li><a href="/wiki/Chess_in_Europe" title="Chess in Europe">Europe</a> <ul><li><a href="/wiki/Chess_in_Armenia" title="Chess in Armenia">Armenia</a></li> <li><a href="/wiki/Chess_in_Spain" title="Chess in Spain">Spain</a></li></ul></li> <li><a href="/wiki/Chess_in_India" title="Chess in India">India</a></li></ul></li> <li><a href="/wiki/List_of_chess_games" title="List of chess games">Notable games</a></li> <li><a href="/wiki/List_of_chess_players" title="List of chess players">List of chess players</a> <ul><li><a href="/wiki/List_of_amateur_chess_players" title="List of amateur chess players">amateurs</a></li> <li><a href="/wiki/List_of_female_chess_players" title="List of female chess players">female</a></li> <li><a href="/wiki/List_of_chess_grandmasters" title="List of chess grandmasters">grandmasters</a></li></ul></li> <li><a href="/wiki/Women_in_chess" title="Women in chess">Women in chess</a></li> <li><a href="/wiki/Category:Chess_museums" title="Category:Chess museums">Chess museums</a> <ul><li><a href="/wiki/Bobby_Fischer_Center" title="Bobby Fischer Center">Bobby Fischer Center</a></li> <li><a href="/wiki/G%C3%B6kyay_Association_Chess_Museum" title="Gökyay Association Chess Museum">Gökyay Association Chess Museum</a></li> <li><a href="/wiki/World_Chess_Hall_of_Fame" title="World Chess Hall of Fame">World Chess Hall of Fame</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Rules_of_chess" title="Rules of chess">Rules</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Castling" title="Castling">Castling</a></li> <li><a href="/wiki/Cheating_in_chess" title="Cheating in chess">Cheating in chess</a></li> <li><a href="/wiki/Check_(chess)" title="Check (chess)">Check</a></li> <li><a href="/wiki/Checkmate" title="Checkmate">Checkmate</a></li> <li><a href="/wiki/Draw_(chess)" title="Draw (chess)">Draw</a> <ul><li><a href="/wiki/Draw_by_agreement" title="Draw by agreement">by agreement</a></li> <li><a href="/wiki/Fifty-move_rule" title="Fifty-move rule">Fifty-move rule</a></li> <li><a href="/wiki/Perpetual_check" title="Perpetual check">Perpetual check</a></li> <li><a href="/wiki/Stalemate" title="Stalemate">Stalemate</a></li> <li><a href="/wiki/Threefold_repetition" title="Threefold repetition">Threefold repetition</a></li></ul></li> <li><i><a href="/wiki/En_passant" title="En passant">En passant</a></i></li> <li><a href="/wiki/Promotion_(chess)" title="Promotion (chess)">Pawn promotion</a></li> <li><a href="/wiki/Time_control" title="Time control">Time control</a> <ul><li><a href="/wiki/Fast_chess" title="Fast chess">Fast chess</a></li></ul></li> <li><a href="/wiki/Touch-move_rule" title="Touch-move rule">Touch-move rule</a></li> <li><a href="/wiki/White_and_Black_in_chess" title="White and Black in chess">White and Black</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Glossary_of_chess" title="Glossary of chess">Terms</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Blunder_(chess)" title="Blunder (chess)">Blunder</a></li> <li><a href="/wiki/Chess_notation" title="Chess notation">Chess notation</a> <ul><li><a href="/wiki/Algebraic_notation_(chess)" title="Algebraic notation (chess)">algebraic</a></li> <li><a href="/wiki/Descriptive_notation" title="Descriptive notation">descriptive</a></li> <li><a href="/wiki/Portable_Game_Notation" title="Portable Game Notation">PGN</a></li> <li><a href="/wiki/Chess_annotation_symbols" title="Chess annotation symbols">annotation symbols</a></li> <li><a href="/wiki/Chess_symbols_in_Unicode" title="Chess symbols in Unicode">symbols in Unicode</a></li></ul></li> <li><a href="/wiki/Fianchetto" title="Fianchetto">Fianchetto</a></li> <li><a href="/wiki/Gambit" title="Gambit">Gambit</a></li> <li><a href="/wiki/Key_square" title="Key square">Key square</a></li> <li><a href="/wiki/King_walk" title="King walk">King walk</a></li> <li><a href="/wiki/Open_file" title="Open file">Open file</a> <ul><li><a href="/wiki/Half-open_file" title="Half-open file">Half-open file</a></li></ul></li> <li><a href="/wiki/Outpost_(chess)" title="Outpost (chess)">Outpost</a></li> <li><a href="/wiki/Pawn_(chess)" title="Pawn (chess)">Pawns</a> <ul><li><a href="/wiki/Backward_pawn" title="Backward pawn">backward</a></li> <li><a href="/wiki/Connected_pawns" title="Connected pawns">connected</a></li> <li><a href="/wiki/Doubled_pawns" title="Doubled pawns">doubled</a></li> <li><a href="/wiki/Isolated_pawn" title="Isolated pawn">isolated</a></li> <li><a href="/wiki/Passed_pawn" title="Passed pawn">passed</a></li></ul></li> <li><a href="/wiki/Swindle_(chess)" title="Swindle (chess)">Swindle</a></li> <li><a href="/wiki/Tempo_(chess)" title="Tempo (chess)">Tempo</a></li> <li><a href="/wiki/Transposition_(chess)" title="Transposition (chess)">Transposition</a></li> <li><a href="/wiki/List_of_chess_traps" title="List of chess traps">Trap</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Chess_tactic" title="Chess tactic">Tactics</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Castling#Artificial_castling" title="Castling">Artificial castling</a></li> <li><a href="/wiki/Battery_(chess)" title="Battery (chess)">Battery</a> <ul><li><a href="/wiki/Alekhine%27s_gun" title="Alekhine's gun">Alekhine's gun</a></li></ul></li> <li><a href="/wiki/Block_(chess)" title="Block (chess)">Block</a></li> <li><a href="/wiki/Checkmate_pattern" title="Checkmate pattern">Checkmate patterns</a></li> <li><a href="/wiki/Combination_(chess)" title="Combination (chess)">Combination</a></li> <li><a href="/wiki/Decoy_(chess)" title="Decoy (chess)">Decoy</a></li> <li><a href="/wiki/Deflection_(chess)" title="Deflection (chess)">Deflection</a></li> <li><a href="/wiki/Desperado_(chess)" title="Desperado (chess)">Desperado</a></li> <li><a href="/wiki/Discovered_attack" title="Discovered attack">Discovered attack</a></li> <li><a href="/wiki/Double_check" title="Double check">Double check</a></li> <li><a href="/wiki/Fork_(chess)" title="Fork (chess)">Fork</a></li> <li><a href="/wiki/Interference_(chess)" title="Interference (chess)">Interference</a></li> <li><a href="/wiki/Overloading_(chess)" title="Overloading (chess)">Overloading</a></li> <li><a href="/wiki/Pawn_storm" title="Pawn storm">Pawn storm</a></li> <li><a href="/wiki/Pin_(chess)" title="Pin (chess)">Pin</a></li> <li><a href="/wiki/Sacrifice_(chess)" title="Sacrifice (chess)">Sacrifice</a> <ul><li><a href="/wiki/Queen_sacrifice" title="Queen sacrifice">Queen sacrifice</a></li></ul></li> <li><a href="/wiki/Skewer_(chess)" title="Skewer (chess)">Skewer</a></li> <li><a href="/wiki/Undermining_(chess)" title="Undermining (chess)">Undermining</a></li> <li><a href="/wiki/Windmill_(chess)" title="Windmill (chess)">Windmill</a></li> <li><a href="/wiki/X-ray_(chess)" title="X-ray (chess)">X-ray</a></li> <li><a href="/wiki/Zwischenzug" title="Zwischenzug">Zwischenzug</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Chess_strategy" title="Chess strategy">Strategy</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Compensation_(chess)" title="Compensation (chess)">Compensation</a></li> <li><a href="/wiki/Exchange_(chess)" title="Exchange (chess)">Exchange</a> <ul><li><a href="/wiki/The_exchange_(chess)" title="The exchange (chess)">the exchange</a></li></ul></li> <li><a href="/wiki/Initiative_(chess)" title="Initiative (chess)">Initiative</a> <ul><li><a href="/wiki/First-move_advantage_in_chess" title="First-move advantage in chess">first-move advantage</a></li></ul></li> <li><a href="/wiki/Chess_middlegame" title="Chess middlegame">Middlegame</a></li> <li><a href="/wiki/Pawn_structure" title="Pawn structure">Pawn structure</a> <ul><li><a href="/wiki/Hedgehog_(chess)" title="Hedgehog (chess)">Hedgehog</a></li> <li><a href="/wiki/Isolated_pawn" title="Isolated pawn">Isolated Queen's Pawn</a></li> <li><a href="/wiki/Mar%C3%B3czy_Bind" title="Maróczy Bind">Maróczy Bind</a></li> <li><a href="/wiki/Minority_attack" title="Minority attack">Minority attack</a></li></ul></li> <li><a href="/wiki/Chess_piece_relative_value" title="Chess piece relative value">Piece values</a></li> <li><a href="/wiki/Prophylaxis_(chess)" title="Prophylaxis (chess)">Prophylaxis</a></li> <li><a href="/wiki/School_of_chess" title="School of chess">School of chess</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Chess_opening" title="Chess opening">Openings</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Flank_opening" title="Flank opening">Flank opening</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/King%27s_Fianchetto_Opening" title="King's Fianchetto Opening">Benko Opening</a></li> <li><a href="/wiki/Bird%27s_Opening" title="Bird's Opening">Bird's Opening</a></li> <li><a href="/wiki/Dunst_Opening" title="Dunst Opening">Dunst Opening</a></li> <li><a href="/wiki/English_Opening" title="English Opening">English Opening</a></li> <li><a href="/wiki/Grob%27s_Attack" title="Grob's Attack">Grob's Attack</a></li> <li><a href="/wiki/Larsen%27s_Opening" class="mw-redirect" title="Larsen's Opening">Larsen's Opening</a></li> <li><a href="/wiki/Zukertort_Opening" title="Zukertort Opening">Zukertort Opening</a> <ul><li><a href="/wiki/King%27s_Indian_Attack" title="King's Indian Attack">King's Indian Attack</a></li> <li><a href="/wiki/R%C3%A9ti_Opening" title="Réti Opening">Réti Opening</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/King%27s_Pawn_Game" title="King's Pawn Game">King's Pawn Game</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Alekhine%27s_Defence" title="Alekhine's Defence">Alekhine's Defence</a></li> <li><a href="/wiki/Caro%E2%80%93Kann_Defence" title="Caro–Kann Defence">Caro–Kann Defence</a></li> <li><a href="/wiki/French_Defence" title="French Defence">French Defence</a></li> <li><a href="/wiki/Modern_Defense" title="Modern Defense">Modern Defence</a></li> <li><a href="/wiki/Nimzowitsch_Defence" title="Nimzowitsch Defence">Nimzowitsch Defence</a></li> <li><a href="/wiki/Open_Game" title="Open Game">Open Game</a> <ul><li><a href="/wiki/Four_Knights_Game" title="Four Knights Game">Four Knights Game</a></li> <li><a href="/wiki/Giuoco_Piano" title="Giuoco Piano">Giuoco Piano</a></li> <li><a href="/wiki/Italian_Game" title="Italian Game">Italian Game</a></li> <li><a href="/wiki/King%27s_Gambit" title="King's Gambit">King's Gambit</a></li> <li><a href="/wiki/Petrov%27s_Defence" title="Petrov's Defence">Petrov's Defence</a></li> <li><a href="/wiki/Philidor_Defence" title="Philidor Defence">Philidor Defence</a></li> <li><a href="/wiki/Ponziani_Opening" title="Ponziani Opening">Ponziani Opening</a></li> <li><a href="/wiki/Ruy_Lopez" title="Ruy Lopez">Ruy Lopez</a></li> <li><a href="/wiki/Semi-Italian_Opening" title="Semi-Italian Opening">Semi-Italian Opening</a></li> <li><a href="/wiki/Scotch_Game" title="Scotch Game">Scotch Game</a></li> <li><a href="/wiki/Two_Knights_Defense" title="Two Knights Defense">Two Knights Defense</a></li> <li><a href="/wiki/Vienna_Game" title="Vienna Game">Vienna Game</a></li></ul></li> <li><a href="/wiki/Owen%27s_Defence" title="Owen's Defence">Owen's Defence</a></li> <li><a href="/wiki/Pirc_Defence" title="Pirc Defence">Pirc Defence</a> <ul><li><a href="/wiki/Pirc_Defence,_Austrian_Attack" title="Pirc Defence, Austrian Attack">Austrian Attack</a></li></ul></li> <li><a href="/wiki/Scandinavian_Defense" title="Scandinavian Defense">Scandinavian Defense</a></li> <li><a href="/wiki/Sicilian_Defence" title="Sicilian Defence">Sicilian Defence</a> <ul><li><a href="/wiki/Sicilian_Defence,_Alapin_Variation" title="Sicilian Defence, Alapin Variation">Alapin</a></li> <li><a href="/wiki/Sicilian_Defence,_Dragon_Variation" title="Sicilian Defence, Dragon Variation">Dragon</a>/<a href="/wiki/Sicilian_Defence,_Accelerated_Dragon" title="Sicilian Defence, Accelerated Dragon">Accelerated Dragon</a></li> <li><a href="/wiki/Sicilian_Defence,_Najdorf_Variation" title="Sicilian Defence, Najdorf Variation">Najdorf</a></li> <li><a href="/wiki/Sicilian_Defence,_Scheveningen_Variation" title="Sicilian Defence, Scheveningen Variation">Scheveningen</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Queen%27s_Pawn_Game" title="Queen's Pawn Game">Queen's Pawn Game</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Budapest_Gambit" title="Budapest Gambit">Budapest Gambit</a></li> <li><a href="/wiki/Colle_System" title="Colle System">Colle System</a></li> <li><a href="/wiki/Dutch_Defence" title="Dutch Defence">Dutch Defence</a></li> <li><a href="/wiki/English_Defence" title="English Defence">English Defence</a></li> <li><a href="/wiki/Indian_Defence" title="Indian Defence">Indian Defence</a> <ul><li><a href="/wiki/Benoni_Defense" title="Benoni Defense">Benoni Defence</a></li> <li><a href="/wiki/Modern_Benoni" title="Modern Benoni">Modern Benoni</a></li> <li><a href="/wiki/Bogo-Indian_Defence" title="Bogo-Indian Defence">Bogo-Indian Defence</a></li> <li><a href="/wiki/Catalan_Opening" title="Catalan Opening">Catalan Opening</a></li> <li><a href="/wiki/Gr%C3%BCnfeld_Defence" title="Grünfeld Defence">Grünfeld Defence</a></li> <li><a href="/wiki/King%27s_Indian_Defence" title="King's Indian Defence">King's Indian Defence</a></li> <li><a href="/wiki/Nimzo-Indian_Defence" title="Nimzo-Indian Defence">Nimzo-Indian Defence</a></li> <li><a href="/wiki/Old_Indian_Defense" title="Old Indian Defense">Old Indian Defense</a></li> <li><a href="/wiki/Queen%27s_Indian_Defense" title="Queen's Indian Defense">Queen's Indian Defence</a></li></ul></li> <li><a href="/wiki/London_System" title="London System">London System</a></li> <li><a href="/wiki/Richter%E2%80%93Veresov_Attack" title="Richter–Veresov Attack">Richter–Veresov Attack</a></li> <li><a href="/wiki/Queen%27s_Gambit" title="Queen's Gambit">Queen's Gambit</a> <ul><li><a href="/wiki/Queen%27s_Gambit_Accepted" title="Queen's Gambit Accepted">Accepted</a></li> <li><a href="/wiki/Queen%27s_Gambit_Declined" title="Queen's Gambit Declined">Declined</a></li> <li><a href="/wiki/Slav_Defense" title="Slav Defense">Slav Defence</a></li> <li><a href="/wiki/Semi-Slav_Defense" title="Semi-Slav Defense">Semi-Slav Defence</a></li> <li><a href="/wiki/Chigorin_Defense" title="Chigorin Defense">Chigorin Defense</a></li></ul></li> <li><a href="/wiki/Torre_Attack" title="Torre Attack">Torre Attack</a></li> <li><a href="/wiki/Trompowsky_Attack" title="Trompowsky Attack">Trompowsky Attack</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_chess_openings" title="List of chess openings">List of openings</a> <ul><li><a href="/wiki/Chess_opening_theory_table" title="Chess opening theory table">theory table</a></li></ul></li> <li><a href="/wiki/List_of_chess_gambits" title="List of chess gambits">List of chess gambits</a></li> <li><a href="/wiki/Irregular_chess_opening" title="Irregular chess opening">Irregular</a> <ul><li><a href="/wiki/Bongcloud_Attack" title="Bongcloud Attack">Bongcloud Attack</a></li> <li><a href="/wiki/Fool%27s_mate" title="Fool's mate">Fool's mate</a></li> <li><a href="/wiki/Scholar%27s_mate" title="Scholar's mate">Scholar's mate</a></li></ul></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Chess_endgame" title="Chess endgame">Endgames</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bishop_and_knight_checkmate" title="Bishop and knight checkmate">Bishop and knight checkmate</a></li> <li><a href="/wiki/King_and_pawn_versus_king_endgame" title="King and pawn versus king endgame">King and pawn vs king</a></li> <li><a href="/wiki/Opposite-colored_bishops_endgame" title="Opposite-colored bishops endgame">Opposite-coloured bishops</a></li> <li><a href="/wiki/Pawnless_chess_endgame" title="Pawnless chess endgame">Pawnless endgame</a></li> <li><a href="/wiki/Queen_and_pawn_versus_queen_endgame" title="Queen and pawn versus queen endgame">Queen and pawn vs queen</a></li> <li><a href="/wiki/Queen_versus_pawn_endgame" title="Queen versus pawn endgame">Queen vs pawn</a></li> <li><a href="/wiki/Queen_versus_rook_endgame" title="Queen versus rook endgame">Queen vs rook</a></li> <li><a href="/wiki/Rook_and_bishop_versus_rook_endgame" title="Rook and bishop versus rook endgame">Rook and bishop vs rook</a></li> <li><a href="/wiki/Rook_and_pawn_versus_rook_endgame" title="Rook and pawn versus rook endgame">Rook and pawn vs rook</a> <ul><li><a href="/wiki/Lucena_position" title="Lucena position">Lucena position</a></li> <li><a href="/wiki/Philidor_position" title="Philidor position">Philidor position</a></li></ul></li> <li>Strategy <ul><li><a href="/wiki/Fortress_(chess)" title="Fortress (chess)">fortress</a></li> <li><a href="/wiki/Opposition_(chess)" title="Opposition (chess)">opposition</a></li> <li><a href="/wiki/Tarrasch_rule" title="Tarrasch rule">Tarrasch rule</a></li> <li><a href="/wiki/Triangulation_(chess)" title="Triangulation (chess)">triangulation</a></li> <li><a href="/wiki/Zugzwang" title="Zugzwang">Zugzwang</a></li></ul></li> <li><a href="/wiki/Endgame_study" title="Endgame study">Study</a></li> <li><a href="/wiki/Endgame_tablebase" title="Endgame tablebase">Tablebase</a></li> <li><a href="/wiki/Two_knights_endgame" title="Two knights endgame">Two knights endgame</a></li> <li><a href="/wiki/Wrong_bishop" title="Wrong bishop">Wrong bishop</a></li> <li><a href="/wiki/Wrong_rook_pawn" title="Wrong rook pawn">Wrong rook pawn</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Chess_tournament" title="Chess tournament">Tournaments</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_strong_chess_tournaments" title="List of strong chess tournaments">List of strong chess tournaments</a></li> <li><a href="/wiki/Chess_Olympiad" title="Chess Olympiad">Chess Olympiad</a> <ul><li><a href="/wiki/Women%27s_Chess_Olympiad" title="Women's Chess Olympiad">Women</a></li></ul></li> <li><a href="/wiki/World_Chess_Championship" title="World Chess Championship">World Chess Championship</a> <ul><li><a href="/wiki/List_of_World_Chess_Championships" title="List of World Chess Championships">List</a></li> <li><a href="/wiki/Candidates_Tournament" title="Candidates Tournament">Candidates Tournament</a></li> <li><a href="/wiki/Chess_World_Cup" title="Chess World Cup">Chess World Cup</a></li> <li><a href="/wiki/FIDE_Grand_Prix" title="FIDE Grand Prix">FIDE Grand Prix</a></li></ul></li> <li>Other world championships <ul><li><a href="/wiki/Women%27s_World_Chess_Championship" title="Women's World Chess Championship">Women</a></li> <li><a href="/wiki/World_Team_Chess_Championship" title="World Team Chess Championship">Team</a></li> <li><a href="/wiki/World_Rapid_Chess_Championship" title="World Rapid Chess Championship">Rapid</a></li> <li><a href="/wiki/World_Blitz_Chess_Championship" title="World Blitz Chess Championship">Blitz</a></li> <li><a href="/wiki/World_Junior_Chess_Championship" title="World Junior Chess Championship">Junior</a></li> <li><a href="/wiki/World_Youth_Chess_Championship" title="World Youth Chess Championship">Youth</a></li> <li><a href="/wiki/World_Senior_Chess_Championship" title="World Senior Chess Championship">Senior</a></li> <li><a href="/wiki/World_Amateur_Chess_Championship" title="World Amateur Chess Championship">Amateur</a></li> <li><a href="/wiki/World_Championship_of_Chess_Composition" title="World Championship of Chess Composition">Chess composition</a></li> <li><a href="/wiki/World_Chess_Solving_Championship" title="World Chess Solving Championship">Solving</a></li></ul></li> <li>Computer chess championships <ul><li><a href="/wiki/Chess.com_Computer_Chess_Championship" class="mw-redirect" title="Chess.com Computer Chess Championship">CCC</a></li> <li><a href="/wiki/Dutch_Open_Computer_Chess_Championship" title="Dutch Open Computer Chess Championship">CSVN</a></li> <li><a href="/wiki/North_American_Computer_Chess_Championship" title="North American Computer Chess Championship">North American</a></li> <li><a href="/wiki/Top_Chess_Engine_Championship" title="Top Chess Engine Championship">TCEC</a></li> <li><a href="/wiki/World_Computer_Chess_Championship" title="World Computer Chess Championship">WCCC</a></li> <li><a href="/wiki/World_Computer_Speed_Chess_Championship" title="World Computer Speed Chess Championship">WCSCC</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Art and media</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ca%C3%AFssa" title="Caïssa">Caïssa</a></li> <li><a href="/wiki/Chess_aesthetics" title="Chess aesthetics">Chess aesthetics</a></li> <li><a href="/wiki/Chess_in_the_arts" title="Chess in the arts">Chess in the arts</a> <ul><li><a href="/wiki/Chess_in_early_literature" title="Chess in early literature">early literature</a></li> <li><a href="/wiki/Category:Films_about_chess" title="Category:Films about chess">film</a></li> <li><a href="/wiki/Category:Novels_about_chess" title="Category:Novels about chess">novels</a></li> <li><a href="/wiki/Category:Chess_paintings" title="Category:Chess paintings">paintings</a></li> <li><a href="/wiki/Category:Poems_about_chess" title="Category:Poems about chess">poetry</a></li> <li><a href="/wiki/Category:Short_stories_about_chess" title="Category:Short stories about chess">short stories</a></li></ul></li> <li><a href="/wiki/List_of_chess_books" title="List of chess books">Chess books</a> <ul><li><a href="/wiki/Chess_opening_book" title="Chess opening book">opening books</a></li> <li><a href="/wiki/Chess_endgame_literature" title="Chess endgame literature">endgame literature</a></li> <li><a href="/wiki/The_Oxford_Companion_to_Chess" title="The Oxford Companion to Chess"><i>Oxford Companion</i></a></li></ul></li> <li><a href="/wiki/Chess_libraries" title="Chess libraries">Chess libraries</a></li> <li><a href="/wiki/Chess_columns_in_newspapers" title="Chess columns in newspapers">Chess newspaper columns</a></li> <li><a href="/wiki/List_of_chess_periodicals" title="List of chess periodicals">Chess periodicals</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Arbiter_(chess)" title="Arbiter (chess)">Arbiter</a></li> <li><a href="/wiki/Chess_boxing" title="Chess boxing">Chess boxing</a></li> <li><a href="/wiki/Chess_club" title="Chess club">Chess club</a></li> <li><a href="/wiki/Chess_composer" title="Chess composer">Chess composer</a></li> <li><a href="/wiki/Chess_engine" title="Chess engine">Chess engine</a> <ul><li><a href="/wiki/AlphaZero" title="AlphaZero">AlphaZero</a></li> <li><a href="/wiki/Deep_Blue_(chess_computer)" title="Deep Blue (chess computer)">Deep Blue</a></li> <li><a href="/wiki/Leela_Chess_Zero" title="Leela Chess Zero">Leela Chess Zero</a></li> <li><a href="/wiki/Stockfish_(chess)" title="Stockfish (chess)">Stockfish</a></li></ul></li> <li><a href="/wiki/Chess_problem" title="Chess problem">Chess problem</a> <ul><li><a href="/wiki/Glossary_of_chess_problems" title="Glossary of chess problems">glossary</a></li> <li><a href="/wiki/Joke_chess_problem" title="Joke chess problem">joke chess</a></li></ul></li> <li><a href="/wiki/Chess_prodigy" title="Chess prodigy">Chess prodigy</a></li> <li><a href="/wiki/Simultaneous_exhibition" title="Simultaneous exhibition">Simultaneous exhibition</a></li> <li><a class="mw-selflink selflink">Solving chess</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="nowrap"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Chess.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/05/Chess.svg/28px-Chess.svg.png" decoding="async" width="28" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/05/Chess.svg/42px-Chess.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/05/Chess.svg/56px-Chess.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> </span><a href="/wiki/Portal:Chess" title="Portal:Chess">Chess portal</a></li> <li><a href="/wiki/Category:Chess" title="Category:Chess">Category</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Topics_of_game_theory" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Game_theory" title="Template:Game theory"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Game_theory" title="Template talk:Game theory"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Game_theory" title="Special:EditPage/Template:Game theory"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Topics_of_game_theory" style="font-size:114%;margin:0 4em">Topics of <a href="/wiki/Game_theory" title="Game theory">game theory</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Definitions</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Congestion_game" title="Congestion game">Congestion game</a></li> <li><a href="/wiki/Cooperative_game_theory" title="Cooperative game theory">Cooperative game</a></li> <li><a href="/wiki/Determinacy" title="Determinacy">Determinacy</a></li> <li><a href="/wiki/Escalation_of_commitment" title="Escalation of commitment">Escalation of commitment</a></li> <li><a href="/wiki/Extensive-form_game" title="Extensive-form game">Extensive-form game</a></li> <li><a href="/wiki/First-player_and_second-player_win" title="First-player and second-player win">First-player and second-player win</a></li> <li><a href="/wiki/Game_complexity" title="Game complexity">Game complexity</a></li> <li><a href="/wiki/Graphical_game_theory" title="Graphical game theory">Graphical game</a></li> <li><a href="/wiki/Hierarchy_of_beliefs" title="Hierarchy of beliefs">Hierarchy of beliefs</a></li> <li><a href="/wiki/Information_set_(game_theory)" title="Information set (game theory)">Information set</a></li> <li><a href="/wiki/Normal-form_game" title="Normal-form game">Normal-form game</a></li> <li><a href="/wiki/Preference_(economics)" title="Preference (economics)">Preference</a></li> <li><a href="/wiki/Sequential_game" title="Sequential game">Sequential game</a></li> <li><a href="/wiki/Simultaneous_game" title="Simultaneous game">Simultaneous game</a></li> <li><a href="/wiki/Simultaneous_action_selection" title="Simultaneous action selection">Simultaneous action selection</a></li> <li><a href="/wiki/Solved_game" title="Solved game">Solved game</a></li> <li><a href="/wiki/Succinct_game" title="Succinct game">Succinct game</a></li> <li><a href="/wiki/Mechanism_design" title="Mechanism design">Mechanism design</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Economic_equilibrium" title="Economic equilibrium">Equilibrium</a><br /><a href="/wiki/Solution_concept" title="Solution concept">concepts</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bayes_correlated_equilibrium" title="Bayes correlated equilibrium">Bayes correlated equilibrium</a></li> <li><a href="/wiki/Bayesian_Nash_equilibrium" class="mw-redirect" title="Bayesian Nash equilibrium">Bayesian Nash equilibrium</a></li> <li><a href="/wiki/Berge_equilibrium" title="Berge equilibrium">Berge equilibrium</a></li> <li><a href="/wiki/Core_(game_theory)" title="Core (game theory)"> Core</a></li> <li><a href="/wiki/Correlated_equilibrium" title="Correlated equilibrium">Correlated equilibrium</a></li> <li><a href="/wiki/Coalition-proof_Nash_equilibrium" title="Coalition-proof Nash equilibrium">Coalition-proof Nash equilibrium</a></li> <li><a href="/wiki/Epsilon-equilibrium" title="Epsilon-equilibrium">Epsilon-equilibrium</a></li> <li><a href="/wiki/Evolutionarily_stable_strategy" title="Evolutionarily stable strategy">Evolutionarily stable strategy</a></li> <li><a href="/wiki/Gibbs_measure" title="Gibbs measure">Gibbs equilibrium</a></li> <li><a href="/wiki/Mertens-stable_equilibrium" title="Mertens-stable equilibrium">Mertens-stable equilibrium</a></li> <li><a href="/wiki/Markov_perfect_equilibrium" title="Markov perfect equilibrium">Markov perfect equilibrium</a></li> <li><a href="/wiki/Nash_equilibrium" title="Nash equilibrium">Nash equilibrium</a></li> <li><a href="/wiki/Pareto_efficiency" title="Pareto efficiency">Pareto efficiency</a></li> <li><a href="/wiki/Perfect_Bayesian_equilibrium" title="Perfect Bayesian equilibrium">Perfect Bayesian equilibrium</a></li> <li><a href="/wiki/Proper_equilibrium" title="Proper equilibrium">Proper equilibrium</a></li> <li><a href="/wiki/Quantal_response_equilibrium" title="Quantal response equilibrium">Quantal response equilibrium</a></li> <li><a href="/wiki/Quasi-perfect_equilibrium" title="Quasi-perfect equilibrium">Quasi-perfect equilibrium</a></li> <li><a href="/wiki/Risk_dominance" title="Risk dominance">Risk dominance</a></li> <li><a href="/wiki/Satisfaction_equilibrium" title="Satisfaction equilibrium">Satisfaction equilibrium</a></li> <li><a href="/wiki/Self-confirming_equilibrium" title="Self-confirming equilibrium">Self-confirming equilibrium</a></li> <li><a href="/wiki/Sequential_equilibrium" title="Sequential equilibrium">Sequential equilibrium</a></li> <li><a href="/wiki/Shapley_value" title="Shapley value">Shapley value</a></li> <li><a href="/wiki/Strong_Nash_equilibrium" title="Strong Nash equilibrium">Strong Nash equilibrium</a></li> <li><a href="/wiki/Subgame_perfect_equilibrium" title="Subgame perfect equilibrium">Subgame perfection</a></li> <li><a href="/wiki/Trembling_hand_perfect_equilibrium" title="Trembling hand perfect equilibrium">Trembling hand equilibrium</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Strategy_(game_theory)" title="Strategy (game theory)">Strategies</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Appeasement" title="Appeasement">Appeasement</a></li> <li><a href="/wiki/Backward_induction" title="Backward induction">Backward induction</a></li> <li><a href="/wiki/Bid_shading" title="Bid shading">Bid shading</a></li> <li><a href="/wiki/Collusion" title="Collusion">Collusion</a></li> <li><a href="/wiki/Cheap_talk" title="Cheap talk">Cheap talk</a></li> <li><a href="/wiki/De-escalation" title="De-escalation">De-escalation</a></li> <li><a href="/wiki/Deterrence_theory" title="Deterrence theory">Deterrence</a></li> <li><a href="/wiki/Conflict_escalation" title="Conflict escalation">Escalation</a></li> <li><a href="/wiki/Forward_induction" class="mw-redirect" title="Forward induction">Forward induction</a></li> <li><a href="/wiki/Grim_trigger" title="Grim trigger">Grim trigger</a></li> <li><a href="/wiki/Markov_strategy" title="Markov strategy">Markov strategy</a></li> <li><a href="/wiki/Pairing_strategy" title="Pairing strategy">Pairing strategy</a></li> <li><a href="/wiki/Strategic_dominance" title="Strategic dominance">Dominant strategies</a></li> <li><a href="/wiki/Strategy_(game_theory)" title="Strategy (game theory)">Pure strategy</a></li> <li><a href="/wiki/Strategy_(game_theory)#Mixed_strategy" title="Strategy (game theory)">Mixed strategy</a></li> <li><a href="/wiki/Strategy-stealing_argument" title="Strategy-stealing argument">Strategy-stealing argument</a></li> <li><a href="/wiki/Tit_for_tat" title="Tit for tat">Tit for tat</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Category:Game_theory_game_classes" title="Category:Game theory game classes">Classes<br />of games</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Auction" title="Auction">Auction</a></li> <li><a href="/wiki/Bargaining_problem" class="mw-redirect" title="Bargaining problem">Bargaining problem</a></li> <li><a href="/wiki/Global_game" title="Global game">Global game</a></li> <li><a href="/wiki/Intransitive_game" title="Intransitive game">Intransitive game</a></li> <li><a href="/wiki/Mean-field_game_theory" title="Mean-field game theory">Mean-field game</a></li> <li><a href="/wiki/N-player_game" title="N-player game"><i>n</i>-player game</a></li> <li><a href="/wiki/Perfect_information" title="Perfect information">Perfect information</a></li> <li><a href="/wiki/Poisson_games" class="mw-redirect" title="Poisson games">Large Poisson game</a></li> <li><a href="/wiki/Potential_game" title="Potential game">Potential game</a></li> <li><a href="/wiki/Repeated_game" title="Repeated game">Repeated game</a></li> <li><a href="/wiki/Screening_game" title="Screening game">Screening game</a></li> <li><a href="/wiki/Signaling_game" title="Signaling game">Signaling game</a></li> <li><a href="/wiki/Strictly_determined_game" title="Strictly determined game">Strictly determined game</a></li> <li><a href="/wiki/Stochastic_game" title="Stochastic game">Stochastic game</a></li> <li><a href="/wiki/Symmetric_game" title="Symmetric game">Symmetric game</a></li> <li><a href="/wiki/Zero-sum_game" title="Zero-sum game">Zero-sum game</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/List_of_games_in_game_theory" title="List of games in game theory">Games</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Go_(game)" title="Go (game)">Go</a></li> <li><a href="/wiki/Chess" title="Chess">Chess</a></li> <li><a href="/wiki/Infinite_chess" title="Infinite chess">Infinite chess</a></li> <li><a href="/wiki/Draughts" class="mw-redirect" title="Draughts">Checkers</a></li> <li><a href="/wiki/All-pay_auction" title="All-pay auction">All-pay auction</a></li> <li><a href="/wiki/Prisoner%27s_dilemma" title="Prisoner's dilemma">Prisoner's dilemma</a></li> <li><a href="/wiki/Gift-exchange_game" title="Gift-exchange game">Gift-exchange game</a></li> <li><a href="/wiki/Optional_prisoner%27s_dilemma" title="Optional prisoner's dilemma">Optional prisoner's dilemma</a></li> <li><a href="/wiki/Traveler%27s_dilemma" title="Traveler's dilemma">Traveler's dilemma</a></li> <li><a href="/wiki/Coordination_game" title="Coordination game">Coordination game</a></li> <li><a href="/wiki/Chicken_(game)" title="Chicken (game)">Chicken</a></li> <li><a href="/wiki/Centipede_game" title="Centipede game">Centipede game</a></li> <li><a href="/wiki/Lewis_signaling_game" title="Lewis signaling game">Lewis signaling game</a></li> <li><a href="/wiki/Volunteer%27s_dilemma" title="Volunteer's dilemma">Volunteer's dilemma</a></li> <li><a href="/wiki/Dollar_auction" title="Dollar auction">Dollar auction</a></li> <li><a href="/wiki/Battle_of_the_sexes_(game_theory)" title="Battle of the sexes (game theory)">Battle of the sexes</a></li> <li><a href="/wiki/Stag_hunt" title="Stag hunt">Stag hunt</a></li> <li><a href="/wiki/Matching_pennies" title="Matching pennies">Matching pennies</a></li> <li><a href="/wiki/Ultimatum_game" title="Ultimatum game">Ultimatum game</a></li> <li><a href="/wiki/Electronic_mail_game" title="Electronic mail game">Electronic mail game</a></li> <li><a href="/wiki/Rock_paper_scissors" title="Rock paper scissors">Rock paper scissors</a></li> <li><a href="/wiki/Pirate_game" title="Pirate game">Pirate game</a></li> <li><a href="/wiki/Dictator_game" title="Dictator game">Dictator game</a></li> <li><a href="/wiki/Public_goods_game" title="Public goods game">Public goods game</a></li> <li><a href="/wiki/Blotto_game" title="Blotto game">Blotto game</a></li> <li><a href="/wiki/War_of_attrition_(game)" title="War of attrition (game)">War of attrition</a></li> <li><a href="/wiki/El_Farol_Bar_problem" title="El Farol Bar problem">El Farol Bar problem</a></li> <li><a href="/wiki/Fair_division" title="Fair division">Fair division</a></li> <li><a href="/wiki/Fair_cake-cutting" title="Fair cake-cutting">Fair cake-cutting</a></li> <li><a href="/wiki/Bertrand_competition" title="Bertrand competition">Bertrand competition</a></li> <li><a href="/wiki/Cournot_competition" title="Cournot competition">Cournot competition</a></li> <li><a href="/wiki/Stackelberg_competition" title="Stackelberg competition">Stackelberg competition</a></li> <li><a href="/wiki/Deadlock_(game_theory)" title="Deadlock (game theory)">Deadlock</a></li> <li><a href="/wiki/Unscrupulous_diner%27s_dilemma" title="Unscrupulous diner's dilemma">Diner's dilemma</a></li> <li><a href="/wiki/Guess_2/3_of_the_average" title="Guess 2/3 of the average">Guess 2/3 of the average</a></li> <li><a href="/wiki/Kuhn_poker" title="Kuhn poker">Kuhn poker</a></li> <li><a href="/wiki/Bargaining_problem" class="mw-redirect" title="Bargaining problem">Nash bargaining game</a></li> <li><a href="/wiki/Induction_puzzles" title="Induction puzzles">Induction puzzles</a></li> <li><a href="/wiki/Dictator_game#Trust_game" title="Dictator game">Trust game</a></li> <li><a href="/wiki/Princess_and_monster_game" title="Princess and monster game">Princess and monster game</a></li> <li><a href="/wiki/Rendezvous_problem" title="Rendezvous problem">Rendezvous problem</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theorems</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Aumann%27s_agreement_theorem" title="Aumann's agreement theorem">Aumann's agreement theorem</a></li> <li><a href="/wiki/Folk_theorem_(game_theory)" title="Folk theorem (game theory)">Folk theorem</a></li> <li><a href="/wiki/Minimax" title="Minimax">Minimax theorem</a></li> <li><a href="/wiki/Nash_equilibrium" title="Nash equilibrium">Nash's theorem</a></li> <li><a href="/wiki/Negamax" title="Negamax">Negamax theorem</a></li> <li><a href="/wiki/Purification_theorem" title="Purification theorem">Purification theorem</a></li> <li><a href="/wiki/Revelation_principle" title="Revelation principle">Revelation principle</a></li> <li><a href="/wiki/Sprague%E2%80%93Grundy_theorem" title="Sprague–Grundy theorem">Sprague–Grundy theorem</a></li> <li><a href="/wiki/Zermelo%27s_theorem_(game_theory)" title="Zermelo's theorem (game theory)">Zermelo's theorem</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Key<br />figures</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Albert_W._Tucker" title="Albert W. Tucker">Albert W. Tucker</a></li> <li><a href="/wiki/Amos_Tversky" title="Amos Tversky">Amos Tversky</a></li> <li><a href="/wiki/Antoine_Augustin_Cournot" title="Antoine Augustin Cournot">Antoine Augustin Cournot</a></li> <li><a href="/wiki/Ariel_Rubinstein" title="Ariel Rubinstein">Ariel Rubinstein</a></li> <li><a href="/wiki/Claude_Shannon" title="Claude Shannon">Claude Shannon</a></li> <li><a href="/wiki/Daniel_Kahneman" title="Daniel Kahneman">Daniel Kahneman</a></li> <li><a href="/wiki/David_K._Levine" title="David K. Levine">David K. Levine</a></li> <li><a href="/wiki/David_M._Kreps" title="David M. Kreps">David M. Kreps</a></li> <li><a href="/wiki/Donald_B._Gillies" title="Donald B. Gillies">Donald B. Gillies</a></li> <li><a href="/wiki/Drew_Fudenberg" title="Drew Fudenberg">Drew Fudenberg</a></li> <li><a href="/wiki/Eric_Maskin" title="Eric Maskin">Eric Maskin</a></li> <li><a href="/wiki/Harold_W._Kuhn" title="Harold W. Kuhn">Harold W. Kuhn</a></li> <li><a href="/wiki/Herbert_A._Simon" title="Herbert A. Simon">Herbert Simon</a></li> <li><a href="/wiki/Herv%C3%A9_Moulin" title="Hervé Moulin">Hervé Moulin</a></li> <li><a href="/wiki/John_Conway" class="mw-redirect" title="John Conway">John Conway</a></li> <li><a href="/wiki/Jean_Tirole" title="Jean Tirole">Jean Tirole</a></li> <li><a href="/wiki/Jean-Fran%C3%A7ois_Mertens" title="Jean-François Mertens">Jean-François Mertens</a></li> <li><a href="/wiki/Jennifer_Tour_Chayes" title="Jennifer Tour Chayes">Jennifer Tour Chayes</a></li> <li><a href="/wiki/John_Harsanyi" title="John Harsanyi">John Harsanyi</a></li> <li><a href="/wiki/John_Maynard_Smith" title="John Maynard Smith">John Maynard Smith</a></li> <li><a href="/wiki/John_Forbes_Nash_Jr." title="John Forbes Nash Jr.">John Nash</a></li> <li><a href="/wiki/John_von_Neumann" title="John von Neumann">John von Neumann</a></li> <li><a href="/wiki/Kenneth_Arrow" title="Kenneth Arrow">Kenneth Arrow</a></li> <li><a href="/wiki/Kenneth_Binmore" title="Kenneth Binmore">Kenneth Binmore</a></li> <li><a href="/wiki/Leonid_Hurwicz" title="Leonid Hurwicz">Leonid Hurwicz</a></li> <li><a href="/wiki/Lloyd_Shapley" title="Lloyd Shapley">Lloyd Shapley</a></li> <li><a href="/wiki/Melvin_Dresher" title="Melvin Dresher">Melvin Dresher</a></li> <li><a href="/wiki/Merrill_M._Flood" title="Merrill M. Flood">Merrill M. Flood</a></li> <li><a href="/wiki/Olga_Bondareva" title="Olga Bondareva">Olga Bondareva</a></li> <li><a href="/wiki/Oskar_Morgenstern" title="Oskar Morgenstern">Oskar Morgenstern</a></li> <li><a href="/wiki/Paul_Milgrom" title="Paul Milgrom">Paul Milgrom</a></li> <li><a href="/wiki/Peyton_Young" title="Peyton Young">Peyton Young</a></li> <li><a href="/wiki/Reinhard_Selten" title="Reinhard Selten">Reinhard Selten</a></li> <li><a href="/wiki/Robert_Axelrod_(political_scientist)" title="Robert Axelrod (political scientist)">Robert Axelrod</a></li> <li><a href="/wiki/Robert_Aumann" title="Robert Aumann">Robert Aumann</a></li> <li><a href="/wiki/Robert_B._Wilson" title="Robert B. Wilson">Robert B. Wilson</a></li> <li><a href="/wiki/Roger_Myerson" title="Roger Myerson">Roger Myerson</a></li> <li><a href="/wiki/Samuel_Bowles_(economist)" title="Samuel Bowles (economist)"> Samuel Bowles</a></li> <li><a href="/wiki/Suzanne_Scotchmer" title="Suzanne Scotchmer">Suzanne Scotchmer</a></li> <li><a href="/wiki/Thomas_Schelling" title="Thomas Schelling">Thomas Schelling</a></li> <li><a href="/wiki/William_Vickrey" title="William Vickrey">William Vickrey</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Search optimizations</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Alpha%E2%80%93beta_pruning" title="Alpha–beta pruning">Alpha–beta pruning</a></li> <li><a href="/wiki/Aspiration_window" title="Aspiration window">Aspiration window</a></li> <li><a href="/wiki/Principal_variation_search" title="Principal variation search">Principal variation search</a></li> <li><a href="/wiki/Max%5En_algorithm" title="Max^n algorithm">max^n algorithm</a></li> <li><a href="/wiki/Paranoid_algorithm" title="Paranoid algorithm">Paranoid algorithm</a></li> <li><a href="/wiki/Lazy_SMP" title="Lazy SMP">Lazy SMP</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Miscellaneous</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bounded_rationality" title="Bounded rationality">Bounded rationality</a></li> <li><a href="/wiki/Combinatorial_game_theory" title="Combinatorial game theory">Combinatorial game theory</a></li> <li><a href="/wiki/Confrontation_analysis" title="Confrontation analysis">Confrontation analysis</a></li> <li><a href="/wiki/Coopetition" title="Coopetition">Coopetition</a></li> <li><a href="/wiki/Evolutionary_game_theory" title="Evolutionary game theory">Evolutionary game theory</a></li> <li><a href="/wiki/Glossary_of_game_theory" title="Glossary of game theory">Glossary of game theory</a></li> <li><a href="/wiki/List_of_game_theorists" title="List of game theorists">List of game theorists</a></li> <li><a href="/wiki/List_of_games_in_game_theory" title="List of games in game theory">List of games in game theory</a></li> <li><a href="/wiki/No-win_situation" title="No-win situation">No-win situation</a></li> <li><a href="/wiki/Topological_game" title="Topological game">Topological game</a></li> <li><a href="/wiki/Tragedy_of_the_commons" title="Tragedy of the commons">Tragedy of the commons</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Solving_chess&oldid=1237722712">https://en.wikipedia.org/w/index.php?title=Solving_chess&oldid=1237722712</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Category</a>: <ul><li><a href="/wiki/Category:Chess_theory" title="Category:Chess theory">Chess theory</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Pages_containing_links_to_subscription-only_content" title="Category:Pages containing links to subscription-only content">Pages containing links to subscription-only content</a></li><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_is_different_from_Wikidata" title="Category:Short description is different from Wikidata">Short description is different from Wikidata</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 31 July 2024, at 05:02<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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