Editing Chess endgame (section)

==Effect of tablebases on endgame theory==
Endgame tablebases have made some minor corrections to historical endgame analysis, but they have made some more significant changes to endgame theory too. (The [[fifty-move rule]] is not taken into account in these studies.) Major changes to endgame theory as a result of tablebases include the following:<ref>{{Harvcol|Müller|Lamprecht|2001|pp=8,400–406}}</ref>
* {{em|Queen versus rook}} (see {{seclink|Philidor position|Queen versus rook}}). There are two changes here enabling the rook to put up a better defense, but the queen still wins. (a) People usually opt for a second-rank defense with the rook on the second rank and the king behind it (or symmetrical positions on the other edges of the board). Tablebases show that a third-rank defense takes a while to breach, which is difficult for a human to do. (b) People had assumed that the rook needs to stay as close to the king for as long as possible, but tablebases show that it is best to move the rook away from the king at some earlier point.<ref>{{Harvcol|Nunn|2002|p=49ff}}</ref>
* {{em|Queen and pawn versus queen}}. Tablebases have shown that this can be won in many more positions than was thought, but the logic of the moves is presently beyond human understanding.<ref>{{Harvcol|Nunn|1995|p=265}}</ref>
* {{em|Queen versus two bishops}}. This was thought to be a draw due to the existence of a drawing [[fortress (chess)|fortress]] position, but the queen can win most of the time by preventing the bishops from getting to the fortress. However, it can take up to 71 moves to force a win.<ref>{{Harvcol|Nunn|2002|pp=290ff}}</ref>
{{Chess diagram small 
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|  |  |  |  |  |kd|  |  
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|  |  |  |  |  |nd|nd|  
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|  |  |ql|  |  |  |  |  
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|This position was thought to be drawn, but White to move wins.  Some similar positions are actually drawn (e.g. with the queen on e2).
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* {{em|Queen versus two knights}}. This was thought to be a draw, and indeed it generally is, but the queen has more winning positions than was previously thought. Also, many analysts gave a position (see diagram) that they thought was a draw but it is actually a win for the queen.<ref>{{Harvcol|Nunn|2002|pp=300ff}}</ref> In the diagram, White checkmates in 43 moves, starting with '''1. Qc7''' (the only winning move). Nunn says "The general result is undoubtedly a draw, but there are many losing positions, some of them very lengthy." On the other hand, 73.44% of positions are won by the queen, almost all of the remainder being positions where the side with two knights can immediately capture the queen – 97.59% of positions with the side with the queen to move are won by that side.<ref name=wilhelm>{{cite web|url=http://www.geocities.com/rba_schach2000/overview_english.htm |title=Chess program Wilhelm |url-status=dead |archive-url=https://web.archive.org/web/20081208015339/http://www.geocities.com/rba_schach2000/overview_english.htm |archive-date=December 8, 2008 }} + {{cite web|url=http://auto-chess.blogspot.ch/2012/11/download-nalimov-end-game-tablebases-2.html|title=Nalimov Engame Tablebases|website=AutoChess|date=11 November 2012}}</ref> However, these percentages can be misleading, and most "general results" are based on the analysis of [[International Grandmaster|grandmasters]] using the tablebase data.<ref>{{Harvcol|Müller|Lamprecht|2001|p=406}}</ref><ref>{{Harvcol|Nunn|2002|p=324}}</ref> For instance, although nearly 90 percent of all of these positions are wins for the queen, it is generally a draw if the king is not separated from the knights and they are on reasonable squares.<ref>{{Harvcol|Müller|Lamprecht|2001|p=339}}</ref>
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|  |  |  |  |  |bl|  |  
|  |nd|  |  |  |  |  |  
|  |kd|  |  |  |  |  |  
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|bl|  |  |  |  |  |  |  
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|This position was thought to be drawn (Kling and Horwitz, 1851), but White wins.
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* {{em|Two bishops versus a knight}}. This was thought to be a draw but the bishops generally win. However, it takes up to 66 moves. The position in the diagram was thought to be a draw for over one hundred years, but tablebases show that White wins in 57 moves. All of the long wins go through this type of semi-fortress position. It takes several moves to force Black out of the temporary fortress in the corner; then precise play with the bishops prevents Black from forming the temporary fortress in another corner.<ref>{{Harvcol|Nunn|1995|pp=265ff}}</ref> Before computer analysis, Speelman listed this position as unresolved, but "probably a draw".<ref>{{Harvcol|Speelman|1981|p=109}}</ref>
* {{em|Queen and bishop versus two rooks}}. This was thought to be a draw but the queen and bishop usually win. It takes up to 84 moves.<ref>{{Harvcol|Nunn|2002|pp=367ff}}</ref>
* {{em|Rook and bishop versus bishop and knight, bishops on opposite colors}}. This was thought to be a draw but the rook and bishop generally win. It takes up to 98 moves.<ref>{{Harvcol|Nunn|2002|pp=342ff}}</ref> [[Magnus Carlsen]] successfully converted this configuration within the 50-move limit against Francisco Vallejo Pons in 2019. Even with best play from the starting RB v BN position, the stronger side would have won a piece well within 50 moves.<ref>[http://www.chessgames.com/perl/chessgame?gid=1954368 Francisco Vallejo Pons vs Magnus Carlsen],  GRENKE Chess Classic, Karlsruhe GER, rd 2, 21 April 2019.</ref>
* {{em|[[Rook and bishop versus rook endgame|Rook and bishop versus rook]]}}. The second-rank defense was discovered using tablebases.<ref>{{Harvcol|Hawkins|2012|pp=198–200}}</ref>
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