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Two knights endgame
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{{Short description|Chess endgame}} {| align="right" | [[Image:Chess kll45.svg]] | [[Image:Chess nll45.svg]] | [[Image:Chess nll45.svg]] | [[Image:Chess kdl45.svg]] |} The '''two knights endgame''' is a [[chess endgame]] with a [[king (chess)|king]] and two [[knight (chess)|knights]] versus a king. In contrast to a king and two [[bishop (chess)|bishops]] (on opposite-colored squares), or a [[bishop and knight checkmate|bishop and a knight]], a king and two knights cannot {{chessgloss|forced mate|force}} [[checkmate]] against a lone king (however, the superior side can force [[stalemate]]<ref>{{Harvcol|Mednis|1996|p=41}}</ref><ref>{{Harvcol|Averbakh|1993|p=14}}</ref>). Although there are checkmate positions, a king and two knights cannot {{chessgloss|forced mate|force}} them against proper, relatively easy defense.<ref>{{Harvcol|Speelman|Tisdall|Wade|1993|p=11}}</ref> {{Chess diagram | tright | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |kl| | | | | | | | |nl|nl| | | | |kd| | | | | | | | Checkmate position, but it cannot be forced from the position with the c2 knight relocated to e2.<ref>{{Harvcol|Seirawan|2003|p=17}}</ref> The knight on d2 could be on ''c3'' or ''a3'' instead, and the white king could be on ''a3'' instead. }} Although the king and two knights cannot {{chessgloss|forced mate|force}} checkmate of the lone king, there are positions in which the king and two knights can force checkmate against a king and some additional material.<ref>{{Harvcol|Troitsky|2006|pp=197β257}}</ref> The extra material of the defending side provides moves that prevent the defending king from being stalemated<ref>{{Harvcol|Averbakh|1993|p=14}}</ref>or, less commonly, the extra material obstructs the defending king from escaping check. The winning chances with two knights are insignificant except against a few pawns.<ref>{{cite journal|url=http://centaur.reading.ac.uk/27847/|title=Western Chess:Endgame Data|date=2009|last=Haworth|first=Guy M<sup>c</sup>C|website=CentAUR}}</ref> These positions were studied extensively by [[A. A. Troitsky]], who discovered the Troitsky line, a line on or behind which the defending side's pawn must be securely blockaded for the attacking side to win. If the side with the knights carelessly captures the other side's extra material, the game devolves to the basic two knights endgame, and the opportunity to force checkmate may be lost. When the defender has a single pawn, the technique (when it is possible) is to block the pawn with one knight, and use the king and the other knight to force the opposing king into a corner or nearby the blocking knight. Then, when the block on the pawn is removed, the knight that was used to block the pawn can be used to checkmate.<ref>{{Harvcol|Dvoretsky|2006|p=280}}</ref> {{algebraic notation|pos=tocleft}}
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