Two Knights Endgame

The two knights endgame is a chess endgame with a king and two knights versus a king, possibly with some other material. The material with the defending king is usually one pawn, but some positions studied involve additional pawns or other pieces. In contrast to a king plus two bishops, or a bishop and a knight, a king and two knights cannot force checkmate against a lone king. (However, the superior side can force stalemate.) Although there are checkmate positions, the superior side cannot force them against proper (and easy) defense (Speelman, Tisdall & Wade 1993:11).

	a	b	c	d	e	f	g	h
8									8
7									7
6									6
5									5
4									4
3									3
2									2
1									1
	a	b	c	d	e	f	g	h

Checkmate position, but it cannot be forced (Seirawan 2003:17). The knight on d2 could be on c3 or a3 instead, and the white king could be on a3 instead.

On the other hand, if the lone king has a pawn (and sometimes with more pawns), then checkmate can be forced in some cases. These positions were studied extensively by A. A. Troitzky. If the defender's pawn is blocked on or before the "Troitzky line", the stronger side can force checkmate, although it may require up to 115 moves with optimal play. The reason that checkmate can be forced is that the pawn gives the defender a piece to move and deprives him of a stalemate defense (Müller & Lamprecht 2001:19–20). The technique (when it is possible) is to block the pawn with one knight and use the king and other knight to force the opposing king into a corner or near the other knight. Then when the block on the pawn is removed, the knight can be used to checkmate (Dvoretsky 2006:280).