Two knights endgame

The two knights endgame is a chess endgame with a king and two knights versus a king. In contrast to a king and two bishops (on opposite-colored squares), 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^[1][2]). Although there are checkmate positions, a king and two knights cannot force them against proper, relatively easy defense.^[3]

	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 from the position with the c2 knight relocated to e2.^[4] The knight on d2 could be on c3 or a3 instead, and the white king could be on a3 instead.

Paradoxically, although the king and two knights cannot 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.^[5] The extra material of the defending side provides moves that prevent the defending king from being stalemated^[6]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.^[7] 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.^[8]