Although there are checkmate positions, a king and two knights cannot force them against proper, relatively easy defense.
[11] Edmar Mednis stated that this inability to force checkmate is "one of the great injustices of chess.
[15] There are also checkmate positions with the inferior side's king on the edge of the board (instead of the corner), but again they cannot be forced.
In this position from a 1949 game[17] between Pal Benko and David Bronstein, Black underpromoted to a knight.
Another example is the eighth game of the 1981 World Chess Championship match between Anatoly Karpov and Viktor Korchnoi.
[21] Also, a complete computational retrograde analysis revealed that they can force checkmate only on the edge of the board.
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.
[25] Another reason is that the pawn can block its own king's path without necessarily moving (e.g. Kling & Horwitz position right).
The Russian theoretician Troitsky made a detailed study of this endgame and discovered the following rule: If the pawn is securely blockaded by a white knight no further down than the line, then Black loses, no matter where the kings are.An example of the application of this rule is given in the diagram Müller and Lamprecht right; "... the position would be lost no matter where the kings are.
In fact, it can require up to 115 moves by White (assuming perfect play),[27] so in competition a draw by the fifty-move rule will occur first.
[29] He undertook this checking after the very ending occurred in a critical variation of his post mortem analysis of a game he lost to Korchnoi in the 1980 Phillips and Drew Tournament in London.
In this study by André Chéron, White wins even though the pawn is well beyond the Troitsky line.
Otherwise, White can force the black king into one of the corners not located in the drawing zone and deliver checkmate.
[34] Anatoly Karpov lost an endgame with a pawn versus two knights to Veselin Topalov[35] although he had a theoretical draw with a pawn past the Troitsky line; because of its rarity, Karpov seemed not to know the theory of drawing and headed for the wrong corner.
[37] This position from a blindfold game between Wang Yue and Viswanathan Anand leads to an example with a forced win even though the pawn is past the Troitsky line.
Black should have played 61...Ne4 62. c4 Nc5!, blocking the pawn on the Troitsky line with a knight, with a forced win.
The knights cannot set up an effective blockade against four connected pawns, so the position generally results in a draw.
[40] In this 1991 game between Paul Motwani and Ilya Gurevich, Black has blockaded the white pawns.
[52] The analysis by Chapais was revised by Guretsky-Cornitz and others, and it was included by Johann Berger in Theory and Practice of the Endgame, first published in 1891.
[53] Troitsky started studying the endgame in the early 20th century and published his extensive analysis in 1937.
[55] Master games with this ending are rare — Troitsky knew of only six when he published his analysis in 1937.
The first master game with a win was in 1931 when Adolf Seitz beat Eugene Znosko-Borovsky.