White wins in one move), decreasing the material advantage and allowing the defending king to have a pawn can actually allow for a forced checkmate. 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. Another reason is that the pawn can block its own king's path without necessarily moving (e.g. Kling & Horwitz position right). The Troitsky line (or Troitsky position) is a key motif in chess endgame theory in the rare but theoretically interesting ending of two knights versus a pawn. The line, assuming White has the two knights and Black the pawn, is shown left. The Russian theoretician Troitsky made a detailed study of this endgame and discovered the following rule: 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." However, the checkmate procedure is difficult and long. In fact, it can require up to 115 moves by White (assuming perfect play), so in competition often a draw by the fifty-move rule will occur first. Troitsky showed that "on any placement of the black king, White undoubtedly wins only against black pawns standing on [the Troitsky line] and above". John Nunn analyzed the endgame of two knights versus a pawn with an endgame tablebase and stated that "the analysis of Troitsky and others is astonishingly accurate". 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. Neither player knew whether the position was a win for the player with the knights (Korchnoi). Even when the position is a theoretical win, it is very complicated and difficult to play correctly. Even grandmasters fail to win it. Andor Lilienthal failed to win it twice in a six-year period, see Norman vs. Lilienthal and Smyslov vs. Lilienthal. But a fine win is in a game by Seitz, see Znosko-Borovsky vs. Seitz. Examples This diagram shows an example of how having the pawn makes things worse for Black (here Black's pawn is past the Troitsky line), by making Black have a move available instead of being stalemated. 1. Ne4 d2 2. Nf6+ Kh8 3. Ne7 (if Black did not have the pawn