Troitzky Line
| 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 |
The Troitzky (or Troitsky) line (or Troitzky position) is a key motif in chess endgame theory in the rare and practically unimportant (but theoretically interesting) ending of two knights versus a pawn. The endgame was analyzed by A. A. Troitzky.
Whilst two knights cannot force checkmate (with the help of their king) against a lone king, a decrease in material advantage allowing the defending king to have a pawn can actually cause his demise. This is due to the fact that a common technique in this endgame is that of reducing the defending king to a position that would be a stalemate except for an available pawn move, and allowing the pawn to move can allow the attacking knights to move in for the kill. For the position with White on the attack, Troitsky established that if a black pawn is blockaded (by one of the white knights) on a square no further forward than the line a4–b6–c5–d4–e4–f5–g6–h4, then White can win the resulting endgame (and similarly in reverse for Black), no matter where the other pieces are placed. However, the checkmate procedure is difficult and long. In fact, it can require up to 115 moves by White, so in competition often a draw by the fifty-move rule will occur first (but see this article and Second Troitzky line section for the zone where the win can be forced within fifty moves). Therefore the ending is more of theoretical than practical interest. If the defending black pawn is past the Troitsky line, there are zones such that if the black king is in one, white still has a theoretical win; otherwise the position is a draw.
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" (Nunn 1995:265).
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 (Giddins 2012:26).
Two knights versus pawn is sometimes called the "Halley's Comet" endgame.
Read more about this topic: Two Knights Endgame
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