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All endgame DVDs by Karsten Müller in one package! More than 70 hours of instruction! from "Basic knowledge for beginners" (volume 1) to "Practical Rook Endgames" (volume 8) to the ever-popular "Golden Guidelines of Endgame Play" (volume 14).
In round 4 Harikrishna played against Parham Maghsoodloo and had the notorious endgame king and two knights vs king and pawn on the board. Every beginner knows that you cannot mate with two knights but things get very tricky when the side with the king still has a pawn.
This kind of endgame was analysed by the famous Russian endgame study composer Alexey Troitzky (1866-1942) and is therefore called the "Troitzky endgame". He found out where the single pawn must be to make the position won or drawn and defined the so-called "Troitzky line".
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.
Karsten Müller and Frank Lamprecht, Fundamental Chess Endings 2001
The Wikipedia, which has an entry about the "Two knights endgame", writes:
John Nunn analyzed the endgame of two knights versus a pawn with an endgame tablebase and stated that "the analysis of Troitzky 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).
In this position White to move can draw as the pawn has crossed the "Troitzky line". Do you know or can you find the only defense for White?
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