Endgame Magic #199: Endgame highlights from the Chess Festival Prague

by Karsten Müller
6/20/2022 – In the Endgame Magic Show #199 Karsten takes a look at interesting endgames from the Chess Festival in Prague. Pentala Harikrishna won the Masters, Vincent Keymer won the Challengers and both scored crucial points in the endgame. | You can watch the Endgame Magic Show on-demand with a ChessBase Premium account.

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Endgame Magic #199

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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Karsten Müller is considered to be one of the greatest endgame experts in the world. His books on the endgame - among them "Fundamentals of Chess Endings", co-authored with Frank Lamprecht, that helped to improve Magnus Carlsen's endgame knowledge - and his endgame columns for the ChessCafe website and the ChessBase Magazine helped to establish and to confirm this reputation. Karsten's Fritztrainer DVDs on the endgame are bestsellers. The mathematician with a PhD lives in Hamburg, and for more than 25 years he has been scoring points for the Hamburger Schachklub (HSK) in the Bundesliga.