In yesterday's rapid game between Nakamura and Karjakin, they played on until bare kings in an endgame. It had seemed drawn for a long time, except for a moment of excitement when Karjakin offered a rook sacrifice on move 42 with 42...Rd2+!?. Nakamura declined the offer, seeing that it would allow Karjakin to queen a pawn, and the game wound on to its drawn conclusion.
Karjakin, who was extremely short of time, did not notice that there was an even better version of his idea--one that would have won on the spot. He could have played
Nakamura-Karjakin after 42...Rd3!! (analysis diagram)
The point is to cover b3 so that White can't recapture with his king after 45...b3+. If 45.Kxd3 b3! queens a pawn. White's rook and knight are so out of position, in fact, that they are helpless to stop 45...b3 regardless of White's next move.
Opposite-colored bishop endings are notoriously (or wonderfully, if you are the defender) drawish. One side can frequently have two, or even more, extra pawns but absolutely no chance of winning, because it cannot overcome a blockade on the squares that its bishop does not cover. Dvoretsky gives the following example:
Despite being up three pawns, Black cannot win. White merely moves his bishop along the h3-c8 diagonal.
If there is more material on the board, one way for the side with the advantage to avoid this fate is to sacrifice some material. The Tata Steel tournament earlier this year witnessed two nice examples of this stratagem.
Jan Smeets has had a tough time of it in the Tata Steel tournament this month. (I am sure that I am not the first to mention it, but doesn't "Tata Steel" sound like a porn star name?)
In the eighth round, Smeets had White against Maxime Vachier-Lagrave (who sounds like a Bond villain). Lagrave played a Modern Defense with 4...a6, which I used to consider daring and exciting long ago when I played it with Black, but also slightly insulting when I faced it with White. In any event, Smeets looked, if anything, better out of the opening, and was certainly no worse until he played 21.Rd8? But, in his usual ferocious time trouble, he wound up defending a difficult pawn-down rook ending, which he proceeded to lose.
I want to suggest that at move 38 (when he probably had seconds left on the clock), Smeets missed a good drawing chance. At this point, after some exchanges, the material was even, though Black had a strong passed pawn on the kingside. In the following position,
Smeets played 38.Kb3? and wound up in a very difficult position after 38...Kc6 39.h4 Kd5 40.h5 Ke4 41.hxg6 Rxg6. He may still have had a draw even then, but I think the draw is more likely after: