A Surprising Missed Winning Opportunity in Nakamura-Karjakin

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 

44...Rd3!!

 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.

Avoiding an Opposite-Colored Bishop Ending Through an Exchange Sacrifice

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.