So it's come down to the last round, and the only two players who can win the event are facing off for the right to play Magnus Carlsen in the next World Championship match, to be held later this year. Sergey Karjakin and Fabiano Caruana are still at +2, half a point ahead of Viswanathan Anand, and while only the first two named have a shot at winning the event Anand can play the spoiler.
Here's the situation: Karjakin has White against Caruana in the last round, while Anand has Black against Peter Svidler. Karjakin wins the event unless one of two scenarios come to pass:
If Karjakin-Caruana is a draw and they're the only two players tied for first, Karjakin takes first on tiebreaks. They will have split their head-to-head matchup, and the next tiebreaker (more wins) decides things in Karjakin's favor. If it winds up in a three-way tie, however, Caruana wins because he had the best score in the head-to-head-to-head: he went +1 against Anand while the other two mini-matches were even.
Both possibilities are attractive. If Karjakin wins, then the match the chess world has expected since 2003 or so will finally taken place, while Caruana has looked like Carlsen's likeliest rival since 2014. Both are also good from a publicity standpoint: Karjakin represents Russia while Caruana represents the U.S., which is especially good since the championship match is going to be held here.
In round 13 both Karjakin and Caruana played for more than 100 moves. Caruana was pushing in his game, trying to grind out a win against Svidler in a rook and bishop vs. rook ending (and near the end he briefly had a theoretically winning ending, though I'm not sure if he had enough moves to convert before the 50-move rule kicked in), while Karjakin had to grimly hang on in his game with Levon Aronian. Both players are young and fit (especially Caruana), but how much will they have left after a marathon game at the end of a long tournament?
In other round 13 action Hikaru Nakamura won again, at the expense of Veselin Topalov, who lost again. Nakamura thus made it back to 50%, while Topalov sunk to -5. Remarkably, Topalov is the only player in the field with a minus score. The other game saw Anish Giri get his 13th draw in 13 games, this one against Levon Aronian. Giri has played a lot of interesting, up and down games, and this was one of them. Somehow, they just end in draws, no matter what happens along the way there.
Last Round Pairings: