Fabiano Caruana, Shakhriyar Mamedyarov and Alexander Grischuk drew their games in Round 11 of the Candidates tournament in Berlin, allowing them to retain their positions at the top of the leaderboard. Caruana, an American, continues to lead, now with seven points, followed by Mamedyarov, who is from Azerbaijan and has 6.5, and Grischuk, a Russian, who has six (Each win is worth one point and each draw is worth a half point.) Grischuk now has company in third place as a compatriot, Sergey Karjakin, beat Levon Aronian to also move to six points. There are still three rounds to play, so the tournament is far from decided, but the four players at the top would seem to be the only ones who still realistically have a chance at first. First place is worth 95,000 euros, but, more importantly, the winner will earn the right to play Magnus Carlsen, the world champion, in a title match in London this November. The tournament is being organized by World Chess, the commercial partner of the World Chess Federation (FIDE), the game’s governing body. The total prize fund is 420,000 euros. The competition features eight players. In addition to Caruana, Mamedyarov, Grischuk, Karjakin, and Aronian, there is also Vladimir Kramnik of Russia, Ding Liren of China, and Wesley So of the United States. The format is a double round-robin, with each player facing all the other competitors twice, once with each color. The venue for the tournament is Kühlhaus (or “cool house” in English), an industrial building in central Berlin that was built in the early 20th century as a cold-storage facility for fresh produce. Among the principal sponsors of the tournament are PhosAgro, a giant Russian fertilizer company; Kaspersky Lab, a global cybersecurity firm; E.G. Capital Advisors, an investment management company; S.T. Dupont, a global luxury goods maker; Prytek, a venture capital firm; and Isklar, a Norwegian mineral water company. The ceremonial first move of the round was made by Richard Lutz, chairman of Deutsche Bahn, the giant German railway company. Caruana had White against Kramnik. The opening was a bit unusual as Caruana broke early in the center and Kramnik temporarily sacrificed a pawn that led to a quick exchange of queens. Caruana was able to force Kramnik to exchange a bishop for a knight, so only Caruana had his bishop pair, but he also had doubled pawns on the queenside. Both players probed a bit for weaknesses, but neither was ever in any danger. Gradually pieces were exchanged until there were only kings and pawns and there was no way for either side to manufacture a passed pawn, so the players agreed to a draw. Kramnik has five points, two behind Caruana. Mamedyarov faced So, with the Black pieces. The opening was a Catalan, which has been one of the most popular systems in the tournament. So eventually won a pawn, but it allowed an ending with bishops of opposite colors, which often leads to a draw. That was true in this game, as the players could not make any progress in the endgame. So has 4.5 points and is in second to last place, 2.5 points behind Caruana. Aronian had White against Karjakin. The opening was yet another Catalan. Aronian was able to establish a pawn on e5, giving a slight edge. The pawn eventually moved to d6 after an exchange of pieces, but the pawn was well blocked and it was a potential weakness as well as a potential strength. Karjakin brought up his king to assist and gradually encircled the pawn. Oddly, it was not the first to fall; instead Aronian lost his a pawn in an effort to keep the d pawn alive. Eventually, the d pawn fell as well. From that point, it was only a matter of time before Karjakin was able to consolidate his position. Aronian played on long after the position had become hopeless, perhaps out of frustration at how the tournament has gone for him. The loss was his sixth of the competition and he is in last place, with 3.5 points. The most frustrated player of the day had to be Ding, and the luckiest was clearly Grischuk, who escaped with a draw when he was dead lost earlier in their game.Ding had White and achieved a comfortable edge out of the opening when Grischuk allowed Ding to seize control of the center. Grischuk did not castle because he was afraid of a kingside attack, but his king was caught in the center and Ding enterprisingly sacrificed two pawns to open lines of attack against it. Grischuk was soon in deep trouble. He made several errors, and after 26… Rc8? (instead of 26… Bg5), Ding had an overwhelming attack. After 28… Bd5, Ding only had to play 29 Nd8 and the game would have been all but over. Instead, he played 29 Nf4. Ding still had a large advantage, but over the next several moves, he made several more inaccurate moves, slowly dissipating his edge. By the first time control, Ding had clearly lost the thread of the game and, after a series of exchanges relieved Grischuk’s remaining problems, chances were more or less equal. The game dragged on for 96 moves and more than seven hours before it was finally drawn. Ding has drawn all his games and is alone in fifth, with 5.5 points. Round 12 is Saturday at 3 PM, local Berlin time. The tournament can be watched live at www.worldchess.com, the official site of the World Championship.