One by one, the pieces came off the chess board, until only the two kings and a lone bishop remained. It was a draw, but Magnus Carlsen, the world champion, shook Ding Liren’s hand with a look of resignation. He had played eight rounds in the Sinquefield Cup, in St. Louis, one of the biggest tournaments of the year, and had come away with eight draws. He clearly wanted a decisive result in this one: his preparation was deep, and his opening was daring. Instead of simply developing his pieces, tucking his king safely away and only then building an attack, he had quickly and persistently tried to create imbalances wherever he could. He had neglected his kingside. He had sacrificed a pawn. And it had very nearly worked: for the better part of three hours, Carlsen had been the aggressor. His bishop was aimed at the king; his rooks were working together; his knight was ready to leap into the action. At several points, he was a move or two from launching a mating attack. But at every critical moment, Ding had found a resource and made the right move. In the end, there was nothing. Afterward, Carlsen sat in an interview studio, wearing a navy suit and black shirt emblazoned with various sponsors’ logos. A trim beard aged his boyish face. “I don’t feel like I could have done too much differently,” he said.
Carlsen has not lost a classical chess game in more than a year, a streak that now stands at ninety games. In early July, he matched his highest classical Elo rating, 2882, which he last achieved in 2014. The 2900 threshold, which has never been crossed, remained distant—a win over an élite player would gain him only a few points at a time—but it was coming into view. It was, Carlsen said, a “half-attainable goal.” But in St. Louis, it seemed to recede. In the ninth round, he’d come away with yet another draw. Elo ratings are self-correcting, and, with every draw to a lower-ranked player, a little of Carlsen’s rating was rubbed away.
The so-called Elo rating, which is named after its inventor, Arpad Elo, is a relative measure meant to compare the strength of any two players, allowing one to predict the results of a head-to-head match with a degree of confidence. Other sports, such as professional tennis, employ ranking systems in which points serve as an inducement and a reward—you might get two thousand points for winning a Grand Slam, and two hundred and fifty or five hundred, say, for a smaller tournament. But for chess, Elo, a physicist who was born in Austria-Hungary and who had won the Wisconsin state chess championship eight times, wanted to create a system that would help tournament organizers accurately seed players, and give club players a real sense of how they stacked up against one another. It was never meant to be an absolute measure. As Elo once wrote, “The measurement of the rating of an individual might well be compared with the measurement of the position of a cork bobbing up and down on the surface of agitated water with a yard stick tied to a rope and which is swaying in the wind.” In St. Louis, the rope kept getting tangled in the lines of Carlsen’s opponents.
In April, the chess engines Stockfish and AlphaZero played a thousand games against each other. Stockfish is a traditional engine, which means that it works from preprogrammed rules and determines the best move by brute calculation. AlphaZero, a game-playing algorithm designed by Google’s DeepMind project, is different. It begins with the rules of chess and then plays itself millions of times, shifting its parameters with every outcome—learning, as it were, from experience. AlphaZero crushed Stockfish by a startling margin: a hundred and fifty-five wins to Stockfish’s six. But no one was surprised that the majority of the games were draws—eight hundred and thirty-nine of them, in fact. Had Stockfish been programmed to try to draw, instead of playing moves that were meant to give it the greatest chance to win, the draw rate would have been even higher.
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Draws are the most common outcome at the highest levels of chess, if not quite at that rate. This has always been true, although, in games where both players are rated 2750 or higher—élite grandmasters—Chess.com found that the drawing rate has increased in the past decade, to around seventy-five per cent of games played. (At the Sinquefield Cup this year, more than eighty per cent of the games were drawn.) Carlsen himself doesn’t draw at an unusually high rate; generally speaking, he plays to win. He is on record saying that he finds early draws distasteful (though he raised eyebrows, in 2018, when he took a calculated one at the end of the world championship). Earlier this year, during his undefeated streak, Carlsen set the record for most consecutive draws, with twenty-one. The stretches of drawn games are generally seen as a sign of some issue with Carlsen—a problem with his choice of openings or perhaps a more general malaise. But they also may be a sign that his opponents simply don’t want to engage. In St. Louis, Carlsen acknowledged both. “I haven’t played well at all,” he said, in a post-match interview on the streaming broadcast. “I’ve been in control—there have been basically no counter chances in any of my games.”
Today, élite grandmasters are not only able to build on the historical developments of the game (so-called chess theory) but they also benefit from the aid of chess engines, which are particularly spectacular defenders. If there is a move that can save a draw from a difficult position, a computer will find it. Part of the influence of computers on chess is, naturally, that players play more like computers: the best ones have become incredible calculators. They can defend well and can also nudge a game into calmer waters from the start. And against Carlsen especially, perhaps, they sometimes have a desire to. In chess, white begins with a slight advantage, and black looks first to equalize. But even when playing with the white pieces, opponents sometimes take a wary approach against Carlsen, forgoing a real chance to win in order to improve their odds of drawing. In the sixth round of the Sinquefield Cup, Hikaru Nakamura—who has a reputation as an attacking player—quietly traded his light-squared bishop for one of Carlsen’s knights during the opening instead of making a more aggressive move. Sure enough, before long, the draw was done. In the tournament’s final and eleventh round, Maxime Vachier-Lagrave showed why taking a bolder approach can backfire: after making the same first few moves as Nakamura did, he played to win. But his pawn structure was dubious, and Carlsen capitalized on a blunder and won. With that victory, which followed a defeat of Wesley So, in the tenth round, Carlsen tied Ding for the lead in the tournament and sent it to tiebreaks.
Carlsen’s success this year has often come from taking risks, as he did against Ding in the eighth round: making unexpected moves and sometimes even sacrifices, and then seizing the advantage from the dynamic compensation that comes. (That, in fact, is closer to what AlphaZero does than what a traditional chess engine does; Carlsen, who likes chess engines less than some other top players, half-jokingly acknowledged that he is inspired by AlphaZero’s approach.) In the past, Carlsen had often won by squeezing out victories; now, he often goes for imbalanced positions, seizing the advantage at crucial moments. Or, when something is off, not. That’s where he felt the difference in St. Louis. “The very few chances that I’ve gotten I haven’t really taken,” he said.
Carlsen came into the playoffs against Ding heavily favored. According to the Norwegian journalist Tarjei Svensen, Carlsen hadn’t lost a playoff since 2007. On Thursday, in the final game, with Ding leading and Carlsen in need of a win, Carlsen made a move that he thought would help him, pushing the pawn in front of his king to attack Ding’s knight, which was also defending Ding’s bishop. But Ding made the right move, a stunning retreat of his bishop into the corner. Then he made another brilliant retreating move, this time with his knight. The game was over; Ding had won, spectacularly. Carlsen’s streak of undefeated classical games was intact—Sinquefield’s playoff uses the rapid and blitz format—but he had lost six rating points. Still, this time, when he reached across the board to shake Ding’s hand, he smiled.