Tackling the Chess Draw Problem


percentage of draws in classical games between 2700+ chess players
Table of Contents

This year’s Airthings Masters tournament featured some interesting twists to encourage more wins and fewer draws. First, wins were worth three times as much as a draw, as opposed to only two times in the traditional system. Second, there were additional prizes based on the Fighting Chess Index, a metric designed to measure the players’ competitive spirit.

Judging by the early returns, the changes are having the desired effect. The preliminary stage featured 84 wins and only 36 draws, which comes out to a whopping 70% of decisive games. Compare that to the Aimchess US Rapid at the end of 2021, a similar round robin format but with the traditional scoring system, where there were 65 wins and 55 draws, for 54% decisive games. Caveats about small sample sizes aside, it certainly seemed like the players were going all out to win.

Draws – and ways to combat them – have a long history in chess. When Magnus Carlsen and Ian Nepomniachtchi drew their first five games in the 2021 world championship match, combined with Carlsen’s previous match with Fabiano Caruana, it added up to 17 consecutive draws in classical world championship games. It was starting to look nearly impossible to win a game against a booked up world champion contender with plenty of time to think.

Then game six changed everything. In the course of eight grueling hours, Carlsen gained the upper hand, wavered, got the better of a mutual time scramble, and finally ground out a win in the endgame. Nepomniachtchi never seemed to recover. In the subsequent games he made uncharacteristic blunders and Carlsen romped to a resounding victory.

The dust had hardly settled on Carlsen’s victory when he dropped another bombshell: he might not defend his title.

“It’s been clear to me for most of the year that this world championship should be the last,” he said. “It doesn’t mean as much any more as it once did. I haven’t felt that the positive outweighs the negative.”

Carlsen made it clear that he’s not quitting chess, just the world championship as it currently stands.

“I will continue to play chess, it gives me a lot of joy. But the world championship has not been so pleasurable.”

Why hasn’t it been pleasurable? Part of the reason must be that it’s too slow. Carlsen has made it known that he has a preference for faster time controls. Days after winning the world championship Magnus was having a beer with his friends while playing in the Lichess Titled Arena, where each player has only one minute for the whole game and the action is fast and furious. Evidently Magnus isn’t sick of chess, just the grind of the world championship.

Another world champion, Vladimir Kramnik, has been thinking a lot about how to breathe new life into classical chess. According to Vladimir Kramnik, the problem is not draws per se, but the lack of “content” in games at the very top level. As opening preparation takes up more of the game there is less room for the players’ creativity. “As a professional sometimes I watch games and I know not only that it’s going to be a draw, but more or less the whole procedure,” he said.

Kramnik has a better perspective on where chess is headed than just about anyone. As a top grandmaster for many years (he retired from competitive play in 2019) he saw the game evolve to require more intricate computer-assisted preparation. Indeed, to a large extent he drove that evolution: some consider him the greatest opening theoretician of all time. More recently, he worked with Google’s DeepMind on research into new chess variants that would shake up the game.

The Berlin

In 2000 Kramnik was preparing to face Garry Kasparov in the world championship match. Since seizing the title from Anatoly Karpov in 1985, Kasparov had defended it five times, three against Karpov and then against Nigel Short and Anand. All the matches were hard fought, especially the legendary battles with archrival Karpov, but Kasparov always came out on top. In short, Kramnik had his work cut out for him.

Especially daunting was Kasparov’s opening preparation. Many players succumbed to terror before even sitting down at the board opposite Kasparov, fearing one of his opening novelties – new moves that had never been played before. Known as a fanatical hard worker, Kasparov refined the subtleties of his opening repertoire with the computer and a cadre of grandmasters in support roles. The computer was far from the monster it would eventually become, but already valuable in certain kinds of positions, and Kasparov was a pioneer in using it in his preparation.

Like most strong players, Kasparov mixed up his openings to keep his opponents guessing, but his main weapon with the white pieces had always been 1.e4, the king’s pawn forward two squares. The most direct and forceful way to start the game, it was a good fit for Kasparov’s uncompromising style. If you want to understand how to play 1. e4, Kramnik has recently released a Chessable course going deep into the key ideas.

Kramnik needed a defense against 1.e4 that could withstand the best efforts of a team of grandmasters, the computer, and of course Kasparov himself over a 16-game match. In his previous career he had often employed the Petrov and the Sicilian, but he had it in mind to throw a curveball in the match against Kasparov. (Surprises are common in world championship matches, where neither side wants to be sized up based on their past games.) In particular, he wanted to revive a variation of the Ruy Lopez known as the Berlin Defence.

1. e4 e5 2. Nf3 Nc6 3. Bb5

draw in the berlin defense variation

In the starting position of the Ruy Lopez, the traditional main line was to first attack the bishop with pawn to a6, and only after it retreats deploy the knight with Nf6. In the Berlin Defence, Black forgoes the pawn push and plays Nf6 immediately. This seemingly minute difference has profound implications for how the play develops. Black can buy time by attacking White’s bishop with a knight retreat, which would not have been possible if the bishop had already been chased back. If both sides play the most forceful and logical moves, the result is a trade of queens leading to a peculiar endgame.

3…Nf6 4. O-O Nxe4 5. d4 Nd6 6. Bxc6 dxc6 7. dxe5 Nf5 8. Qxd8+ Kxd8

This endgame is highly imbalanced, meaning the position is asymmetrical – the two sides have radically different strengths and weaknesses. Black’s position has two major problems: on account of moving the king he has lost the right to castle; and the pawns on the c-file are doubled, rendering them less mobile. On the other hand, Black has the pair of bishops (typically superior to bishop plus knight) and no weaknesses in his camp.

Traditional wisdom held that these imbalances came out in White’s favor. Kramnik’s intuition told him otherwise, but he had to contend with the computer, which insisted that White was clearly better. He trusted his intuition, but also knew it wasn’t enough: he had to try to falsify it with analysis. If he could find a way through, Kasparov would surely find it too, and the opening would have to be scrapped. But he wasn’t finding it; the opening seemed to be sound. If there was a flaw, it would have to be exceedingly intricate. As he told Ben Johnson on the Perpetual Chess podcast, “I understood that things are not so rosy, there is no obvious way for White to get an advantage. It’s a very complicated, strange position and so for me, there was no doubt that I’m going to play it.” Kramnik had his defence to 1.e4.

In the first game of the match, Kramnik had Black. Kasparov played e4 as expected and Kramnik sprung the surprise. Kasparov went for the endgame, but with deft defensive maneuvers Kramnik frustrated all Garry’s attempts to advance. In only 25 moves, Kasparov had to agree to a draw. For at least one game, the Berlin had held.

In the next game Kramnik won with White and suddenly Kasparov was in massive trouble. He stuck with 1.e4 and Kramnik replied with the Berlin again. This time the game went longer and at some point Kasparov seemed to be pressing for the win, but in the end it was another draw. In his next two white games, Kasparov switched to 1.c4, the English opening. For the time being he had hit a wall against the Berlin, but there was no doubt that outside of the games he and his seconds were furiously looking for new ideas. In his next three white games, Kasparov returned to 1.e4, but it only resulted in three more draws. Meanwhile, Kramnik added another win with White to go up two points in the match.

In game 15, needing a win to keep the match going, Kasparov started with 1.d4. In some sense it was already an admission of defeat: Kramnik had succeeded in forcing him away from his favorite 1.e4. It made no difference: that game ended in a draw as well, giving Kramnik the match. The Berlin held firm and defined the trajectory of the match.

A world championship match tends to set the fashions in the chess world. Taking Kramnik’s lead, many players added the Berlin to their repertoire. As more grandmaster practice piled up, it became clear that there was no refutation. It was simply a good opening. More advanced engines began to come around as well, appreciating the hidden resources in Black’s position.

For Kramnik, the legacy was bittersweet. He had pitted his intuition against the accumulated wisdom of masters and the iron calculations of the engine and been proven right. The Berlin, the speculative opening choice that he pinned his World Championship hopes on, was nothing more or less than absolutely correct. As such, it led to the correct result of a chess game perfectly played: a draw. “For me it’s a bit sad,” he said. “Everyone is hitting the wall. Against the Berlin, no one has anything.”

Is Chess a Draw?

Chess is not a solved game, although people sometimes claim that it is. What they mean is that the best computers can beat the best humans. But a solved game has a specific meaning in game theory: it means that the outcome of the game can be predicted from any position, assuming both players play correctly.

This is not the case for chess. You can see it in the positional evaluations used by the engines, which are typically expressed as centipawns. One hundred centipawns equal one pawn. Thus, an evaluation of +50 can be interpreted as, “White is ahead by half a pawn.” From the perspective of a solved game, this evaluation makes no sense. There are only three “real” evaluations: White is winning, Black is winning, or the game is drawn. The centipawn evaluation is a sort of hedge: the engine prefers White’s position, but it doesn’t know if the correct result with best play is a win or a draw.

The sheer number of possibilities in chess messes with your intuition. A modern computer can calculate up to 200 million moves per second, sometimes more. That’s far more moves than you can imagine, but nowhere near the total number of possibilities. No one knows exactly how many moves are possible in a chess game, but a typical game lasts around 80 moves (40 for each player) and there are about 35 legal moves in a typical position. This leads to an estimate of 35⁸⁰, or 10¹²³. In contrast, the number of atoms in the observable universe is estimated to be 10⁸⁰.

Computers are a long way from solving chess, but they don’t need to solve it to run circles around us. After the world championship match Magnus Carlsen has a rating of 2865. The latest version of Stockfish, the current top chess engine, has an estimated rating of 3548. Humans these days rarely play head-to-head with computers because it’s too depressing, but if Carlsen were to play Stockfish, the rating difference would correspond to an expected win rate higher than 99% for the computer.

In other words, we’re in no position to second-guess the computers. And the better they get, the more they seem to draw. (When playing each other of course, against humans they win ever more easily.) In a recent paper by DeepMind they had AlphaZero, their chess AI, play itself many times. Out of 10,000 games with 1 second per move, 8820 (88%) were drawn. In 1,000 games with 1 minute per move, 979 (98%) were drawn. In other words, when you give the computer more time to think, it produces more draws.

If chess is not a draw with perfect play, that would mean one side or the other has a forced win. If that were the case, you’d expect to see the opposite pattern in computer games: the stronger they got and the more time you gave them, the more they’d win, as they honed in on an unstoppable sequence. But if such a sequence exists, no hint of it has yet appeared. Chess will not be solved any time soon, but the evidence that it’s a draw seems overwhelming.

You might feel all the computer analysis is overkill. Even before the advent of super-strong computers most experts believed chess to be a draw with perfect play in theory, but what about in practice? If you extend the history of draws in World Championship matches, the draw rate does seem to be increasing, but not always in a straightforward way.

draws in world chess championship matches

In terms of sheer length the 1984 match between Kasparov and Karpov stands out. This match was played in a first to six wins format, which meant in theory there was no limit to how long the match could go – the players could make draws indefinitely. At first, that didn’t seem like it would be an issue. Karpov jumped out to a 4-0 lead after nine games and a 6-0 shutout seemed imminent. But Kasparov found his footing and held his own in the next 17 games, all draws. As in the Carlsen-Nepomniachtchi match, the decisive games seemed to come in clusters. Long strings of draws could suddenly explode in decisive games if one player lost his poise. In the case of the Kasparov-Karpov match, after five months it was controversially called off without having decided a winner.

The other match that sticks out is the 2018 Carlsen-Caruana encounter, the only world championship match without a single win in the classical portion. Following that match concern about the draw problem was at a high point. Analysis by Matt Jensen showed that draws at the top level had been increasing more or less steadily between 2008 and 2018. However, in 2020 something odd happened: the draw rate went back down.

It’s been a weird couple years for the world at large and the chess world specifically. Many tournaments were canceled because of the Covid-19 pandemic. Of the tournaments that were played, some took place online, which had previously been a rarity for top-level chess. Additionally, neural network engines like Leela Chess Zero played a larger role in preparation and were considered to have a more aggressive style than traditional engines. To what extent the dip in draw rate was caused by the pandemic, the influence of new engines, or other factors is hard to say, but it complicates the story about draws. And then Carlsen reminded everyone that he is still capable of winning games in a world championship match, sometimes in buckets. If draws overall are increasing, it’s not in an obvious or overwhelming way.

It’s also worth pointing out that, to the extent that draws are a problem, it’s only for the top handful of players in the world, those capable of playing a nearly perfect game. For the rest of us stringing a few moves together without a blunder remains quite a challenge. Draw rates below the grandmaster level are generally quite low.

Then there’s Kramnik’s point that the problem is not really the number of draws but the lack of content in the games – quality, not quantity. This is harder to measure, but fans took note, for instance, when Hikaru Nakamura and Wesley So played the exact same sequence in the Berlin move-for-move to a draw in ten games in 2020 and 2021.

Perhaps the perception of draws is more important than the actual frequency. The big challenge facing organizers right now is how to present chess as a vibrant spectator sport, especially to the big crop of new fans who picked up chess during the pandemic. Not every game can end in a knockout, but every game needs to at least have the potential for excitement.

The Experiment

In 2018 Kramnik competed in the Candidates Tournament to determine the next challenger to the World Champion. After defeating Kasparov in 2000, he had lost the title in a tournament in 2007 and in 2008 failed to win a match against Anand, who in turn was dethroned by Carlsen in 2013. The 2018 Candidates was his chance to get back on top.

Kramnik came in guns blazing. He played ambitious, enterprising chess, going all out to win in every game. He had moments of astounding brilliance, but they were counterbalanced by lapses at critical moments. In the end, he had seven decisive games in 14 rounds, tied for most in the tournament, but those decisive games included four losses to three wins. The American Fabiano Caruana won the tournament with five wins and only one loss. In January of 2019, Kramnik announced his retirement from competitive chess.

Freed from the constant grind of keeping up with opening preparation, he had time for other pursuits. In 2020 he co-authored a paper with researchers from Google’s DeepMind project, Assessing Game Balance with AlphaZero: Exploring Alternative Rule Sets in Chess. Their idea was that by making subtle changes to the rules of chess they could reinvigorate the game, wiping out large chunks of opening theory and freeing the players to compete using their own wits. They leveraged AlphaZero’s ability to quickly teach itself any game to evaluate the viability of each variant: How rich were the possibilities? How often did the game end in a draw?

In the variants tested, most games still ended in draws. It turns out that if a game is balanced, AlphaZero will most likely find a way to draw it. But that doesn’t mean the experiment was a failure. What the variants would do would be to effectively wipe out known opening theory, allowing players to start from a blank slate. The result of a perfectly played game would still be a draw, but there would be vast new reaches of uncharted territory to explore.

Of the nine variants tested, two stood out as most promising: no-castling chess and self-capture chess. As Kramnik points out, if you think about it, it’s kind of weird that you’re allowed to castle in the first place. “It’s actually a strange rule. It goes against the logic of chess. With one move, you can move two pieces at the same time. There’s no other rule that does it. And I started to think, but why?”

Kramnik has some theories as to why castling was introduced to chess. One is that players in the middle ages – not as booked up as masters today – got sick of getting checkmated in the opening. Castling gave them a way to secure the king and led to a longer, more satisfying game. Another theory is that it may have prepared soldiers to accept that in a battle the king would not necessarily stick out his own neck, as in Game of Thrones when King Joffrey is called away by his mother on “urgent business.”

At any rate, removing castling would, if anything, make the rules of chess more elegant. It also leads to some interesting strategic tension. Castling is such a good move that it’s often a no-brainer, but when securing the king requires walking him gingerly one square at a time out of the danger zone, how and when to do so becomes a difficult decision.

The other most promising variant was self-capture chess. In this variant, you’re allowed to capture your own pieces, which of course isn’t allowed in the current rules. Most of the time you want to keep as many pieces as possible, but occasionally offing one of your own pieces can open a crucial line. In AlphaZero’s games against itself, self-captures occurred rarely (about one in three games), but that could make them even more exciting. Chess fans already love sacrifices, when one side deliberately allows the other to take one of their pieces in exchange for an attack or initiative. Taking your own piece is an even more emphatic statement, a sort of super-sacrifice.

Would the chess world accept these variants? Chess players in general tend to be a conservative lot, but there have already been tournaments featuring the top players competing in Fischer Random, another variant where the pieces are randomly shuffled on the back rank before the game starts. With a World Champion hungry for change and a new crop of chess fans eager for excitement, some kind of shakeup seems inevitable. As Kramnik says, “We can’t just keep playing like it’s the 18th century.”

Was this helpful? Share it with a friend :)

4.9 with 3.65K user reviews

Check them on individual course pages