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After spherical 3 of the FIDE World Championship 2021 got here to a draw between GM Magnus Carlsen and GM Ian Nepomniachtchi, the Lichess broadcast chat instantly pounced upon the unbelievable accuracy the 2 gamers displayed.

The broadcast chat can often get a bit… excitable (significantly with what it thinks are blunders), however we determined to test it out. For varied causes, a few of our staff know the lifetime common centipawn loss (ACPL) of some prime gamers all through historical past, and of earlier FIDE World Championship matches. So we instantly knew that the accuracy as decided by laptop evaluation did certainly appear to be actually fairly low, even by super-GM requirements: 2 ACPL for Magnus Carlsen, and three ACPL for Ian Nepomniachtchi.

So, our man on the bottom in Dubai felt snug asking “how do both players feel, having played what appears to be one of the most accurate FIDE World Championship games played in history, as assessed by engines?” At the time, the staff had solely manually checked by the 2010s – however after getting the solutions from the gamers, we determined to fact-check ourselves and examine the query extra deeply.

A Brief History of Chess Engines and ACPL

But first, let’s take a step again. Some could also be feeling confused by what laptop evaluation is, or what ACPL actually means. So, let’s focus on laptop evaluation, chess engines, and ACPL briefly.

Almost since computer systems have existed, programmers have tried creating software program which might play chess. The father of contemporary computing, Alan Turing, was the primary recorded to have tried, making a programme referred to as Turochamp in 1948. Too complicated for computer systems of the day to run, it performed its first sport in 1952 (and misplaced in beneath 30 strikes in opposition to an novice).

The Ferranti Mk 1 laptop, the mannequin Turochamp ran on. Note the numerous cabinets full of {hardware} wired as much as it

Since then, the software program has improved considerably, with Deep Blue created by IBM famously defeating GM Garry Kasparov in 1997 — a landmark second in standard tradition the place it appeared machines had lastly overtaken people. Chess software program (now referred to as “chess engines”) continued to enhance, and have become able to assessing and evaluating the most effective traces of chess to be performed.

Stockfish is the title of 1 such chess engine — which simply so occurs to be free, open supply software program (identical to Lichess). Stockfish’s neighborhood had made it one of many strongest chess engines on this planet, capable of trivially beat the strongest chess gamers on this planet working on a cell phone, when it was pitted in opposition to Google DeepThoughts’s AlphaZero in 2017. Stockfish 8 (the quantity referring to the model of the software program) was fully annihilated by AlphaZero, in what stays to be a considerably controversial matchup.

But even when Stockfish actually had been preventing with one arm behind its again, it was nonetheless clearly outclassed. Consequently, the Neural Network methodology of assessing and evaluating positions that was initially utilized in Shogi engines was finally applied in Stockfish, later additionally in collaboration with one other standard and highly effective chess engine impressed by AlphaZero, referred to as Lc0 (or Leela chess Zero). The newest model of this fruitful cooperation is named Stockfish 14 NNUE, which is the chess engine Lichess makes use of for all post-game evaluation when a person requests it, and the chess engine we used to measure the accuracy of all World Championship video games. 

Lichess’s analysis of the Round 3 sport utilizing Stockfish 14 NNUE

To assist consider the accuracy of positions and gameplay, engines current their analysis in centipawns (1/a hundredth of a pawn). For instance, if a transfer misplaced 100 centipawns, that’s the equal of a participant shedding a pawn. It doesn’t essentially imply they really bodily misplaced a pawn — a lack of house or a worse place may very well be the equal of giving up a pawn bodily.

The common centipawn loss (ACPL) measures this centipawn loss throughout a complete sport — so the decrease the ACPL a participant has, the extra completely they performed, within the eyes of the engine assessing it. 

What we did

With that background out of the way in which, on to our course of. We determined to run all World Championship video games by Stockfish 14 NNUE, to attempt to rank their accuracy, and see if our preliminary declare was appropriate.

The first step was deciding what counted as World Championship matches, then accumulating all of them, and compiling them. This wasn’t so simple as it sounds. FIDE has solely existed since 1924, however there are historic matches unofficially handled as World Championships. Likewise, the World Championship crown was briefly break up between two competing organisations, and we needed to take into account how you can deal with that break up.

Following most fashionable commentators, we determined the primary historic match which was worthy of the World Championship title was performed in 1886. We additionally recognised a few of the PCA tournaments, and a Kramnik match, earlier than FIDE reunified in 2007.

Once that was determined, we positioned the PGN (algebraic notation) of the historic video games, and made a Lichess research for every match, with a chapter every for a sport.

After that step, all the video games and all the matches had been analysed by Stockfish 14 NNUE. However, the info nonetheless wanted to be cleaned and ready to make it structured and readable. Some of our builders collaborated on how to do that, with some fine-tuning of code required. A quick abstract of this course of follows, from the developer staff:

“After downloading the analysed PGNs, we essentially replicated the process that Lichess uses to calculate the ACPL for a game — the code is available on GitHub for those interested in delving deeper. But at the end we had a CSV file with every game from WCC history, alongside the ACPLs of the players and the combined ACPL.”

The prime 5 most correct and backside 5 least correct World Championship video games performed after engine evaluation

With the info ready and cleaned, it was time for the info to be visually offered, to make it extra simply interpreted by people. From a easy tabular type, it was clear that the preliminary declare was supported — and slightly than the spherical 3 sport being “one of the most accurate games played in a World Championship” it was truly the most correct ever performed in World Championship historical past.

The charts

Quite a lot of charts had been created, however typically all confirmed the identical traits. We ignored forfeits (Fischer and Kramnik forfeited).

Box and whisker plot representing the accuracy of World Championship matches performed that 12 months

Over time, it may be seen that chess has trended from being performed fairly inaccurately even on the very highest ranges, to being performed with virtually a laser precision. 

For instance, on the Victorian finish of the size, there are some outlier video games which have over 200 ACPL mixed – many fashionable bullet video games between membership stage gamers are performed extra precisely!

The World Champions Lasker and Capablanca then rapidly improved the standard, to be comparable with the trendy pre-computer period.

The bars signify interquartile vary and median for ACPL of video games performed that 12 months

Following Botvinnik, Smyslov and Tal, the vary of the ACPL typically tightened, with much less important fluctuations, and with much less dramatic outliers.

In the pc period, from round 2007, the ACPL of gamers dropped additional and tightened much more considerably — exhibiting the significance chess engines have performed inside prime stage chess. Anand might be seen specifically as embracing the function of computer systems and considerably enhancing his accuracy over time, largely in parallel as chess engines developed energy. 

And, regardless of solely being 3 video games in on the time of the evaluation, the present World Championship seems to be on observe as probably the most correct but.

Showing the road of greatest match over time

Perhaps surprisingly, on their greatest days even the champions from the 1910s and Nineteen Twenties performed with a comparable accuracy to those that got here later. It’s additionally extremely outstanding simply how correct a few of the video games performed previous to the pc period had been, with names like Fischer, Kasparov and Karpov all showing within the prime 5 most correct video games (aside from Carlsen, solely Karpov seems twice). But unsurprisingly, the largest jumps have undoubtedly come from these chess gamers who handled the sport as a science, slightly than as an artwork, and the enduring enchancment and affect chess engines have had on the chess elite. 

But, as Magnus Carlsen’s pithy response highlights (“I’m very proud, but it’s still only half a point”), while these items is fascinating general, it virtually means little or no within the context of competitors if the gamers aren’t capable of convert the accuracy to factors. Ian Nepomniachtchi was equally nonchalant when requested how he felt to be a part of probably the most correct sport in World Championship historical past: “that’s a very murky question to ask before the anti-doping tests”.


The greatest chess gamers humanity has to supply are doubtlessly pondering extra like machines than ever earlier than — or a minimum of enjoying in a mode which has the approval of the strongest chess engines; doubtless the exact same chess engines they use to arrange and prepare in opposition to. 

Thanks to reddit person ChezMere for the thought

At the time of publishing, the final decisive sport within the World Championship was sport 10 of the World Championships 2016 — 1835 days in the past, or 5 years and 9 days. Is the singularity being reached, with man and machine minds melding in direction of inevitable monochromatic matches?

Some bias of chess engines should be touched upon, regardless. There is a lightweight on the finish of the tunnel. Humans aren’t machines, no matter how a lot a participant could imitate or study from them. Generally, all the most correct video games performed had been comparatively brief. They normally featured openings with a number of strikes permitting correct play, or very deeply theorised traces. Pieces — which permit for issues and human-like errors to creep in — had been usually equally exchanged in a short time. The endgames that they moved into had been normally all theoretical or compelled attracts, with all strikes being equally correct. So, reintroducing these longer video games, or these issues into the combo — and we’re nonetheless removed from the singularity. All of probably the most correct video games would have been purely after the pc period, in any other case. 

So, while many followers of chess could really feel stunned by the variety of attracts occurring within the World Championship, it’s too quickly to say if that’s as a result of growing accuracy inside chess. After all, even previous to engines the 1984/5 World Championship match between Anatoly Karpov and Garry Kasparov featured 17 successive attracts (sport 10 to sport 27) after which one other 14 successive attracts (sport 33 to sport 47). Sometimes, the most effective on this planet simply can’t get previous one another.


Various issues ought to be thought of when reviewing the info.

First of all, if you need to attempt to reproduce it, you’re welcome to, and please tell us what outcomes you get. It’s doubtless you’ll get barely completely different outcomes from us, primarily based on the parameters you utilize (for instance, the depth of the search), and even the machine you run the engine on. Each machine will usually give some small fluctuations, even with the identical parameters, so while your prime 5 video games ought to nonetheless be the identical, that may’t be assured.

Secondly, gamers usually prepare with computer systems rather more highly effective and at a a lot deeper depth than the evaluation we used to make the leaderboard. So, the ACPL we obtained could be an artefact of that distinction of depth. What’s thought of unhealthy by Stockfish 14 NNUE at depth 20, may very well be thought of good at depth 45.

Thirdly, as touched on within the article, if the gamers are getting ready and coaching with Stockfish 14 NNUE, it’ll want the strikes and proposals it will make itself. Consequently, each gamers may simply be enjoying most precisely within the eyes of Stockfish 14 NNUE, just because they’re utilizing and following the traces of Stockfish 14 NNUE. If we’d used a unique chess engine, even a weaker model of the identical one  — similar to Stockfish 12  — it might have discovered the 2018 World Championship probably the most correct in historical past (assuming each gamers ready and educated utilizing Stockfish 12 in 2018).

Fourthly, that is all considered within the eyes of an engine. It shouldn’t low cost the sensible chess being performed. It doesn’t low cost the human evaluation made by commentators, the engine shouldn’t be a divine being. These are just a few fascinating findings and a little bit of an exploration of them. Nothing extra ought to be learn into it than that!

Special thanks

All this was made potential by the Lichess neighborhood, however primarily by:


The full code, information and charts might be discovered on this GitHub repo.



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