Once a Cheat, Always a Cheat?
Chess Drama, Bayesian Inference and Other Thoughts
The chess world has just seen what is considered to be the biggest piece of chess drama in recent chess history. During the third round of the classical stage of the Sinquefield Cup, which features some of the best players in chess, grandmaster Hans Niemann pulled off a shocking underdog victory against grandmaster Magnus Carlsen, the chess world champion, and indisputably the best chess player the world has ever seen.
But what was even more surprising came afterwards: Carlsen failed to show up to the tournament the next day, posting on twitter that he will be withdrawing from the tournament, also attaching a not-so-cryptic video on the tweet of football coach Jose Mourinho.
In the video, Mourinho responds during a press conference, “I prefer not to speak. If I speak I am in big trouble, big trouble, and I don’t want to be in big trouble.” To most chess fans, the message is crystal clear: Carlsen is suspicious that something is wrong, and it is highly likely that he suspects Niemann of cheating in the tournament. However, Carlsen does not want to openly and directly accuse Niemann of cheating because he has no evidence backing the claim, and it would put his name and brand on the line, hence the attached video of Mourinho. Keep in mind, Carlsen has never withdrawn from a tournament before, which lets you know that he is very serious about it and wants it looked into.
So let’s look into it.
Cheating and Bayesian Inference
How can you tell if someone is cheating if you do not have concrete evidence? Well, the one thing that is certain is that you cannot be certain. However, bits and pieces of new information might sway your beliefs either way. This is the process of Bayesian inference, where you update the probability of your beliefs based on any new information which comes your way.
To start off, let me pose you this question: Given two chess grandmasters (without knowing their names) playing a classical chess game against each other, what is the likelihood that the one playing the white pieces is cheating? There isn’t a lot of information to work on, but given how few grandmasters have been caught cheating, your initial thoughts would be that the probability is an extremely low number.
Now, let me give you more information. These two grandmasters are playing in the 2022 Sinquefield Cup, a prestigious tournament with a $350,000 cash fund and tight security protocols. Taking into account this new piece of information, different people would update their credence (initial beliefs) differently. The large cash fund is an additional incentive to cheat, while tight security protocols might deter potential cheats. However, it is difficult to quantify the magnitude of these push/pull factors, unless very specific studies have been conducted on this matter, so the many online detectives like us are free to discuss and weigh these new factors based on their own experiences and values.
That being said, there are two pieces of information that stand out to many, and are worth discussing in depth.
A player’s FIDE rating reflects their skill level in chess. More importantly, looking at the difference of the players’ FIDE ratings, one can quantify the probabilities of the outcome of the chess game.
The FIDE rating system has evolved over the history of chess. The system currently in place is known as the Elo rating system, named after Arpad Emmerich Elo, who was a chess master and a physics professor. He designed a system which assumes that a player’s chess performance falls under a logistic distribution, with the mean being the player’s rating. The Elo rating is set up such that a difference of 200 points would result in a 76% expected score for the stronger player.
However, this does not mean that the stronger player wins 76% of the time, as draws are part of the game of chess as well. Knowing each players’ rating, calculating the expected outcome of the game is elementary, but calculating the exact probability of a player winning is not so. This is because incorporating draws into the calculation makes things more complex, especially since draw prevalence differ at different levels of chess. A blog by Steven E. Pav explains how to calculate this, by using data from over a million grandmaster chess games.
Using the formulas which Pav has provided, one can easily plug in the FIDE ratings of Carlsen and Niemann, and evaluate that the probability of Niemann winning is less than 5% (This has not accounted for the fact that Niemann is playing with the black pieces, which is slightly worse than the white pieces)! It’s not impossible, but it’s certainly an improbability.
A Background of Cheating
The main reason why the notorious tweet of Carlsen’s blew up is that Niemann had admitted to cheating while playing online chess in the past. With that at the back of everyone’s mind, it is natural that grandmasters and laypeople alike will be suspicious of him.
Most would agree that cheating is not a one-off case a lot of the time. As GM Daniel Naroditsky puts it, if you look at all the recent players who have cheated in over-the-board chess, most of them would have cheated in online chess in the past as well. Although there is no such statistic to back up his claim, the proposition seems logical.
Despite the lack of chess cheating data, one can turn to the research on cheating in examinations as a parallel. Studies have shown that cheating is a rather addictive habit, with 64% of students who cheated in high school also cheating in college (Bowers 1964). Other studies with other sample populations also drew a strong relationship between the cheating behaviour in high school and university, as well as further on in life (Harding et. al 2003, 2004, Beck & Ajzen 1991, Fass 1990).
However, without data on chess cheating specifically, it is difficult to quantify the extent to which a person’s cheating past influences the likelihood that they cheat today, such as in the case of Niemann
Here are a few other considerations which chess enthusiasts are suspicious of:
- Niemann’s interviews and post-game analysis. Some popular chess grandmasters have commented that Niemann’s post-game analysis is especially lackluster for a player of his caliber (or one suggested by his rating). He oversimplifies positions which are clearly very complex, and fails to explore chess lines in depth, which is uncharacteristic of many chess grandmasters.
- Niemann’s rating rise. Many chess grandmasters have also commented about Niemann’s unprecedented rise in FIDE rating. Niemann’s FIDE rating has increased by more than 200 in over 2 years, which is unheard of for someone his age.
- Niemann’s opening preparation against Carlsen. After triumphing over Carlsen, Niemann stated that he was lucky as he looked into a rare line played by Carlsen in London a few years ago, but that game does not exist. Instead, Carlsen only played that rare line in one occasion, but not the one described by Niemann. Could he just have mistaken the details, or is he making it up?
Depending on your initial beliefs, and how certain pieces of information shifts your beliefs, you may or may not think that Niemann cheated against Carlsen. Due to the difficulty of quantifying the weight of the available information, there is no right or wrong beliefs, as long as your beliefs are well-justified.
However, regardless of whether Niemann cheated in the event, the majority of the chess community remembers him for having cheated in the past. Learning about the chess drama, one takeaway I have is that people will always remember your acts of dishonesty and judge you for it, especially those from the same profession. Even if the wrongdoing was performed at a young age, or if you work hard to make up for it, that dark past will haunt your career indefinitely, making it ever more difficult for you to recover your footing.
Sometimes, it’s tempting to take the shortcut out of convenience or greed. Even if it was for a petty reason, remember that people will subconsciously judge you for that one incident when you were caught. Is it ever worth risking what you have been working so hard on? At that moment of temptation, it’s better to think twice about it.