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Why do GMs repeat moves instead of offering a draw?
Watching recaps of the 2021 Candidates Tournaments, so many games end in consecutive repeating moves. I have a general impression that lots of top level games are drawn by repeating moves. Why do the grandmasters do this instead of offering a draw?

A repetition giving the opponent the opportunity to claim a draw is a de facto draw offer but not a de jure draw offer.
What does that mean? Well the "de facto" part means that in practice it has the same effect as a formal draw offer while the "de jure" part means that legally it is not a formal draw offer.
Psychologically it makes a subtle difference but practically it makes an important difference. The difference is the legal aspect. Why is this important?
According to article 11.5 of the FIDE Laws of Chess:

11.5 It is forbidden to distract or annoy the opponent in any manner whatsoever. This includes unreasonable claims, unreasonable offers of a draw or the introduction of a source of noise into the playing area.

Normally arbiters interpret this to mean repeated draw offers in a small number of moves. That is why you are instructed to notate your game as follows in Appendix C.12 -

C.12 The offer of a draw shall be marked as (=).

Repeating the position does not constitute a formal draw offer and so cannot be part of a claim of disturbance due to repeated draw offers.

What do you think the psychological difference is?

When you ask for a draw you are a supplicant. It's like you are asking for a favour. "Will you please give me a draw?"
When you repeat the position you are saying something completely different which is why in some positions the experts advise you to repeat once (so no possible draw offer) to demonstrate dominance, let the other player know who is the boss.
If you are a much lower rated player and you repeat twice in a forcing situation you are effectively saying "What ya gone do, punk? Repeat and give me the draw? Or deviate, play a bad move and give me a chance to win?"
I have won several games with that exact tactic. It's surprising when it works but some players have more ego than common sense. It's like their response is something like "No way am I accepting a draw against you. I'm so much better than you that I can beat you from a losing position". I have to admit I've been on the opposite side too. I've played a bad move rather than accept the draw and I've paid the price.

It's worth emphasizing the point that sometimes, the only good move is to repeat and either side will be at a disadvantage if they don't. So by repeating moves instead of offering a draw, you give the opponent an opportunity to make a bad move.

I seem to recall a famous Reti-Alekhine game where Alekhine won brilliantly after Reti refused to draw by repetition. This came after Alekhine had tried to claim the draw before the third repetition.

@bof Was this the game you refer to?  The comments mention something similar, and moves 16-19 look like they fit the bill

@CortAmmon Yes, that's the one, thanks!

"in some positions the experts advise you to repeat once (so no possible draw offer) to demonstrate dominance" Huh, interesting.

@CortAmmon That first move reminds me of an article about a certain chess coach who, after watching one of his pupils place such a first move, said "This game is no longer interesting to me" and stopped watching (!)

In many top level tournaments you are not allowed to offer a draw before a certain number of moves are played (often 30 or 40). The purpose of such a rule is to prevent very quick draws.
However, one of the ways to make a draw anyway is to simply repeat moves.
Even if that rule is either not active or the move number has passed, it may still be encouraged to do, if nothing else to have the game end naturally for the spectators, rather than by agreement.

Very informative, I had no idea there was such a restriction on offering draws

+1 And even if the 3 identical positions draw rule was only in place starting on move 30, players could just continue to repeat the moves a few dozen times until they got up to the mimimum draw length and then from there if they wanted to draw from an early game position.

Often, Grandmasters need to reach the 40-move mark. This standard time controls gives them 30 extra minutes if this milestone is reached. Often times, they will play very similar moves just to get pushed past this time, and may end up drawing here as well
In the endgame, grandmasters seldom offer draws. So may games end in draws, but they will always try to play them out. Offering a draw is not as concrete as playing a draw, where there is still a chance to continue it out.

"Offering a draw is not as concrete as playing a draw" wdym

I see loads of games end in consecutive repetition, does what you explain in your first paragraph actually ever occur? I have never seen it

Often yeah. Grandmasters take a lot of time t think, and they use up almost all their time in 30min to an hour. This quick playstyle either draws or brings up some extra moves for their time. For the question, it means that when you offer a draw it's different then physically playing it out.

While the existing answers are great, and relevant to especially OTB tournaments, it's worth noting in online matches there are often extremely short time controls with players moving (or even pre-moving) so quickly, it's only possible to obtain a draw by repetition. The act of offering a draw and waiting for the opponent to accept or decline would simply take far too long.
A recent example of a draw offer ending badly would be the GM Eric Hansen vs GM Hikaru Nakamura match, described here on Reddit. Also see the video for yourself if you wish to make your own mind up what happened.
Quote from the Reddit post linked above

Eric and Hikaru are playing a blitz match, Hikaru is winning 2-1.
They reach an endgame that is better for Eric, although theoretically a draw. Hikaru has around 10 seconds, Eric 5.
Hikaru doesn't offer a draw, instead tries to flag Eric. Eric doesn't go down easy though, and almost neutralizes Hikaru's time advantage. Eric offers a draw, which Hikaru doesn't respond to and keeps playing. Eventually Hikaru loses his time advantage completely, and they both have 4 seconds each.
Hikaru offers a draw which Eric didn't notice since he assumed Hikaru was trying to flag him. Hikaru simply lets his clock run down to 0 and accuses Eric of intentionally trying to flag Hikaru to gain rating.
Hikaru leaves and starts playing Alireza instead, calling Eric a liar and saying that he has bad etiquette, which is SUPER ironic since Hikaru is the one who flags his opponents in the most dead drawn positions.


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Is chess a good game for recovering addicts?
In this interview to FIDE Master and psychologist Maria Rodrigo the interviewer asked her about chess and addictions:

XL. There are those who are not able to prioritize and get hooked.
M.R. Yes, because the dopamine rush during a game can be brutal. And that is something you have to learn to control. If you don't, you start a game, and then another, and another… And there is no one to stop. You lose hours of sleep… The problem of addiction is more typical in men than in women. Men are more hooked on video games and women on social networks.

I am a recovering addict. I passed through this clinic in Barcelona to recover from my addiction to alcohol and cannabis. They had a group where they used chess as therapy, so as a lover of the game I said to myself that chess couldn't be harmful for my therapy. But they banned me from chess, arguing I played obsessively. They said I could play once my two years treatment is finished. It was true that I played lots of online blitz, but I felt disgusted: why was I banned when they used chess as therapy for others?
Nowadays, I am in the ninth month of recovery. I left the clinic and I went to a psychologist. I don't play online blitz, but I play correspondence and I joined my club to play standard over the board games. My psychologist approve it but he is not specialist in addictions. At the clinic they wouldn't approve I am playing before two years of recovery.
I can read articles like this one on Chessbase where it is said they started a cognitive training through chess at a therapeutic community "recovering the cognitive functions (attention, memory, etc.) deteriorated by drug use, with the help of chess". But maybe this is focused on teaching how to play chess to people that didn't play lots of online chess while consuming drugs. And dopamine plays a role in addictions. At the clinic they said we were addicts to dopamine highs, so reading FIDE Master Rodrigo I would say it could still be harmful to my therapy and bring me closer to a relapse.
It is clear chess is good to treat other mental diseases like schizophrenia, and it looks good to teach recovering addicts how to play chess to recover the cognitive functions damaged by drug abuse (according to Chessbase article and my clinic), but is chess good for a recovering addict that played chess before his treatment started? Can it bring the patient closer to a relapse in drug use?

I am not qualified to answer the question, but you may want to read The Grass Arena by John Healy.

I believe there is a slight difference in playing online and blitz games that can lead to more hard dopamine rush than playing over the board clasical games

After one year an a half, I got the most important thing: I am out of alcohol and alcohol was destroying my life. I only play over the board games with my club. I am not convinced about what I heard in the clinic. It costed 60.000$. They followed a method taken from USA. They also forbide me to programm. After all I decided to enter in the clinic because of alcohol troubles and I have stoped drinking. I payed but I got the objective. I go with my friends to pubs and I take 0,0% beers wich would also be forbidden if I'd continue with the american method. I am not convinced about the answer marc

@Universal_learner I dont believe that this question should be on the chess stack exchange. The chess stack exchange are for chess hobbyists but I would recommend you asking this question in the psychology stackexchange over there you will get answers from many people who study the brain and psychology for a living. This question is well worded. I will recommend not changing but just copy and paste the question there.

@Varun W. Done https://psychology.stackexchange.com/questions/28165/is-chess-a-good-game-for-recovering-addicts

I'm not the right person to answer or a psychological therapist, but I did get over some common 'bad baby habits' because I was 3 years old then and was starting to learn how to move pieces, but I think it would be easier to recover from addictions if you're new to chess and interested in the game/activity and addicted to chess. I was addicted to chess at a point to a point that it became more like a distraction. Any interesting activity would divert you from the others. So the answer can be yes or no depending on many things. As others have suggested, check out psychology SE. Good luck, TC.

Addiction is a complicated and multi-faceted issue, and although dopamine plays a role it's far from the only important factor to consider; this also depends on which type of addiction we're dealing with.
If we're talking about some sort of substance abuse (say, smoking, alcohol, hard drugs, etc.) then it's very common that a person becomes addicted to a substance that artificially affects the chemical balance in the brain/body. In this kind of scenario it is very hard to see how chess can make the original addiction worse, as any dopamine rush derived from chess is not caused by taking a substance to artificially affect the biochemistry of the brain. When considering how chess could have a positive effect on addiction in this regard it mostly comes down to it being a potentially effective form of distraction; one major problem with addiction is that a person can easily become a bit obsessed with whatever they're addicted to (especially when bored!), and in this case chess can serve as a good distraction making it easier to break the addiction/toxic habit.
Although chess can work as a therapy form for addiction it's not guaranteed to work. But it's a rather non-invasive kind of intervention in general, which is why I suspect you've seen it being used. Generally speaking, therapists tend to try the least invasive forms of therapy first and only go for more invasive methods if the addiction proves too strong (a common theme in, say, heroin addiction, where addicts often recieve "replacement drugs" so that they can weane themselves off of the heavier stuff).
So far I've only brought up substance abuse, but there are other forms of addiction that are worth addressing as well. Broadly speaking, practically anything can become an addiction, including chess itself. In this case, chess therapy would most likely not be a great idea, and I suspect if one has a problem with, for instance, online gambling, online blitz/bullet could prove to become a problem as well. In this case it's worth noting, however, that online blitz/bullet is not as financially draining as online gambling, although it can still have massive negative effects on the one suffering from the addiction. In essence, if your addiction is a form of "thrill chasing", then chess could end up being another addiction on the same theme if you're not careful.
At the end of the day, I'd say that chess as a therapy form depends on the addiction in question. So when you consider chess as a form of treatment for your addiction you must first have a clear idea of how your addiction works. What kind of addiction, what kind of triggers, how severe is it, etc.?
Whatever you take from this answer, I hope that your recovery process keeps on being successful. The answer I've given here is a rather non-specific one, and whether chess is the right thing for you is a question that only you can answer in the end.

Addiction works through the reward pathway of our brains. In many ways, the actual thing you are addicted to is almost irrelevant. It has been demonstrated (sorry no link, personal communication with colleagues working on addiction) that the biochemical manifestation of addiction to gambling is the same as that of addiction to heroin or any other substance. So it does actually make sense that the OP could be harming their recovery if they just transfer from one addiction to another even if the new one has no externally consumed substance.

@terdon If I read your comment correctly, I assume that you mean that addiction itself (no matter the cause) leads to a certain type of damage to the reward pathways, correct? I have no reason to doubt this, but does this imply that if I'm addicted to, say, alcohol, then I will automatically be more susceptible to every other form of addiction? Or am I just more likely to become addicted to substances similar to alcohol? I didn't see anything about this in the wiki article.

Not damage to the pathway, no. It is more that those pathways play an essential role in addiction (this is why the ritual surrounding the addiction is often part of the addiction itself, the same effect as Pavlov's famous dog). This is not my field, I am a geneticist, but my understanding is that since there is an important aspect of addiction that is the same no matter what one is addicted to, that means that you need to break the cycle of addictive behavior and you cannot do that by switching to a different addiction.

Stack Exchange has a site dedicated to medical sciences.
If you open that, you'll immediately see that on the right column there's a disclaimer that you won't find on any other Stack Exchange site. It's a bit long, so let me cut the most important parts:

Stack Exchange Inc., and its sites including Medical Sciences Stack Exchange, is not a medical practice or healthcare provider and does not provide medical advice.
[...]
Consult your own doctor for medical advice.
[...]
Medical Sciences Stack Exchange is for information exchange only, and is not a substitute for medical advice, individualized diagnosis or treatment by a healthcare provider.

This obviously covers the legal aspect, but it's more than that. Even if there were no lawyers and lawsuits in this world, that disclaimer would still have value. Because, well, it's true. In general you cannot trust users on any of these sites to really know what they are saying. Your health is too important to blindly trust some random stranger on the web, no matter how high their reputation is or how sincerely they are trying to help.
Besides, it seems to me that you've already got the answer from your clinic:

But they banned me from chess, arguing I played obsessively.

I'm sorry, but I'm afraid you'll have to accept it.
I hope I won't sound judgmental if I tell you that what you are really doing here is not looking for an answer (you've already got one; only, it's one you don't like), but rather for an excuse that will let you keep playing and ease your conscience.
Imagine someone posted an answer along the lines of

Don't worry, those doctors don't understand anything! Playing chess can't be a problem, just go ahead and play as much as you want!

I suppose you'd be very happy to read it. And yet, who would you rather trust: the doctors that visited you and know your case specifically, or someone who probably has no idea what they are talking about, and who certainly doesn't know you, your clinical history, anything about you at all?
So do the right thing, and do what your doctors say. Or in any case discuss with them what you should do.
My best wishes for your full recovery!

I agree but I feel like this question is better off asked in the psychology stackexchange.

I would actually completely flip-flop it and say: don't trust doctors but do trust what people say on stackexchange sites. I am not trying to be funny: in my experience individual doctors are often wrong, however, the numbers (as in votes and reputation scores) absolutely tell the story.

@postoronnim I agree 100% but I mean for the sake of this question I told  psychology stackexchange because they have more experienced people.

First, others have indicated this, but Stack Exchange really isn't a substitute for competent medical advice from someone who knows all of the details of your specific case.
One general comment I will make, though: there is no "one-size-fits-all" in recovery from addictions, or even to your own recovery. That being said, the answer to your question is "some people will benefit and some people won't." You may find that things will even affect you differently in different phases of your recovery - something that helped you may stop working, and something that previously didn't help you could start helping you.
A direct implication of this, of course, is that the mere fact that it's therapeutic for some other people doesn't necessarily mean that it's therapeutic for you; it can be helpful for some people and useless, or even counterproductive, for other people. This is where you really need to consider the specifics of your case.
Also, let me pose the question in a different way: does the way you play chess cause you problems? Do you play it in a way that most people would consider excessive or unreasonable? Does it cause you problems in other areas of your life, such as work or personal relationships? If you answer "yes" to either of these, you should discuss with your psychologist whether you're playing in a way that's compulsive; otherwise, if you've discussed it with your psychologist and neither of those hold, I wouldn't worry too much about it - just make sure that you're being honest with your psychologist about whether or not those are the case.
Also, dopamine plays a role in any pleasurable activity, so personally I find the "dopamine argument" overly simplistic. Dopamine is involved in drug use because, at risk of oversimplifying things myself, addicts like taking drugs and alcohol. If there was no sense in which taking these substances was either positively or negatively reinforcing, no one would take them. (See, for comparison, the original brain simulation reward research, which helped to establish the biological mechanisms for addiction).
One more aspect of this that I would like to point out: besides the cognitive aspects of this, if you enjoy chess, it provides you with something to do other than drugs and alcohol, and a chess club can provide a social outlet that's a more positive influence in your life than spending time with people that are actively drinking or using.

Congratulations on your 9 months of recovery, @Universal_learner! I'm grateful for over 30 years of recovery, primarily from cannabis but alcohol as well. The years have flown by faster than I could have imagined.
One thing that I've learned is that recovery from addiction is not just a matter of abstaining from unhealthy habits. It's also a matter of replacing the unhealthy habits with healthy ones. My experience is supported by neuroscience and the concept of neural pathways.
Your explicit questions are understandably generalized, but I believe how it affects you personally is what's truly important here. The answers to your questions aren't black and white. Treatment centers have to set rules in order for them to function successfully. Ultimately the decision is between you and your higher power. (For those unfamiliar with the 12-step concept of a higher power, I believe it's widely misunderstood. It can also be explained from a neurobiological perspective.)
Clearly you've made a distinction in separating what you believe to be unhealthy addictive chess versus chess that enables you to engage socially without drugs and alcohol. It sounds like you're sincerely trying to check and make sure you're being honest with yourself. IMHO, just keep doing that, with the support of your therapist and higher power.
In early recovery, I would make difficult decisions by asking my higher power and myself which decision felt like it was most supportive of my sobriety versus leading to relapse. Over the years that question has evolved into seeking spiritual guidance to do the next right thing. That guidance this evening was to answer your question, and that answer was different than I expected!
Best wishes to you on your journey, @Universal_learner! May you answer a question like this 30 years from now, one day at a time!

Anything you can find that keeps you sober is a great activity and since the relapse rate is so high ignore anybody who thinks they got sobriety figured out if they did they would be an instant celebrity and could name their price on consultation. If you find that playing keeps you from obsessing on your former life then dive on in. The first year is probably the hardest so I would keep a journal and document your journey.
When you are successful perhaps even publish your recipe so others may follow.

Yes, of course.
Any game - any activity - that depends on continued application of the powers of the mind should help recovering addicts.
Unless no games are good, how could chess not be?

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Why is my rating not increasing on lichess.org?
I played some rated games and don't understand why my score doesn't go up. Usually, my score either goes up or goes down, depending on if I win or not. This time, it didn't even change. It is weird.

Can you link your profile?

You probably have accepted an unrated friendly match. Friendly games don't affect your rating on lichess.

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Why do women have a lower Elo requirement to obtaining (women) FIDE titles?
As well as FIDE norms, you need a certain Elo to obtain a certain title. Women need around 200 points lower Elo to obtain the analogous women's only title:

Grandmaster (GM) 2500+
International master (IM) 2400+
FIDE master (FM) 2300+
Candidate master (CM) 2200+

Woman grandmaster (WGM) 2300+
Woman international master (WIM) 2200+
Woman FIDE master (WFM) 2100+
Woman candidate master (WCM) 2000+

I have read many times the reason why women don't reach the super GM level is social and not cognitive. For example in this interview to WFM Rodrigo she is asked:

XL. Why are there still no women in the elite?
M.R. For various reasons, but basically for two. For a statistical
question (we are less players) and for a cultural factor.
Evolutionarily, women are more used to collaborating and men to
compete. It is an imprint that comes to us from the hunter-gatherer
tribes. In addition, the male brain processes visual information
faster, which favors the recognition of patterns on the board, while
women have more developed memory. But in ten years we will see girls
fighting for the world title.

So why is FIDE giving titles to women with less chess knowledge than players who have the equivalent open title? I know there are fewer women players than men, but women can play in men's tournaments.

That's quite a comment, that men's brains are different in their abilities. I reject this as dangerous nonsense. Forget not, Judit Polgar the best in the world for her age, set records and I don't know what the odds would have been set against her eventually becoming world champ when she made GM, but I would have glad put up a lot at anything over 20:1. Same could have been said of the sisters. Let us get rid of any separate treatment of women in chess.

That quote by M.R. does not give remotely any evidence that if a (woman, man) pair were raised under the exact same conditions, over some distribution of possible conditions, that the woman is expected to perform any worse than the man.

I think WFM Rodrigo is correct when she says that the reasons are statistical and that having fewer female players means having far fewer players at the top.
If you assume that males and females have the same mean and standard deviation (we shall see soon that this assumption is false) and you draw the two normal curves you see that the curve with fewer members (females make up only 15% of FIDE registered players) tails off to zero long before the one with more members.
However WFM Rodrigo also mentions "cultural" reasons. Translated into mathematical terms I think she is suggesting that females have a lower mean (average) FIDE rating than males. This we can check by loading the latest FIDE rating data into a database and doing some SQL queries.
Doing that gives us:
Female
Mean = 1505, standard deviation = 339
Male
Mean = 1675, standard deviation = 346
We see that there is little difference between male and female standard deviation but the mean female ELO is 170 points lower than the mean male ELO. This is half a standard deviation which is a lot. It looks to me that WFM Rodrigo is right about this too.
Comparing these figures with the rating differences between the open (there are no male only titles) titles and the female only titles it looks like FIDE are being generous to the females by a margin of 30 points. Perhaps they rounded the difference up to the nearest hundred?

A slight nitpick re the rounding: is 'latest' data perhaps not as relevant as compared to data immediately prior to when the women's fide titles were 1st released? maybe the difference is at the time was around 190-210 points and then that's why they made it 200 points. of course, 170 is still close enough to 200.

I don't think the average rating of men and women is a relevant statistic at all. For starters, female players are on average much younger, so we should correct for that.

@David well relevance is 'subject to gradation', sooo...do you mean it's: not really relevant? not as relevant as other statistics (that are as practical to compute)? completely irrelevant like 0%?

@David what did you have in mind: get mean and std dev for each age? at least 'for starters'. but after the start...surely there must be a million factors you want to account for eg country, income of parents, any quantifiable measures of sexism in the country, etc right? we can't possibly account for all this can we? besides, FIDE is not doing 170 points flat. i believe the round up to 200 points is like 'let's round it up to hopefully account for all those other factors'. i mean surely say 500 points more than accounts for the other factors right? do you think 200 ain't enough?

@BCLC I mean it in the sense of "It's anecdotal". If the chess world was flooded by 20,000 new eight-year-old boys overnight, the average rating of men would sudenly become lower, but that doesn't mean men became "worse" at chess. It's not a matter of "how much is enough" but about calculating more relevant metrics.

@David is a more relevant statistic then mean/std dev for rating for 2,000+? https://chess.stackexchange.com/questions/36883/what-is-the-mean-and-standard-deviation-for-mens-and-then-womens-standard-fide i believe this will not be impacted/affected significantly by such a flood

@BCLC It could be, but I think the best option would be to calculate a different mean for each possible age.

Brian Towers♦ (1/2) 1 - is your answer unchanged re 'but the mean female ELO is 170 points lower than the mean male ELO' and 'it looks like FIDE are being generous to the females by a margin of 30 points. Perhaps they rounded the difference up to the nearest hundred?' like 200 pts in title difference might be based on 200 pts difference (probably at their time it was around 200 pts as well) based on your answer in the new question? (eg only 1870-1817=53 pts difference for 1500+) 2 - if yes, then ok thanks. if no, then thanks so what changes?

Brian Towers♦ (2/2) i think: on 1 hand based on the 1500+ (at least as of apr 2021) the women titles ostensibly have too low an elo requirement based on -- hmmm how shall call i this -- the 'probability' (like a priori choosing elo requirement based initially on conditional average). but on the other hand, the elo requirement currently seems to be just fine based on the 'statistics' in my answer i.e. plainly it works, but the 2000+ and hell even the 1500+ ostensibly tells a different story.

Note: This addresses the previous revision of the question w/c said 'Women need less ELO to obtain the same title than men.'

It's not the same title. Women Grandmaster (WGM) for example is clearly less prestigious than GM because the requirements are lower. FIDE isn't giving out the same title to women who have less knowledge than men, they are giving out exclusive titles for women. In the same way there are female players who have achieved the actual GM title (e.g. Hou Yifan is a WGM and a GM).
As for why they would do that - why not? Chess is heavily male dominated, and a WGM title makes the game more inclusive. Can you think of a good reason not to have the titles?

I suspect it's related to why women can compete in women's chess championships without being a GM.

Eg 1 the US women's chess championship or the british/UK women's chess championship have been recently won by non-GMs: Nazí Paikidze, Jennifer Yu, Sabina-Francesca Foisor, Jovanka Houska (current), Akshaya Kalaiyalahan.

1.1. The current US women's champion is GM Irina Krush, who has last been champion for 2012-5. However for 2016-9, Krush participated in all, but besides that e didn't win, actually none of the winners were GMs! See for yourself: 2016, 7, 8, 9

Eg 2 Wait actually I just looked up to be sure and apparently WGM is even good enough to compete in the world's women chess championship:

2.1. In 2015, the runner up was WGM Natalia Pogonina (and really wasn't an IM, afaik).

2.2. Of course as expected every winner or runner up since 2016 is really GM. In particular, in 2020 (when they returned 'to match format only'), all the candidates were GM. However, in Nov2018, the preceding world women's championship, there were even WFM's competing.

You can see this as like 'semi-begging' the question in the sense of converting to another question on women's chess championships, but as for this current question...
Conclusion:
I think these recent results show (well at least for the UK and the UK/Great Britain) that 'WGM' as in '2300+' (and norms or whatever else is required) is good enough to compete in (at least local/national if not international) women's chess championships.
So, if we suppose on the contrary that we didn't/don't have women's titles, then we'd be describing winners/runner-ups of women's chess championships as just FMs. I believe the WGM title would be more descriptive for these winners/runner-ups.

Bonus:

Of course, you can argue, since/if/if it would be that many WGMs now/later on as compared to before are also IM, that we might increase WGM to 2400+ from 2300+ so as to distinguish a WGM like Nemo Zhou [see here] from a WGM like IM Jovanka Houska (current British women's champion), but that's another story.

If in the future winners/runner-ups of women's chess championships and even most participants are GMs, then who knows maybe requirements for women's titles will increase, maybe even to the point that they will be the same as the open titles (and thus there would not need to be women's titles).

I think they can have the same requirements if there were more women exclusive tournaments. In this way it's less difficult to obtain say 2500+ for WGM if women play only other women as compared to getting 2500+ if women are up against both men and women.
Plainly, there are not so many of these tournaments, so the next best thing is to just do make the requirement lower.


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Why do children move so quickly?
I played a game against a 6 years old child where I launched a strong attack against the poor child:
[fen ""]
[white "Me"]
[Black "6 years old child"]

1. e4 c5 2. Nf3 e6 3. d4 cxd4 4.Nxd4 Be7 5.c4 Qc7 6.Be2 a6 7.O-O Nf6 8.f3 Bc5 9.Be3 Qb6 10.Nc3 Nc6 11. Na4 Qa7(11...Bxd4 12.Nxb6 Bxe3+ 13.Kh1 Bxb6)  12. Nxc5 Qxc5 13. Nf5 Qf8 14. Nd6+ Kd8 15. Bb6+ Ke7 16.Bc5 Qg8 17.Nxc8+ Ke8 18.Nd6+ Kd8 19. Bb6+ Ke7 20. Nxb7 Qb8 21.Bc5+ Ke8 22. Nd6+ Ke7 23. f4 Kf8 24. e5 Ne8 25.Nf5+ Kg8 26.Ne7+ Nxe7 27.Bxe7 Qc7 28.Rf3 g6 29.Rd3 Ra7 30.Qa4 Qb6+ 31.c5 Qxb2 32.Re1 Qb7 33.Bf3 Qc7 34.Red1 Kg7 35.Rxd7 Qb8 36.Rd8 Qb5 37.Qxb5 axb5 38.Bf6+ Nxf6 39.exf6+ Kxf6 40.Rxh8 Rc7 41.c6 Ke7 42.Rhd8 Kf6 43.R1d7 Rxc6 44.Bxc6 h5 45.Rf8 Kf5 46.Rdxf7+ Kg4 47. Rg7 Kh4 48.g3+ Kg4 49.Rxg6+ Kh3 50.Bg2++

He played strange moves in a few seconds in the opening, e.g. as 5...Qc7 or more concretely 11...Qa7 missing the exchange of 3 pieces for a queen (which Stockfish says is good for black) much better than the position where black finishes after 13. Nf5. He also moved his bishop twice in the opening, his queen twice... all this with his clock over 1 hour and 30 minutes in a standard 90'+30'' game.
Once he lost a piece he spent some minutes to play his king's moves after the checks with only two or three possible moves. It seems that he thought more about it when defending himself, but when I checkmated him his clock was on 1 hour 12 minutes for a 90'+30'' game.
Why do children move so quickly in standard games, specially in the openings?
In the tournament I am playing half of the players are children and after one hour and a half all children have finished their games and there are only adults playing.
I know many children play forced by their parents to attend chess after school and might find boring to play chess, but I am asking about childs that like the game itself. I assume once a child joins a chess tournament it means he or she doesn't find boring to play a chess game. I am asking why children that like the game and play tournament games frequently don't spend minutes in tricky moves as adults do. Why don't they use their time?

The answer is very simple. A 6 year old child does not have an adult brain. It has the very immature, underdeveloped brain of a 6 year old. It has a short attention span and struggles to sit still for 5 minutes let alone spend 5 minutes on just one move.
A few years ago I was chief arbiter for three junior tournaments held at the same time. I got one of the coaches who is also a qualified arbiter to help me. Obviously he wasn't allowed to help his players even in the breaks between rounds.
Instead before every round he stood up and made the same speech basically begging the kids to take more time over their moves. The time control was something like 25+5 and yet most games were over in less than 10 minutes with the players thoughtlessly blitzing out moves.
As he explained to me, kids tend to move too fast in games which are just friendly, relaxed games. But when it is a competition and clocks are involved their brains interpret it as some kind of race and they have even less control of their time management. Adrenaline takes over and calm calculation flies out of the window.

Some of use keep that immature pre-frontal cortex.  But work hard to hide it.  Till the end.  but yes, that makes the user of such immature (why so much connotation) brain, quick explorers.  And possibly learners as well. This comment not really helpful. Unless adults tried to emulate some of that behavior... maybe that could be an option...
Cortisol for kids,,, I do not approve.... I would have run away.  And still do not approach.

I would propose another plausible explanation:
Time moves slower for children.
I don't mean that in a gobbledey-gook spiritual sense but in the sense that the way humans experience temporality is relative to age.
One Year for a 5 year old is 20% of their life. One year for a 20 year old person is a mere 5%. This transmutes down to smaller time periods too. A standard TC rapid game of say, 30 minutes, corresponds to a much larger proportion of a child's life than it does yours, hence they may lose focus and act more impatiently than you. (Of course there are a multitude of factors at play).
Indeed, there is a neurological basis for this phenomena:

The common explanation is that most external and internal experiences are new for young children but repetitive for adults. Children have to be extremely engaged (i.e. dedicate many neural resources or significant brain power) in the present moment because they must constantly reconfigure their mental models of the world to assimilate it and manage behaviour properly.

...Consequently, the subjective perception is often that time passes by at a faster rate with age.

Assuming you are an adult, you are probably have a much different sense of time than your more youthful opponents, for whom 30 minutes may seem like an eternity.

Incentives and/or tactical ability tend to explain this.
Sloppy chess against similar fast-moving and reckless competition (U600 - U1200 tourneys or sections within larger tournaments) produces flip-coin level results  (or better, if you are slightly less sloppy) results and that's enough for a kid to feel they did okay (or worse yet, report back to the parental control units at home that they fared satisfactorily and won 25-50% of their games). The rare exception are the few who are focused enough on winning at all costs (and are willing to self-correct + change their time management behaviors) and they will stand out amongst this pack. Though chances are, that guy or girl is already taking his/her time, even if his/her time management is just marginally better than his/her peers.
Now at the higher rating club levels where grown-ups tend to congregate, you'll still see this pattern with kids because they are tactical beasts who really don't see incentive to play positionally when they are cleaning adults clocks because they consistently visualize + calculate really well thanks to natural or well-trained tactical vision and the 40-year old across the board spent more time on the Najdorf than figuring out how to hold a 3-ply ahead position in their head and look for forcing moves. I mean who cares coming up with long, time consuming dynamic evaluations when I know (and this is their incentive!) this grown-up is going to miss a tactical motif within the next 10-15 moves and I've got them?

I have another aspect to offer. Being a life long kids chess trainer ("Think, for gods sake!!") and a still lightning-fast old geezer now, I think it might also be linked to self-esteem. I do not think longer now to calculate, but because I don't trust my intuition anymore, and back it up with as untrustworthy calculation. As a kid, you are still the Godhead. You never even think about that you could be wrong. You'll never overlook a tactics that favors you. Too bad the opponent also has some...


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What is the algebraic notation for the bishop?
Let's say that I have a pawn at b2 and a bishop at d2 and I want to capture the pawn on c3 with my bishop. The expression I used is bc3. However, it uses my pawn at b2 to capture the pawn at c3. I then tried b2c3, but it did the same.
How do you use bishop to capture the pawn at c3 with algebraic expression in this case?
[FEN "rnbqkbnr/pppp1ppp/8/8/8/2p5/PP1BPPPP/RN1QKBNR w KQkq - 0 4"]

1.Bxc3 (1.bxc3)

@mateenulhaq your edit makes the question contain its own answer :)

The expression I used is bc3

Lowercase letters ALWAYS refer to pawns/files. Uppercase ALWAYS refers to pieces. You need to use Bxc3 for "Bishop at d2"xc3.

"Lowercase letters ALWAYS refer to pawns/files. Uppercase ALWAYS refers to pieces." Well, not exactly. "x" is a lowercase letter that always refers to a capture. O is an uppercase letter that always refers to part of a castling manoeuvre.


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How to move knights so that black moves first?
From move 0, what shortest-possible sequence of moves could be played so that the pieces are arranged exactly as standard board setup (with allowed swapping of same-color knights), but it is black's turn to move?  Is it even possible?
I thought about it and conjectured white would have to make an odd number of knight moves, and black would have to make an even number of knight moves. I think this is impossible when the knights need to end up where they started, or even swap with each other (because even though this is an odd number of moves for one knight, the other knight would also have to make an odd number of moves). Am I correct? How can it be proven?
I also guess that this is a famous or at least previously explored problem. Maybe it's trivial.

Given how the initial position and all the moves are symmetric, switching black to move first would technically make no effect game-wise. It'd just swap left and right and the colors.

If the "first" move from Black after the swap would be a double-move with a pawn, the players could co-operate so to make it look like Black made the initial move.

It's impossible. Knights require an even number of moves to reach a square of the same color as where they started, or correspondingly an odd number of moves to reach the opposite color. Both sides need to make an even number of moves to reach the starting position.

The conclusion is correct but the analysis is incomplete.
Once a Knight moves, the Rook near it can start moving too.
But that doesn't help because the Rook is limited to two squares,
so when it returns to its home square the Rook has made
an even number of moves too.  Also, the question allowed
Nb1 to switch places with Ng1, and/or Nb8 with Ng8;
but that doesn't help because each of those Knights then makes
an odd number of moves.

@NoamD.Elkies, I don't think considering rook moves in necessary, because after rook moves the position changes, castle with that rook is no longer allowed, and therefore we would not be able to go back to the starting position.

Yes, the position would be different in that sense; but the question
asked only "that the pieces are arranged exactly as standard board setup",
without specifying that castling rights be retained.

And what about the knights exchanging positions (i.e., the queen's knight going to the king's knight square)? I suppose it would make no difference, because odd + odd = even, but it would be goof to clarify in the answer.

I think the question is clear that swapping knights is ok, it just doesn't help.

More simply, after each knight move, the number of knights on white squares changes by one. Initially there are an even number of knights on white squares, so after an odd number of knight moves there are an odd number of knights on white squares, and after an even number of knight moves there are an even number of knights on white squares. Therefore, in order to have knights on the same squares as in the initial position (never mind whether they are the same knights), there must have been an even number of knight moves.

@bof You can even extend that argument to include rooks: after each move, the total number of knights and rooks on white squares changes by one.

@NoamD.Elkies that thought is interesting. of course the original task is not possible, but if the pawn in front of the knight moves one step forward (same for black), and you get the bishop temporarily out of the way you could move the castel 2 steps to the left and then in two moves back. So basically you could end up with 2 pawns (one white, one black) one step moved, but now it is blacks turn.

@lalala Or you could instead move the bishop out 2 spaces, then back 1 at a time, and this would not prevent you from castling later.  The queen could pull the same trick.

This is impossible because.

In the initial position, the 4 knights cover 2 white and 2 black squares.
each white move will lead to the knights being on 3 white squares and 1 black square or 1 white and 3 black.
each other black move would lead to 2 & 2 or 4 & 0.

In order for "black to go first" the knights will need to be on the initial position (2 white, 2 black).
This is not possible after a white's move as shown above.

You are basically trying to make a knight lose a tempo, which is known to be impossible.

I have no idea what this means

@theonlygusti, see: https://en.wikipedia.org/wiki/Tempo_(chess) Basically, you can't "waste" a single move with a knight, because of the alternation between black and white squares. That's what the existing answers already say, and much better.

I was about to say this! I wish this could be the accepted answer. @theonlygusti it's a rule of endgames that knights can't lose a tempo. Do you know like triangulation or losing a move or reaching the same position but with the opposite player move? (eg it's currently your move but you can maneuver pieces to make it the same position but your opponent's move) You can do triangulation with kings and bishops (and i guess rooks and queens), but you can't with knights! Remark: Your question about the opening is answered by an endgame principle. (Wait I'll make this comment a cw answer.)

converting to comment to answer, but just a cw answer to emphasise postoronnim's answer:

I was about to say this! I wish this could be the accepted answer. @theonlygusti it's a rule of endgames that knights can't lose a tempo. Do you know like triangulation or losing a move or reaching the same position but with the opposite player move? (eg it's currently your move but you can maneuver pieces to make it the same position but your opponent's move) You can do triangulation with kings and bishops (and i guess rooks and queens), but you can't with knights!

Remark: Your question about the opening phase is answered by a principle of the endgame phase.

Re triangulation, try checking out: 1, 2


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Can a 2000 Elo rated player teach me middlegame play properly?
I have reached 2500 in the chess.com tactics trainer while I haven't study theory and my FIDE rating is 1637 (I reached 1930 in rapids a year in France).
I want to study with a coach and there is one at my club who knows a lot of openings and endgames theory but is rated only 2000. Is his rating a limitation to teach me? I guess I need lessons not only in openings and endgames but in middlegame play. Should I search for a better trainer out of my club or it is enough that this coach train me?

You say the guy at your club "knows a lot of openings and endgames theory" but you want them to "teach middlegame play propertly"; isn't it a bit illogical?

@sleepy he is the only coach available at my club, then asking if I need to search outside

Magnus Carlsen has been coached by players over 200+ lower rated than him.

Studying chess is not into my priorities. I like to play 90+30 games from time to time to share my mistakes with my friends in this awesome forum. i have a premium account in chess.com to watch some videos, but think i am too much old to become FM. The funniest new of last weeks is Anatoly crunching Karjhaking lol

Is his rating a limitation to teach me?

No.
As I say in this answer, "you are too fixated on rating". High rating does not guarantee coaching ability. Low rating does not preclude coaching ability.
Today the guy in our club who does the most coaching is rated about 1900. 50 years ago, the first time we played for the same club, he was rated about 2150. He has coached a surprisingly large number of the players in our region who are now rated 2100-2300, although they moved on to better high level coaches before they got to those levels.
It is always interesting to watch him play one of his former students. Is the student going to give him a draw for old time's sake? Or crush him? If they give him a draw then afterwards the coach in him will tell them why they shouldn't do that while also saying "Thank you!"

I need lessons not only in openings and endgames but in middlegame play. Should I search for a better trainer out of my club or it is enough that this coach train me?

We don't know the trainer so we haven't a clue. Probably the best approach for you is to have a trial lesson and see what you think. Did you learn anything? Was it worth it?
Taking a trainer is not like getting married. If you find it is not helping you then you can just stop and walk away.


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Development problems for black after f4 in French Defence
I am a French player as black. I am having problems in lines where white advances their e pawn and plays f4 to defend e5. I feel like the break on f6 is useless. I am afraid to castle short. My bad bishop gets trapped and in general I get a misdevelopment of my pieces while I cannot stop white's space opening in queenside.
Here is a game I played today against a FIDE Master (FM).
[FEN ""]
[White "Fide Master Urriza (2289)"]
[Black "Manuel Ignacio Muro Sabater (1637)"]
[startply "9"]

1. e4 e6 2. d4 d5 3. Nd2 Nf6 4. e5 Nfd7 5. f4 c5 6. c3 Nc6 7.Ndf3 cxd4 8. cxd4 Qb6 9. g3  Bb4+ 10. Kf2 f6 (10...g5 {very strong move suggested in answers that opens the position with good perspectives for black})  11. Kg2 Kf7 12. Bd3 Nf8 13. Ne2 Ng6 14. h4 h5 15. a3 Be7 16. b4 Bd7 17. Nc3 Rac8 18. Bb2 a6 19. Na4 Qa7 20. Rf1 f5 21. Nc5 Bxc5 22. dxc5 Nce7 (22...Nge7 23. Ng5+ Ke8 24. Be2 g6) 23. Ng5+ Kf8 Be2 1-0

If I had moved the other knight in words of the FIDE Master "White has still some work", but my position was suffocating, an engine gives an advantage for white practically all the game.
How could I develop better my pieces in lines with f4 in the French?

You're playing a very sharp opening line that only works thanks to the option of playing 10...g5!. You should only enter this type of position if you're aware of what you're doing. Otherwise you'd be better sticking to quieter, easier positions. If you choose to play a theory-heavy line, then you should definitely know the theory first!

Of course if you don't know the theory in the first place, you couldn't know that it was a theory heavy line.

Very strong move that profites the position of white's king and finish with my development troubles. Noted for further times I face this position. Thanks coach!

@jf328 You can. I don't know much about the Najdorf but I know it has a lot of theory

I am pretty sure the first 10 moves are pretty ok, but after Kg2 you are supposed to play either 0-0 or g5 (maybe some other moves are fine too; fxe fxe 0-0 is also not too bad I suppose), but Kf7 looks weird. Generally, in this line black is indeed suffocating unless he sacs a knight on e5 to open up files in the middle and then attack the white king. I remember a few games by Korchnoi in this line; feel free to check your favourite database.
On a different note, I know Bb4+ has been played multiple times, but I could never figure out myself why the bishop on b4 is placed better than on e7...

The problems you are mentioning are real and the line you are playing is more or less dubious. That's the price to pay, if you are insist to opt for a loong fighting game with black. Your choice.
I haven't checked with an engine, but what you did looked not that bad from the outset -- except for 11..Kf7.
Although it is a closed position, it is highly dynamic. You must act quickly and with determination, or white's attack on the king side will come.
White also really like to suffocate you with a3,b4 here. This must be always on your radar and you need a good answer for that. Best is, to play a5 as early as possible and then sooner or later ..a4. If white has played b4, challenge that with a5.
The next top priority is to develop the queen side and reroute the knight on d7. We have seen that it does nothing on g6 and is also only a target there. Typical could be to play Qc7, Nb6, Bd7. Another option is sometimes the funny Nb8! and then Na6, as I have learned from Stockfish.
Rook can go to b8 or c8. Knight can go via a5 to c4. In a later stage you can activate your b-pawn.
Don't be shy and don't underestimate your potential on the queenside. If white does nothing but waiting, eventually you will come to him. And then you win.
Old FM Roese (https://lichess.org/@/fiskaren)

What is the last line a reference to (for this post)? What is the purpose of it? E.g., is that you or somebody else? Is it a kind of source? Can you make it more clear, e.g. by editing your answer (without "Edit:", "Update:", or similar - the answer should appear as if it was written today)?

As of my understanding of chess, in closed postions it is quite useful to have a repertoire of maneuvers at hand, to ponder over. And since Nb8 looks funny, i just wanted to give that sugggestion a bit more credibility, by reporting that were was some similar postions were it really was best, as shown by stockfish.
Of course i missed the best idea (10..g5), so speaking of this postion only, this comment is just obsolet. That's the nature of chess (sigh). One critical move can change the nature of the position completely.


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Chess health benefits
I recently read an interesting article, and was surprised to see that there are actually mental health benefits to playing chess. How often does this happen, and in what instances?

Why not give a link or at least reference to the article? Otherwise, you are asking others to comment on second-hand detail-free information. Without seeing the article itself, my replication crisis detector is sounding an alarm. There have been hundreds of published studies of the form "______ is correlated with healthy _____" (fill in the blanks) and such studies have been notoriously hard to replicate.


text:
Do people cheat at a 1500 level on chess.com while lichess is clean?
I play correspondence since many years ago. I have been playing in lichess for years having a rating ~1900-2000. I recently open a premium account in chess.com and I started to play 50 simultaneous games. I couldn't pass throw 1500 rating while my tactics trainer rating is 2600 and I returned to play in lichess.
I know there are some reasons why chess.com has stronger players with the same rating than lichess ones, but analyzing the games I faced players that do have plus than 95 of accurancy in complicated games, so I think the reason may be those player use engines at least when the move is complicated, as they are rated 1500 and not making blunders. This is not what I found in lichess where profiting of blunders allow me to beat easily 1500 or even 1700 players.
I read a post of Erick, the owner of chess.com saying cheating happens at a +2300 level. But my concern is, at a lower level and in correspondence, I miss blunders in chess.com. In lichess I have not troubles to reach 1900-2000 rating beating easily the 1500 players. I think those users are using engines when the position is complicated but playing a fair game the rest of the game. That might evitate them to be catched and allow them to play at a 1500 level while they are poor players that should have a rating <1500. I have seen other users that have a curve of rating that grows and decreases. I think when they loose rating they start to use the engine so they can mantain a rating and play the games they want to play with overrated players than them.
chess.com is a big entreprise, they should have programmers versed in machine learning techniques to detect cheaters. Are lichess programmers better than chess.com and succeded to send cheaters away from his correspondence rooms even at low rating levels while chess.com programmers not? Do they use similar technics or lichess ones are more sofisticated?
Or it is just a matter about rating strenghts and I am being paranoic?
It might be just 1500 rated players make blunders in lichess while chess.com 1500 rated players not?

the answer is no in my opinion. But both sites are filled with chess players suspicious of their opponents of cheating.

I've played "correspondence" for years on chess.com and never felt that anyone cheated.  I did get some rating points back when someone I played was later banned.

From my experience in Lichess correspondence, below 2000 it's mostly "simultaneous bullet", with blunders all over the place. At around 2000, people suddenly start to get serious and you see almost no blunders anymore. If that threshold is lower on chess.com (and it probably is, as they start with lower numbers), that easily explains why your experience is so much different on both sites, while playing at roughly the same numbers (1500). Got to compare chess.com ~1500 with Lichess ~2000.

If someone is cheating but has a rating of 1500, they must not be very efficient in their cheating. I am skeptical that someone could have that rating without making a fair number of blunders. Perhaps at that level they are 2-move blunders rather than 1-move blunders, but the blunders should be there. Your question might be helped if you give an example of a game that strikes you as being a likely case of cheating.

I am also 2000 lichess and 1500 chess.com, that's just how it is. lichess also starts you off at 1500 provisional whereas chess.com starts you off as 1200.

100 rated people cheat. Cheating is universal

Chess.com is a for-profit business, so they have more incentive to be sure that a player is cheating before banning a potentially paying customer. Since lichess is fully free, there's less cost associated with a false positive ban. Thus it would make sense for chess.com to have a higher threshold of confidence for banning cheaters, but I can't say whether this motivation does actually impact their choices or not.

And for that reason players using engines prefer not to play at lichess

Do you have any statistics to back up the claim that lichess hands bans more often than chess.com under the same circumstances?

Strongly disagree. First, I have never heard anyone complaining about being falsely banned on lichess, while there is a lot of such people wrt chesscom. Second, chesscom officials claiming they ban a gazillion "cheaters" per week just do not sound very convincing. Most probably they just run a script  blindly, and they don't care much about false bans of customers who did not pay for the subscription. Since lichess is free, they do not make this distinction and do not have this issue.

Lichess dissuades cheaters by inflating all ratings and thus their egos, giving them a sense of accomplishment. It also helps they do not make anyone feel negatively about their personal finances. /s

Different sites have different rating systems and player pools. They're not directly comparable. Lichess ratings tend to be higher than chess.com ratings for the same reaosn a person's weight tends to be higher than his height

This question I posted says it is common in correspondence players use engines to play 3rd and 4th lines of engines. Are you sure I am being paranoic and it is not a matter that lichess cheating detection is better and players using engines evitate lichess? I was searching an answer comparing both cheating detection systems as it is difficult to realize when a player is cheating in correspondence. They might not being using engines alltime but just consultate it when tricky tactics appeared. The fact is I miss blunders in such a low rating games

What you're saying is correct but there is no reason to expect one site to be better at catching cheaters than the other. Did you get any notifications of rating points being awarded back to you after a cheater was caught?

No I didn't. I read a post by chess.com owner saying cheating happens at +2300 rating. Maybe chess.com only checks highly rated players. But a player can be using an engine ocasionally to avoid tactics blunders and mantain his 1600 rating to play rated games. Lichess has a tactics rating system taken from games with stockfish. Might lichess being catching 1600 players solving allways highly rated tactic problems? is my concern. They might migrate to other platforms as chess.com. But you might be right and this is a rating system concern.

The main reason why lichess does not have many cheaters is because they have a really powerful cheat detection/anti-cheat system. For eg. If you are playing a game and you are taking some assistance from a software(for eg. stockfish) then lichess will automatically detect that you are cheating. How they detect? If you are playing moves really slowly and playing the best moves, then a message will appear "Cheat detected. White/black is victorious" Whereas chess.com takes much more games to find out whether you are cheating or not

In correspondence, Lichess' anti-cheat system sometimes "fail" because correspondence is more than a day game so you are given plenty of time to calculate lines and moves , so sometimes they think that player is not cheating and is playing fairly.

@Universal_learner it's perfectly reasonable for a 1600 to solve highly rated "puzzles" in correspondence games. When you have unlimited time and you're allowed to move pieces on an auxiliary board, the strength of a player can improve significantly. Unless there's a good amount of evidence supporting otherwise, I'd stay with my "null hypothesis".

@algebrology what you're saying is basically that Lichess detects cheaters by detecting cheaters. Note that any system will be a compromise between accuracy (mark only cheaters as cheaters) and recall (mark as many cheaters as possible). Faster does not necessarely mean better

"a person's weight tends to be higher than his height" - only in the USA - everywhere else in the world, a person is twice as tall as they're heavy.

@JohnDvorak: That surely depends on the units, doesn't it? I mean I'm 1.8 tall and ~80 heavy. (According to google, anyway).

@sharur 80 is bigger than 1.8 so in those units weight is bigger. But sure you can also measure Elo in Kilopoints!

@JohnDvorak I'm aobut 90kg heavy and 1.8m tall. 90>1.8

Different website have a different rating scale. I'm sure lichess gives higher rating than chess.com for the same player. In fact, the lichess rating is also higher than the FIDE rating. I personally know a lot of FIDE 2200 rated players achieve ~ 2600 on lichess, equivalent to GM on FIDE scale (but they are not GM).
I'm personally also a few hundred ELO points behind on chess.com than lichess. I've found much more challenging to defeat a chess.com 2000 rated player than lichess 2000.

To be fair, a lot of 2400, 2500 FIDE players achieve 2700/2900/3000+ ratings on chess.com too. Levy Rozman as an example. Also players like Hikaru achieving insane 3500+ ratings.

Just about the cheating, cheaters are not the smartest, and that's why there are algorithms which can detect cheaters. Those algorithms are not the smartest either, and that's where the differences are. Most cheaters have really powerful engines playing for them, but don't pick the best of the best move because the most basic anti-cheat would detect that (except if you are titled as BOT). That's why they pick the second, third of fourth line the engine suggests. If this behaviour is happening a lot of the moves (which could variate between Lichess and chess.com), a cheat could be detected. If you play about the same time per move in combination (that margin can also differ and this can be bypassed by using different depths) with this, that means you are playing against Stockfish instead of Irsu85.
The chances are also low a human can see a very complex but winning line with a hundred pins after 30 ply. This could also be used in anti cheat, but I don't know if that is a thing on chess.com or on lichess

The dynamics of postal chess allows more in-depth analysis of the games. This makes mistakes rare. Some sites prefer to maintain the rule that in correspondence chess you should not use assistance of any kind (as if it were face-to-face chess) and others have reasoned that it is too difficult to know if chess engines or other assistance have been used. For example, the International Correspondence Chess Federation, (ICCF) allows the consultation of tables of endings of seven pieces to decide the winner of the ending of a game. I guess to save time at the big tournaments.
Some tournaments are centered on certain openings (thematic tournament) and others are pure competition. In the latter, the chess player must foresee the opponent's move, either by investigating the lines of play that can be derived from the position or if suspect that his opponent uses engines to chose his moves, consider also the lines that an engine would choose, especially in the opening to take him to a disadvantageous position due to a better understanding of the strategy and trying to uncoordinate the opponent's pieces, so that can't benefit from the engine.
In the middlegame, some player can choose the type of endgame he prefers and look for, for example, a triple repetition draw or aim for an endgame with more than seven pieces to prevent his opponent from benefiting from the Lomonosov endgame tables.
Now, the reason why you suspect that chess_com players rely more on engines than Lichess players, its perhaps an appreciation that should be validated comparing the analyses of correspondence games from same players on both platforms.
Your hypothesis could be explained by the slow pace that makes difficult for chess_com or Lichess to monitor the use of engines by the players, because somebody spending an hour or more time of analysis, could discover moves that the reference engine (stockfish on chess.com an Lichess) won't detect as an engine move.
Another reason could be that Lichess and chess.com may process suspicions of cheating differently.


text:
Does it makes sense to have a 1315 Blitz rating and a Rapid rating of 1729?
I am rated 1330 for Blitz on Lichess.  I was trounced by a clearly better player who had a lower ranking of 1315 for Blitz.  Their profile also shows a Rapid rating of 1729.
Is it possible for these both the Blitz (34 percentile) and Rapid (70 percentile) ratings to be a true reflection of the player's ability?  Both ratings are on over 300 games.

On chess.com my ratings are:

Blitz: 1339
Rapid: 1721
Daily: 2153

My understanding of chess doesn't change based on time control.  I am poor at quickly performing safety checks and so blunder more at faster time controls.

There are several factors involved with rating differences:

There is no one-to-one mapping between blitz and rapid ratings on online sites such as lichess and chess.com. Usually, the blitz pool has much more experienced and stronger players, thus your rating in blitz could be (much) lower. But this is also subject to your actual rating. For example, if your rating is 1200 in blitz, then your rapid rating could be 1600 since lower-rated players in rapid are weaker than blitz pool (with the same rating I mean: 1300 blitz player is usually much stronger than 1300 rapid player). But if your blitz rating is high, e.g., 2600 blitz, then it could be that your rapid rating is not much higher than your blitz since not many high rated players actively play rapid online, thus you don't get a chance to actually increase your rating too much.

Many players are good in the middle game but they don't have a good opening knowledge, so at the start they have to think about their moves, and consequently, they are not good at blitz, since there you should be rather quick in the opening.

Clearly one other factor is the cheating possibilities. It is much easier to cheat in a rapid game than a blitz match, especially for those who are not good at chess. I'm not playing rapid in lichess so I don't know what is the exact cheating situation there, but for chess.com, I can tell there is a good chance of facing a cheater in a handful of games (at least in my rating bracket).

Why do you say the blitz pool has stronger players?

@qwr, according to my experience with online chess. E.g. check high-rated players (chess.com or lichess), and see how much rapid game they played, and compare it with their blitz game. The number of their rapid games usually tends to be zero (clearly there are exceptions), but they play blitz and bullet quite often. Even if you argue that rapid games are longer, e.g. they need 3x more time to play than blitz games, usually, such players play multiple of magnitude more blitz games than rapid (even their rapids are usually for prizes). Thus online blitz has a much stronger pool of active players

First of all, offhand I don't see what advantage "differential sandbagging" would bring on Lichess, but then, I never played online. That said, I can come up with much more legit possibilities for person X having a vast rating difference in different modes:

It's genuine and style-based. I bet my own rating would be vastly higher in Blitz (even with 60 :-), at least 100 points.
Even on same (OTB tournament) mode, my ELO was constantly 100 points higher than my national rating. This is the influence of the opponents sample (naturally my ELO opponents are far stronger in average), and can be prevalent in this example too.
Also, in statistic you must ask: On how many games is the rating based? Especially in the weaker echelon, huge "daily" strength fluctuations can occur.
All kids of my chess club love playing online, and I clicked a bit through their profiles. Already the third also had 400 points difference between blitz and rapid, with around 50 games each. Given that the number of Lichess players is a few orders higher than the number of kids in my chess club (too bad), the probability of a stable 400 point difference caused merely by a statistic fluke skyrockets.
I know another guy in my chess club, who has (had?) about 1000 rating points less than me and constantly brought me into trouble since he knew openings. Same could happen here, if you start already bad out of the opening, trounceville.
That said, have you checked the errors of the game with a computer? If, objectively, you constantly handed points back and fro (rather common at 1300), it still can feel like a trounce.

tl;dr: I wouldn't think for a second of any foul play.

statistic fluke skyrockets?!

@MichaelWest: I'm a German ;-) (difference CLAUSE skyrockets is how it should parse...)

My real FIDE Elo was 2400 at max in 199x and in 2018 my real blitz rating was 17xx(Now I got few hundred points back in few tournaments). Not everybody who plays on platforms or even in tournaments have your "professional attitude" and cares about rating - I don't care about my - I play for fun, intentionally go for high risk combinations often loose to 1500-1600 players but at same time when I meet GMs I pretty often beat them or play on equals as that game for me makes sense and I'm concentrating and not playing fake combos just for fun. My online ratings are fluctuating like hell as I often play at work while in boring meetings and just resign when asked question and have to go or sometimes loose stupidly due to double focus! My own top rating on lichess is 23xx and often it falls to 22xx or even 20xx, but at the same time I have a 2400+ player against whom I lead 6:0, because I play those games - they make sense to work for me - if I play you I may easily loose as I don't care - I know I'm better player, nothing to prove.
So only 400 points diff between 2 online ratings and with different time controls - good but slow player. Or may be like me - does not care ratings!
Obviously it can be both - true reflection of players ability to play at certain speeds(lot of old people are just not good with mouse controls for example, so they loose fast games by quickly getting into time trouble) and it can be reflection of players true rating due to careless play or fun attitude!
Players like you who are analyzing his opponent ratings after the game instead of game itself never learn a game itself. If you will not change your attitude you will never learn to play chess!

@SaeedAmiri try to play careless - will see how easy it is to loose :D. As I said - you are bad at reading: Q: Is it possible for these both the Blitz (34 percentile) and Rapid (70 percentile) ratings to be a true reflection of the player's ability? Both ratings are on over 300 games? A: Obviously it can be both - true reflection of players ability to play at certain speeds(lot of old people are just not good with mouse controls for example, so they loose fast games by quickly getting into time trouble) and it can be reflection of players true rating due to careless play or fun attitude!

Check out https://chessgoals.com/rating-comparison/
They have a table showing a Lichess blitz of 1365 generally corresponds with rapid of 1550 +/- 140, so upper bound of 1690 one standard deviation away. This means in their analysis, 16% of Lichess players would have around 1365 blitz and above 1690 rapid.
This is really not a huge difference, and if you were wondering whether they are cheating, 1700 Lichess rapid is pretty low (would be about 1300 USCF).

According to https://www.chessratingcomparison.com/graphs

A rating of 1315 in LiChess.org: Blitz would equal 1535 in LiChess.org: Rapid, with an average variation of plus/minus of 101 points.

See for yourself

Perhaps you're a little underrated in blitz. Try playing more games maybe?


text:
Why is there association between a queenless position and the endgame?
Why does there seem to be some idea that trading queens is the start of the endgame? What does trading queens have to do with the endgame? Why are queenless positions often considered to be endgame positions?
I have also heard repeatedly people saying "trading queens doesn't mean it's the endgame guys" so it seems like an "urban myth" kind of thing. How everyone loves debunking common knowledge. That actually shouldn't count as common knowledge anymore because everyone debunks it.
There is definitely some association between having no queens, and the endgame. How did this association begin and why does it exist?

Just a rule of thumb. When the queens leave the board the endgame is seldom far away (if not already there). Don't overthink it. Nobody seriously thinks that all queenless positions count as endgame positions.

@JohnColeman thanks for some insight. I already understood that nobody seriously thinks that, I was just wondering why the association has become such a "thing". And how can you be so certain trading queens does mean you are close to the endgame

For one thing, queen trades typically come after other trades hence in positions that are already closer to being endgame positions. For another thing, liquidation tactics (to transition into easily won endgames) often involve forcing a queen trade.

@JohnColeman It might be a bit of an overstatement to say that "Nobody seriously thinks that all queenless positions count as endgame positions." GM Joe Gallagher, on p. 96 of his book Winning with the King's Gambit, referring to the position after 1.e4 e5 2.f4 exf5 3.Nf3 d5 4.exd5 Nf6 5.Bb5+ c6 6.dxc6 bxc6 7.Bc4 Bd6 8.Qe2+, writes: "The endgame (I have to admit to being one of those people who regard virtually everything after a queen exchange as an endgame) after 8...Qe7 9.Qxe7+ Kxe7 is better for White . . ."

@bof Good point -- but even he hedged his bets with the word "virtually", and the mere fact that he felt compelled to write that suggests that he knew it was a problematic view. I think that the idea appeals to people who don't like fuzzy notions (and "end game" is a fuzzy notion).

Funny, I seem to recall playing some queen endgames...

Some say the endgame begins when the kings can come out and join the fight. Usually it's not safe for them to do so until queens are off the board.

To assume that the game has reached the endgame just because the Queens have been exchanged is a bad conceptual mistake that can lead to disaster.
A classic example is a game Verlinski-Alekhine where Queens are traded very early in the game and white plays the early middlegame "as if" it was an endgame already with the result of getting run over by the young future world champion.
The game is #2 in the collected Alekhine's games written by himself.

(Added) In the classic book of Romanovski, a cornerstone of the soviet school of chess, the endgame is defined as the phase of the game when the Kings take an active role.

Interesting game (which I added a link to as a friendly edit), though it could be argued that the mistake was that Verlinski just played the endgame poorly, neglecting king safety.

@JohnColeman, underestimating the risks your King may run into in the next several moves is an obvious symptom that you think to be playing an endgame while it is actually still a middlegame. Verlinsky did not survive the middlegame ...

Some positions are clearly not end games and some others clearly are. Unfortunately there are some positions in between that seem to defy classification. Why is that?
Wikipedia The start of the endgame does an excellent job on surveying opinions of highly knowledgable players.
Note the quote from the fourth World Chess Champion

Alexander Alekhine:
"We cannot define when the middle game ends and the end-game starts."

Hence sometimes we should take the borderline cases out of the defintion of the general concept, to make it more abstract, simpler and more elastic.
For the offending cases, fundamental strategic questions like king safety, importance of material, have to be decided on a case by case basis.


text:
Why do receive higher ranked players a downfloat in fide swiss pairing?
I am trying to grok the  fide specification of the swiss pairing algorithm, having a hard time with that.
For example rule A.4.b reads:
A4
[...]
b
After two players with different scores have played each other in a round, the higher ranked
player receives a downfloat, the lower one an upfloat.
[...]

According to definition A.2 the player rank changes dynamically, round after round.
My main question here is, at what time the rank of the two players is considered, before or after the round? I personally see arguments for both interpretations.
If I understand correctly, swiss system tries very hard, not to pair moved down players against each other, this is only considered if all other possibilities are exhausted.
Hence if a player was moved down because of rule A.4.b or for some other reason he will be likely paired against a player with different score which is lower ranked before the game and subsequently be eligible for another application of rule A.4.b, either unconditionally or if he stays on top of this opponent.
Hence because of rule A.4.b I expect downfloats to be positively correlated, which seems to contradict the main pairing construction.
It would be helpful if someone with experience in this matters, could either confirm or correct this interpretation and provide some intuition, for what rule A.4.b was introduced for.

After two players with different scores have played each other in a round, the higher ranked player receives a downfloat, the lower one an upfloat.

This is just marking the fact that the higher ranked player had to downfloat and the lower ranked player had to upfloat. The algorithm tries to minimize the number of times this happens to the same player, at least for the next couple of rounds.
It uses the ranking from the start of the round, not the one after the game is completed. It would make little sense to consider an upfloated player to have downfloated just because they won the game. I imagine that it's applied after the game just to take into account the possibility of a forfeit; you wouldn't get an upfloat or downfloat marked to you just because you were paired that way if you never actually played the game.

Only one of the players is moved down to the next bracket for purposes of the algorithm, but both players are playing someone outside their score group, so both are marked with a float.

According to definition A.2 the player rank changes dynamically, round after round

No, I don't think you fully understand what is going on. During the pairing process for a particular round in a given score group the ranking within a score group is fixed according to what the original ranking before the first round.

A.2 Order
For pairings purposes only, the players are ranked in order of, respectively
a score
b pairing numbers assigned to the players accordingly to the initial ranking list and subsequent modifications depending on possible late entries or rating adjustments

If there are no new players to add and no initial entry errors to correct then the initial rankings apply for the complete tournament.
There are only two situations which can give rise to changes to these rankings. These are:

a new player joins the tournament after the initial ranking. In this case the ranking list is changed by inserting the new player in their slot according to their rating.
an error is discovered in the rating entered for a player in the initial ranking. In this case the rating is corrected and if this changes the place of the player in the ranking then this change in position is confirmed.

An example might make it clearer. Suppose in the first round of an 8 player Swiss, with players called in ranking order, "1", "2", "3", "4", "5", "6", "7", "8", with player 1 having white and where all the white players win. Then for the second round there will be 2 score groups with the 2 groups having the following internal rankings.
Score Group 1 point
1
3
5
7
Score Group 0 points
2
4
6
8
Suppose then that a new player, player 9, joins with a rating between player 2 and 3. Then the new overall ranking would be: 1, 2, 9, 3, 4, 5, 6, 7, 8 and this ranking would remain for the rest of the tournament. However for round 2 this would change the second score group as follows:
Score Group 0 points
2
9
4
6
8


text:
Is it true that Grand Master Julio Granda has only read one chess book?
Wikipedia spanish entry for GM Julio Granda says (Google translates):

Julio Granda does not study opening theory. He has stated that he has only read one chess book, the third volume of Roberto Grau's General Chess Treaty.

Is it true?

I heard he also read "Bobby Fischer's Picture Book of Naughty Chess Girls", but I am not sure if that counts.

After several searches I can only find one source in which Granda is quoted about Grau's books. It's this part:

"Yo tenía muchas limitaciones técnicas, así que me ganó con bastante facilidad, pero fue muy generoso porque le dijo a mi padre ‘Che, al pibe le falta Grau’. Mi padre, que no tenía mucho conocimiento de ajedrez en ese entonces, preguntó qué tenía que ver el almirante Grau con el ajedrez, pero en realidad Jorge Szmetan se refería a Roberto Grau, un maestro que dejó una obra muy importante que se llama ‘Tratado General del Ajedrez’. Tuvo el detalle de enviarme los cuatro tomos desde Argentina. Lo anecdótico es que en el correo se perdieron el segundo y el tercero, que son los más importantes, pero mi padre hizo un esfuerzo y pudo conseguirlos"

There he explains that a stronger player (Jorge Szmetan) suggested his father to study Grau's books. Then Granda explains that Jorge himself sent the books by mail, that the second and third ones got lost during the sending, but nevertheless Granda's father eventually got all of them. Then in the same link (and in other similar ones I've found) it explains that his father had him working during weekends on the Grau's books.
All the mentions I've found about "he only read the third tome of Grau" were not quoted and were almost identical to each other.
EDIT: here's another mention to Szmetan and Grau. He explains that his father made him study several books, including the ones by Grau. While he was studying chess his brothers were playing soccer, so he just developed sort of a hate for studying chess. He even mentions it was like a "torture" to him.
EDIT 2: Ok, this is it! At the very beginning of this interview Granda is specifically asked about the Graus and the books he's read.
First things first; he doesn't make any specific mention to the 3rd volume of the Graus (it's a 4 volumes collection).
Secondly, after getting the Graus via Szmeta, it was his father who, during weekends, read the Graus to Granda. So it seems like, literally, Granda didn't read (but listened to) any of the Graus. In any case he states in this interview that the Graus was his only theoretical training.
Also, in this part of the interview he explains that during a one month waiting for his next tournament, he bought a book (El mosaico ajedrecístico, probably this one written by Karpov and Gik) and fully read it without a board ("I was so bored"). Then he states that he's currently (the video is from 2017) studying seriously the game.
So after watching this video it seems like the only book training Granda received were the four volumes by Grau, read to him during weekends by his father when he was about 10 (the game vs Szmetan was in 1977, Granda was born in 1967). After that he only read "El mosaico ajedrecístico". So it seems fair to claim that the legend about "the third volume of the the Graus" seems to be just a legend, but on the other hand it seems like the four volumes by Grau were his only "book training" during all his career (at least until his temporal retirement in the 90s), what looks really like quite and achievement.

"Needs citation!" (xkcd)
That Wiki entry should be either disputed or given a reliable source. I googled a bit:
Chicago Tribune article
Sounds like from an interview, but I'm still not 100% satisfied.
Another link, the danger is everyone is copypasting from everyone else. E.g. here would be the place I expect that it would be mentioned, but it isn't.


text:
How does white stop the three pawns and win this?
I arrived to this position, black, me, to play, in a tournament game, with plenty of time to think on both sides. Stockfish gives initially +55 and finally mate in 27 for white. Fortunately for me, my opponent made a couple of blunders and I won the game.
[white "Opponent"]
[black "Me"]
[StartFlipped "2"]
[FEN "7Q/8/8/8/p2pkp2/Pp2p3/1P2K3/8 b - - 0 1"]

1...f3+ 2. Kf1 {?} Kd3 3. Qc8 {?} Kd2 4. Qd7 {?, now Stockfish says black wins} e2+ 5. Kf2 e1=Q+ 6. Kxf3 Qe3+ 7. Kg2 Qe2+ 8. Kg1 Qd1+ 9. Kf2 Kc1 10. Qc6+ Qc2+ 0-1

Is it so easy to stop the three pawns given the fact the king is protecting one row?
Do you think it is so easy?

Good job winning queen vs 3 pawns, esp with +55 or +74.0 or whatever eval!

Why have this board upside down? The question itself is from the White perspective.

@John Coleman: Presuming it is inadvertent, how could it be changed? Using StartFlipped? And/or using an even number of moves (remove the first or add one)?

The fundamental principle in king-and-pawn endings is that you want to get your king in front of your pawn(s). If your king is behind your pawn then your opponent can block with their king much more easily. Therefore 2.Kf1 is a mistake, because it allows the white king to get in front of the pawns and also attack the black pawns. Whether it is a game losing blunder I'm not so sure, but it does make winning much more difficult. Either 2.Kd1 or 2.Ke1 would be much better with Ke1 being my favourite as it stays in line with the middle pawn.
In general, white's winning plan is to immobilize the black passed pawns and then start winning the pawns when the win becomes easy.
Here's what happens if black still tries to penetrate with 2... Kd3
[fen "7Q/8/8/8/p2pkp2/Pp2p3/1P2K3/8 b - - 0 1"]

1... f3+ 2. Ke1 Kd3 3. Qh7+ {It is vitally important to keep the white king out} Kc4 4. Qf5 {Still keeping the white king out and threatening the f pawn} f2+ {only move to hang on to the pawn for now} 5. Ke2 {Zugzwang! The black king has no moves} f1=Q 6. Qxf1 Kc5 7. Kd3 {and the two center pawns will soon drop}

So the immediate 2... Kd3 is a mistake. Can black still manage it by first driving the white king to f1? Now white can keep maximum pressure by bringing the queen to e4 forcing black to keep defending the e5 pawn, because if black allows Qxe5 with Kc2 going after the b2 pawn then the queen also defends the b2 pawn.
[fen "7Q/8/8/8/p2pkp2/Pp2p3/1P2K3/8 b - - 0 1"]

1... f3+ 2. Ke1 f2+ 3. Kf1 Kd3 4. Qe5 Kc4 5. Qe4 Kc5 6. Ke2 {forcing white to abandon the c pawn} Kb5 (6... Kc4 7. Qc6#) 7. Qxd4

The pawns can indeed be stopped. The problem here is that White has barely tried at all! For instance, after 2.Qh7+ Kd2 3.Qb1, the pawns can go no further: against ...e2+, White can go Kf2 and against ...f2, Kg2 followed by Qf1 should be enough.
2.Qh1 could be an even simpler alternative, preventing the king from marching forward while also preventing ...e2 (because of Kf2) and ...f2.

f2 Kg2 d3 Qf1 Kc2?

@BCLC I guess Kf3 does the job there but I'm not entirely sure... 2.Qh1 may be the easier option


text:
What is the longest known 7-piece checkmate?
What is the longest known 7-piece checkmate?

549 moves. Here is the link to the Lomonosov tablebase for this special position. This record was generated and discovered in 2014 by Guy Haworth; his publication "Chess Endgame Records" can be found at online..
[FEN "1n1k4/6Q1/5KP1/8/7b/1r6/8/8 w - - 0 1"]

1.Kf5 Rb5+ 2.Kg4 Rb4+ 3.Kf3 Nd7 4.Qh8+ Ke7 5.g7 Bf6 6.g8=N+ Ke6 7.Qh3+ Kd6 8.Kg2 Rb2+ 9.Kf1 Rb1+ 10.Ke2 Rb2+ 11.Kd1 Rb1+ 12.Kc2 Rb2+ 13.Kc1 Rb5 14.Qh6 Rc5+ 15.Kb1 Rb5+ 16.Ka2 Ra5+ 17.Kb3 Rf5 18.Ka3 Rf3+ 19.Ka2 Ke6 20.Qh7 Ne5 21.Nh6 Rf2+ 22.Kb1 Rf4 23.Qg8+ Kd6 24.Ka2 Nc6 25.Ng4 Bd4 26.Qg6+ Kd5 27.Qg5+ Ke4 28.Kb1 Nb4 29.Qe7+ Kd3 30.Qh7+ Ke2 31.Qh2+ Kf3 32.Qh3+ Ke4 33.Qg2+ Kd3 34.Qg3+ Ke4 35.Qe1+ Kd3 36.Qd1+ Ke4 37.Qe2+ Kd5 38.Kc1 Kd6 39.Qh2 Nd5 40.Kd2 Bc3+ 41.Ke2 Bd4 42.Qh6+ Kd7 43.Qh7+ Kc6 44.Qg8 Kc5 45.Kd3 Nb4+ 46.Kd2 Nd5 47.Qc8+ Kd6 48.Nh6 Bc3+ 49.Ke2 Re4+ 50.Kf2 Rf4+ 51.Kg1 Bd4+ 52.Kh2 Ne3 53.Qd8+ Kc6 54.Qe8+ Kc5 55.Nf7 Rf2+ 56.Kh3 Rf3+ 57.Kh4 Rf5 58.Nh6 Rf1 59.Qa8 Kb4 60.Kh5 Kc3 61.Qc8+ Kd3 62.Kg6 Rf2 63.Qa8 Rf1 64.Qb8 Kd2 65.Qb3 Ke2 66.Qb5+ Kd2 67.Qg5 Kc2 68.Kh7 Kd3 69.Qb5+ Kc3 70.Qa5+ Kd3 71.Qg5 Rf6 72.Qb5+ Ke4 73.Qb7+ Kd3 74.Qd7 Kc3 75.Qe8 Kd2 76.Qb5 Kc2 77.Qe2+ Kc3 78.Qh5 Rf1 79.Qg6 Rf6 80.Qe4 Kc4 81.Qe8 Kd3 82.Ng8 Rf1 83.Ne7 Rh1+ 84.Kg6 Rg1+ 85.Kf7 Rf1+ 86.Ke6 Rf6+ 87.Kd7 Bc5 88.Nc6 Nd5 89.Nd8 Rd6+ 90.Kc8 Ne7+ 91.Kc7 Nd5+ 92.Kb7 Rb6+ 93.Kc8 Ne7+ 94.Kd7 Nd5 95.Qe1 Rd6+ 96.Kc8 Be3 97.Qd1+ Ke4 98.Qc2+ Kd4 99.Qa4+ Ke5 100.Qh4 Kf5 101.Qh3+ Ke4 102.Nf7 Rc6+ 103.Kd8 Kd4 104.Ke8 Rc7 105.Kf8 Bf4 106.Qe6 Ra7 107.Qe2 Be3 108.Qg4+ Kc5 109.Qc8+ Kd4 110.Qb8 Kd3 111.Kg8 Rc7 112.Qb5+ Kd4 113.Qa4+ Kc5 114.Qa6 Kd4 115.Kf8 Bd2 116.Qf1 Bc3 117.Kg7 Rc6 118.Kg8 Nf6+ 119.Kf8 Rc8+ 120.Kg7 Ne4 121.Qb5 Ke3+ 122.Kh7 Rc7 123.Qb6+ Rc5 124.Qe6 Kf4 125.Qh6+ Kf3 126.Qh3+ Ke2 127.Kg8 Rc6 128.Kf8 Bb4+ 129.Kg7 Bc3+ 130.Kg8 Rf6 131.Qh4 Kd3 132.Nd8 Kd4 133.Qg4 Ke5 134.Qe2 Kf4 135.Qc4 Kf3 136.Qb3 Kf2 137.Ne6 Ke3 138.Qa2 Rf3 139.Qc2 Be5 140.Qd1 Bc3 141.Qc1+ Kd3 142.Nf4+ Kc4 143.Ng2 Rf2 144.Nh4 Nf6+ 145.Kg7 Ne4+ 146.Kg6 Rf6+ 147.Kh5 Kd4 148.Qd1+ Ke3 149.Qb1 Bd2 150.Ng6 Ng3+ 151.Kh6 Bc3 152.Qc1+ Kd3 153.Qg1 Ne4 154.Kh7 Rd6 155.Kg8 Rd8+ 156.Kf7 Rd7+ 157.Ke6 Rd6+ 158.Ke7 Bf6+ 159.Ke8 Rd8+ 160.Kf7 Rd7+ 161.Ke6 Rd6+ 162.Kf5 Rd5+ 163.Kf4 Bg5+ 164.Kg4 Ke2 165.Qa7 Bd2 166.Qe7 Rg5+ 167.Kh3 Ke3 168.Nh4 Rg3+ 169.Kh2 Rg4 170.Qa3+ Bc3 171.Qa7+ Ke2 172.Ng2 Be5+ 173.Kg1 Nd2 174.Qf2+ Kd1 175.Kh1 Bd4 176.Qe1+ Kc2 177.Qe2 Re4 178.Qh5 Nf1 179.Qd5 Nd2 180.Qf5 Kd1 181.Nf4 Be5 182.Qh5+ Kc2 183.Ng6 Bf6 184.Kg2 Bg5 185.Qh7 Kd1 186.Qh8 Be3 187.Qh5+ Kc2 188.Nh4 Bd4 189.Nf5 Be5 190.Qe8 Rg4+ 191.Kh3 Re4 192.Qc8+ Kd1 193.Qc5 Nc4 194.Nh6 Nd2 195.Ng4 Bd4 196.Qb5 Rf4 197.Kh4 Be3 198.Qd3 Bd4 199.Kh5 Re4 200.Qa3 Rf4 201.Qd6 Re4 202.Nh6 Bf2 203.Kg6 Rc4 204.Qe5 Bb6 205.Qg3 Rc6+ 206.Kg7 Rc4 207.Nf7 Bc7 208.Qg1+ Kc2 209.Nh6 Be5+ 210.Kg8 Re4 211.Nf5 Bf4 212.Qh1 Be5 213.Qh3 Kd1 214.Kf8 Bf4 215.Qg4+ Ke1 216.Qg2 Be5 217.Qh1+ Ke2 218.Ke8 Bg3+ 219.Kd7 Bf2 220.Ne7 Rd4+ 221.Nd5 Kd3 222.Kc6 Rh4 223.Qg2 Rc4+ 224.Kb5 Be3 225.Qh1 Bc5 226.Qh7+ Ke2 227.Qh5+ Ke1 228.Kc6 Bd4+ 229.Kd6 Bf2 230.Kd7 Rd4 231.Qh1+ Ke2 232.Ke6 Rh4 233.Qg2 Rc4 234.Ke7 Nf3 235.Qh3 Re4+ 236.Kd8 Rd4 237.Qh5 Bg3 238.Qe8+ Be5 239.Qb5+ Kf2 240.Kc8 Re4 241.Kb7 Bd4 242.Qc6 Rg4 243.Ka6 Rg7 244.Nb4 Re7 245.Nd3+ Ke3 246.Qc1+ Ke4 247.Nb4 Re5 248.Qb1+ Ke3 249.Qc2 Rc5 250.Qd3+ Kf4 251.Qe2 Kg3 252.Qe7 Rh5 253.Nd3 Rh6+ 254.Ka5 Rh4 255.Qe6 Bc3+ 256.Ka6 Bd4 257.Qc6 Be3 258.Qe8 Bd4 259.Qb8+ Kg2 260.Qg8+ Kh3 261.Qg6 Rg4 262.Qc6 Kg3 263.Qc7+ Kh3 264.Nf4+ Kh4 265.Qd6 Kg3 266.Ng6+ Kf2 267.Qe6 Rg1 268.Nf4 Ra1+ 269.Kb7 Ra7+ 270.Kb8 Ra3 271.Qe2+ Kg3 272.Nd3 Rb3+ 273.Kc8 Rb6 274.Qe4 Rf6 275.Kd7 Bc3 276.Nc5 Bd4 277.Ne6 Be5 278.Ng5 Bb2 279.Qe3 Kg4 280.Ne4 Rf7+ 281.Kc6 Rf5 282.Nf2+ Kg3 283.Nd3 Be5 284.Kd7 Rf7+ 285.Ke8 Rf5 286.Qc5 Kg4 287.Nf2+ Kg5 288.Qd5 Kg6 289.Nd3 Bg7 290.Qe4 Kg5 291.Ke7 Bd4 292.Kd7 Rf6 293.Kc8 Rf8+ 294.Kb7 Rf7+ 295.Ka6 Rf6+ 296.Ka5 Bc3+ 297.Ka4 Ra6+ 298.Kb5 Ra5+ 299.Kb6 Rf5 300.Qe7+ Kg6 301.Qe8+ Kg5 302.Kb7 Bd4 303.Qe7+ Kh5 304.Qe4 Rf7+ 305.Ka6 Rf6+ 306.Kb5 Kg5 307.Nb4 Be5 308.Nd5 Rf5 309.Qe3+ Kh5 310.Ka6 Rf7 311.Qf2 Ng5 312.Qc2 Nf3 313.Qc8 Kg5 314.Qe6 Rf5 315.Kb7 Bd4 316.Qe7+ Bf6 317.Qe3+ Kh5 318.Qe4 Kg5 319.Nc7 Nd4 320.Qg2+ Kh5 321.Nd5 Nf3 322.Ne3 Rf4 323.Qh3+ Nh4 324.Qe6 Kg5 325.Qd5+ Kg6 326.Qd6 Kg5 327.Qc5+ Kg6 328.Qc7 Kg5 329.Nd5 Rf3 330.Qc1+ Kg4 331.Ne3+ Kg5 332.Nc4+ Rf4 333.Nb6 Kg4 334.Qd1+ Kg3 335.Nd5 Rf3 336.Qd2 Kg4 337.Ne3+ Kh5 338.Nc4 Bg5 339.Qd1 Bf4 340.Nb6 Bg3 341.Nd7 Kg5 342.Qd5+ Rf5 343.Qe4 Rf4 344.Qe7+ Kg4 345.Qe6+ Kf3 346.Nf6 Kg2 347.Qd5+ Kh2 348.Ne4 Nf5 349.Ng5 Nd6+ 350.Kb6 Bf2+ 351.Kc7 Bg3 352.Kd7 Nf5 353.Qd2+ Rf2 354.Qd1 Rf4 355.Qe2+ Rf2 356.Qh5+ Kg2 357.Kc6 Rc2+ 358.Kd5 Rd2+ 359.Kc4 Rf2 360.Qh3+ Kg1 361.Kb4 Rf1 362.Ka5 Rf4 363.Ka6 Ra4+ 364.Kb5 Rf4 365.Ka5 Rf2 366.Qh8 Kg2 367.Qc3 Rf4 368.Qd2+ Kf1 369.Qd5 Nd4 370.Kb6 Bf2 371.Kc7 Rh4 372.Qe5 Kg2 373.Ne4 Kf3 374.Nd2+ Kg2 375.Qd5+ Kh2 376.Kb7 Rh7+ 377.Ka6 Rh6+ 378.Ka5 Rh4 379.Qd6+ Kh3 380.Qd7+ Kg2 381.Qb7+ Kg3 382.Qg7+ Rg4 383.Nf1+ Kh3 384.Qd7 Kh4 385.Qh7+ Kg5 386.Qg7+ Kf4 387.Qc7+ Kg5 388.Nd2 Rf4 389.Qg7+ Kf5 390.Nc4 Nf3 391.Nd6+ Ke6 392.Ne8 Kf5 393.Ka6 Bd4 394.Nd6+ Ke6 395.Qg8+ Kf6 396.Qh7 Ke6 397.Ne4 Kd5 398.Qb7+ Ke6 399.Ng3 Be5 400.Qb3+ Kd6 401.Qb6+ Ke7 402.Ne4 Kf7 403.Qh6 Kg8 404.Qe6+ Kh8 405.Qe7 Rf5 406.Kb6 Bg7 407.Ng3 Rf6+ 408.Kb5 Nd4+ 409.Kc4 Rc6+ 410.Kd3 Rc3+ 411.Ke4 Rc6 412.Qe8+ Kh7 413.Kd3 Rd6 414.Qh5+ Kg8 415.Ne4 Rd8 416.Ke3 Bh6+ 417.Kf2 Rf8+ 418.Kg2 Kh7 419.Ng3 Ne6 420.Qh4 Ng7 421.Qe4+ Kg8 422.Qd5+ Kh7 423.Qd6 Rf7 424.Qd3+ Kg8 425.Qd5 Bc1 426.Kh3 Ba3 427.Kg4 Be7 428.Qc4 Kf8 429.Qc8+ Ne8 430.Nf5 Rf6 431.Qd7 Rf7 432.Qd3 Bf6 433.Qe3 Be7 434.Qh6+ Kg8 435.Qh1 Rh7 436.Qd5+ Kf8 437.Kf3 Nf6 438.Qe5 Ne8 439.Ke2 Bf6 440.Qd5 Rf7 441.Kd2 Bg5+ 442.Kc2 Rc7+ 443.Kb2 Bf6+ 444.Kb1 Rh7 445.Qf3 Ra7 446.Qb3 Rc7 447.Qb4+ Kf7 448.Qb6 Rd7 449.Qb3+ Kf8 450.Nh6 Rg7 451.Qa3+ Be7 452.Qf3+ Bf6 453.Ng4 Ke7 454.Kc2 Rg5 455.Qe3+ Kf7 456.Qb3+ Kf8 457.Qe6 Bg7 458.Ne3 Re5 459.Qb6 Bf6 460.Ng4 Rf5 461.Qe6 Rf4 462.Qc8 Bd4 463.Qd7 Bg7 464.Ne3 Rf2+ 465.Kb1 Rf7 466.Qc8 Rc7 467.Qa6 Rd7 468.Qa3+ Kf7 469.Qb3+ Kf8 470.Qb4+ Nd6 471.Qf4+ Kg8 472.Nd5 Nf7 473.Qc4 Ra7 474.Nf4 Rb7+ 475.Kc2 Rb2+ 476.Kd1 Rb6 477.Qc8+ Kh7 478.Qc7 Rd6+ 479.Ke2 Kg8 480.Qe7 Bf8 481.Qe8 Ng5 482.Qc8 Rf6 483.Qg4 Bh6 484.Nh5 Re6+ 485.Kf1 Re5 486.Qc8+ Bf8 487.Qc2 Re6 488.Qa2 Kh7 489.Qg2 Kh6 490.Qh1 Rb6 491.Nf4+ Kg7 492.Qh5 Nh7 493.Qg4+ Kf7 494.Qd7+ Be7 495.Qd5+ Kf8 496.Ne6+ Ke8 497.Qh5+ Kd7 498.Ng7 Nf6 499.Qf5+ Kc7 500.Qe5+ Kd7 501.Qd4+ Kc7 502.Qe3 Nd5 503.Qe5+ Kc6 504.Nf5 Rb7 505.Qe4 Kc5 506.Qc2+ Kb6 507.Qb3+ Kc6 508.Nd4+ Kc5 509.Qxb7 Kxd4 510.Kf2 Ke4 511.Qb1+ Kd4 512.Qg6 Bf6 513.Kf3 Be7 514.Qg1+ Kc4 515.Qg4+ Kc5 516.Ke2 Nf6 517.Qf5+ Kd4 518.Qf4+ Kd5 519.Kf3 Ke6 520.Qc4+ Kf5 521.Qa6 Nd7 522.Qd3+ Ke6 523.Qe3+ Kd6 524.Kf4 Nc5 525.Kf5 Bf8 526.Qf3 Nd7 527.Qc3 Ke7 528.Qd4 Ke8 529.Ke6 Nc5+ 530.Kd5 Nd7 531.Kc6 Nb8+ 532.Kb6 Nd7+ 533.Kc7 Nc5 534.Qc4 Be7 535.Qg8+ Bf8 536.Kc6 Na6 537.Qe6+ Be7 538.Qc8+ Kf7 539.Qxa6 Ke6 540.Qd3 Bg5 541.Qe4+ Kf6 542.Kd6 Bd2 543.Qe5+ Kg6 544.Ke6 Bg5 545.Qf5+ Kh5 546.Qf3+ Kh6 547.Qf7 Bh4 548.Kf5 Bg5 549.Qg6#

How do you know it's the longest?

If you follow the link it asserts it is the longest, though I think the answer would be improved if there was a little bit of text saying here is a link to the relevant database, and on the link asserts that this is the longest solution in the database

Very interesting that the line includes a promotion to knight.

The "human-comprehensible" part starts around move 498 (maybe earlier for GMs). It's incredible that all the moves before build up to that attack on the rook.

@theonlygusti the key part is that we have a full 7-piece ending database, so we know that it's the longest by comparing it to every single other 7-piece ending possible and observing that they have a shorter checkmate.