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Is there a relationship between our lichess rating and our intelligence ?

Yes, infact cheaters with 3200 rating are very smart.
I'd say 50%50.
Because the Rating number is a reflection of how skilled you are at chess, many things could be taken into consideration here,such as : are you physically fit at the times you play or you playing on an empty stomach. All of those things have an influence on performance .
If you are playing for example on an empty stomach, then you are risking losing rating points due to lack of concentration etc...
I know from own experience, I sometimes decide to play before I'm due to go to sleep, and end up losing 3 games, therefore losing around 15 rating points, that doesn't alter intelligence in general.
So yeah 50% yes and no.....
Not really

I know some 1800s (yes I know I’m 1800 I’m not talking about myself) that are some of the smartest people I know

I also know 2200s that might be some of the dumbest people I know
Sure there is a relation between intelligence and Lichess rating because smart people play on Lichess...
Of course.

There is a correlation between chess rating and certain kinds of intelligence -- like spatial intelligence.

To be good at chess you must be able to recognize patterns and manipulate objects in your mind, so you would expect a GM to have a high score on something like the Raven's test. Maybe 125 minimum for GM level.

But correlation isn't causation. Many people have high spatial intelligence, yet they are not good at chess because they don't study the game. To be a GM, you need to study chess. It's not enough to have high spatial.

And how many people want to spend 10,000 hours studying theory?

Not me.

It takes a very dedicated person to achieve that level of play.
@Sleprithslayer said in #8:
> There is a correlation between chess rating and certain kinds of intelligence -- like spatial intelligence.

One might think so, but strangely enough, when Garry Kasparov actually did a formal IQ test in 1987, designed especially for the occasion and conducted by London psychologist Jürgen Eysenck for the German magazine DER SPIEGEL, one of the findings was that his spatial intelligence was "seriously underdeveloped" ("stark unterentwickelt") and failed to reach the average level of either a control group of German chess players or of a group of Berlin school children that Eysenck had perform the same test.

Given as a number, Kasparov's IQ overall was measured as 135 in one of the test suites, and as 123 in another.

www.spiegel.de/politik/genieblitze-und-blackouts-a-1a1cbaba-0002-0001-0000-000013526693

Yet, if you browse the internet, you'll find fantasy IQ values given for all kinds of intellectuals (Einstein, Goethe, John Stuart Mill etc) who often lived before the era of IQ tests and were certainly never tested. Near the very top of those fantasy lists you'll often see Garry Kasparov listed as having a flashy 200+ IQ.

Plenty of GMs, including Magnus Carlsen, have come out claiming that they don't believe there's much of a correlation between chess playing strength and IQ. But unfortunately, people refuse to believe them.