I'm better at chess than chess is at me.
What do you say when people ask how good at chess you are ?

Non chess players who ask how good are you (you are?) at chess, usually are asking how smart are you. They think chess as a strategy game where a person have to be really smart to be good at... So you can safety answer i am pretty smart .. (at this game).
since everything is relative. this answer "I am pretty smart (at this game)" is probably a good answer for most of us...
but it pays to be Coy (or uncertain) when you are asked because you really can't know how strong they other person is.
I still think that when I ask someone if they are good at chess, and they come across as very arrogant- most of the time THEY are not good at chess, at all...
people that don't play online in with a club, sometimes think they are much better than they are. so being uncertain about that question, is the mark of someone who knows just how chess can be.
Yeah, if your intention is to impress someone, it's usually better to act like you're not very good. People, even 1000s of years ago, seem to be intuitively aware of the Dunning-Kruger thing.
Some relatives who lived in China for over a decade said part of their culture is a true master (whether it's enlightenment or a skill) is humble and unassuming. Someone you'd never guess was amazing until you saw it for yourself... not that other cultures don't have this, but I thought it was interesting.

If someone asks that, a correct answer is probably "better than you". (otherwise they will probably ask, if anything, what your FIDE/ELO/USCF/ECF rating is lol)
I mean, I'm not good at chess. But I've played a lot, so I can beat someone who hasn't. It's not some entirely intellectual activity that anyone can pick up how to do well in through reasoning; it's just like most things, practice is everything.
It is annoying when people insist you're good though. Like I could beat anyone at school pretty easily when I was still there and had just picked up chess and studied basic strategy and tactics, and everyone said I was really good at chess, but I knew, having like a 1000 rating on here, that I was crap really. It's all relative, I guess.

People can be impressed easily on subject that they don't or know little about. Specially when generally chess is considered intellectual game. And why not take advantage? In my area there is big chess club for children 6-14 years of age. Every time when some kid wins local tournament or shows good results it receives medals, a cup, list of paper saying he is awesome, big pictures posted on facebook, respect from other kids and a lot of smiles and happy parents who pays a lot for their kids to practice chess. As you know chess lessons are expensive.
And Imagine you are at party and a woman with kid heard you are pretty good at chess and wants her kid to learn it too and it pays you.. easy money.

Where are you from? Chess here , or at least was, something to brag about, specially 10y ago when Topalov was World Champion. If you knew how to play "good" you get a lot of respect.
I think that would make it hard though, to tell people in Bulgaria you are very good maybe they will expect GM?

Well generally speaking our nation have been almost always close to top - if you check olympiad records and we have high standarts, but not everywhere - a lof of small cities you can be considered an expert. And thats not uscf expert, but actually a master

I'm better at chess than chess is at me.
Good one 👍 👏
Thank you, sir.

I'm better at chess than chess is at me.
Good one 👍 👏
Thank you, sir.
haaave .. no idea what this means xD

This question can only really come from a non chess player, otherwise they would ask what your rating is.
If you want to give an honest answer, you can give them a quick overview of the Elo scale. E.g. my rating is x, a beginner is about 800, an average club player is about 1500, strong club player about 2000, a professional about 2500, the world champion about 2800.
do people get impressed by your ability ?