Check out this thread -
https://bitcointalk.org/index.php?topic=717790.0It contains a list of casinos with info on whether they request for kyc or not, you can also read their terms for the exact amount that triggers the requirement to submit documents.
You won't have trouble with kyc on most casinos here on the forum if you're withdrawing below $2,000 to $3,000, but always do your research before depositing and bear in mind that casinos always reserve the rights to request for kyc at any time.
Not 100% true and you shouldn't give advice if you're not 100% sure of what you are saying. Some casinos might let you wd $2000 or $3000 a few times but when you hit a certain threshold hold, maybe 20k in total wd, that might trigger kyc.
Bottom line, if the ToS mentions kyc blah blah anything, be prepared that at some point they will likely nail you for documents.