Check out this thread - https://bitcointalk.org/index.php?topic=717790.0
It 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 herebon the form if you're withdrawing below $2,000 to $3,000, but always do your research before depositing.