maybe I can help...
I have no casino play(as I am Far too young and can not count anyway) however, I believe it mainly depens on the joint, your bankroll and your bet ramp, for example, if you're playing a 1-10 black chip spread at a green chip you might get one backoff before a barring. If your're playing a 1-10 red chip spread at the mgm grand in las vegas they probably won't even notice you. however, if your playing 1-10 black or purple chip spread at the mgm in vegas they will most likely take notice and depending on how long you've been watched you might get one back off. Of course this again all depends on a number of factors, if you play at a local joint where they know you (especially if you always play during the same shift), if you have a players card(this makes easier to track your play), length of sessions(it's is less likely they'll be able to gain enough information to decide weather your winning is luck or skill if you only play for 1 or 2 hours at a time instead of say 4 or 5) and last but not least when you play(busy holiday weekends or wednesday afternoons, the busier the time the easier it is to blend in and not be noticed)
So I would conclude one maybe two backoffs tops before a barring. However, this is purely an opinion formed on what I've read and nothing more. Maybe some one with more experience can can tell us if I'm right. Any takers?