Most of the time casinos are quite happy for you to attempt whatever system you think you have, card counting or whatever. Most people are bad at it, and even if you're good, you can't actually "flip" the odds as much as nudge them slightly into your favor. You figure out when you're a _little_ more likely to win and increase your bets by an order of magnitude. If you've done it right (and you probably haven't) and the casino hasn't neutralized your advantage by tweaking the game rules, you will still lose those larger bets a good percentage of the time.
Casinos are quite happy to let you do this, because the average joe doesn't even have the bankroll sit through 3 shoes hoping for a chance to 10x his bet. At a $15 minimum bet table, you could lose $500 in a single shoe, no problem. They'll let you count to your little heart's content, and then when your count is finally advantageous, you'll up your bet to $150/hand and that's when they'll shut you down.