This is a highly possible scenario in a physical casino that you will be beaten up for counting the cards and only in movies i have seen these kind of scenarios but i a virtual casino the house knows the situation and there will be a timer to counter that, not sure what is the solution they are using but these virtual casino will be aware of the thing and will have a solution to counter those.
I'm counting in my head pretty fast. Also, if you know even the basic of probability theory, there will be enough just one look into what hand do you have to choose what to do next.
Here is my old post about probabilities in BJ and this is in fact finished pattern for you to act (at least i used it few times i played BJ with not bad results).
1.
More cards - worse. Less cards - better.
2. You just looking what you have on your hands (some number N).
21 - N = this is what do you need in card suits
3. (N*4 - needed_suits_on_your_hand) / 52 (full deck of cards) is the probability what do you need.