Card counting is keeping track of cards between hands in an effort to figure out altered odds on the current hand. For example, if you're playing single shoe blackjack and have seen 10 high cards out of 11 cards, you know low cards have a higher probability than normal.

That doesn't exist in Holdem, because there's no carry over between hands. Each is an individual event, with no altered probability from previous hands. You can calculate odds, but that's easy even for a human at holdem- if there's X cards which you think will give you the winning hand (called outs), your odds are X/47 on the turn and X/46 on the river, or just under 2% per out. For seeing both cards on the flop its 1-(47-X)*(46-X)/(47*46), or about 4% per out. Generally you just use 2% and 4%, as the nature of holdem makes it unlikely that percent or two you'd be off will make a long term difference.

So there are odds calculation. But there's no card counting. Also, card counting isn't the amazing thing some people think it is- if you don't play deep into a shoe, it isn't much of an advantage. In some games like baccarat its been mathematically proven to not give an advantage at all.

There are 2 poker games where it does help- razz and 7 card stud. This is because each player has a unique hand, including individual up cards. When they fold their hands are mucked. Remembering all the cards which were showing at any time is an advantage, as it can effect the odds of drawing to a straight/flush/full house. I would suspect a computer may have a big edge over beginners on those games due to that. But a pro at those games knows how to remember the dead cards already, I'm not sure it would be much of an advantage at high end stud.