When people think of card counters they tend to think of Dustin Hoffman’s Rainman where the card sharpe can reel off the exact cards that have gone past in order, which isn't to say that those sort of people don't exist. However card counting enough to be able to get the odds in your favour at, say, blackjack is within the remit of everyone.
Ignoring draws where will assume that you just remake your original bet the probability of winning a normal hand of blackjack is 46.36%. Overall the house wins, which is the point, they are trying to make money after all. This figure assumes you play perfectly every time, but in practice that isn't too hard to do compared with other deterministic games. You only have two cards and the dealer has one visible card which only gives a small number of possible situations. Usually it is only the total of your cards that matters, but having an ace or having a pair opens up different possibilities. Here is the entirety of the strategy and you can commit it to memory in an evening:
But learning the strategy of a game which leads to a net loss for you in the long run isn't particularly inspiring. Even the simplest of card counting strategies named the Hi-Lo method lowers the house odds to essentially 0, and a few extra tricks can increase it into your favour (slightly). The Hi-Lo count is to add 1 to a total in your head every time you see a 2, 3, 4, 5 or 6 and to subtract 1 for every 10, J, Q, K or A. When the count is large we say the deck is hot and it is time to increase your bids. The idea is that getting a blackjack itself (an ace plus any of the cards worth 10) pays out 3 to 2 which greatly benefits the punter. As the count dips into the negatives it’s time to lower your bids or move to another table.
Typically blackjack works with 6 to 8 decks all mixed up and placed in “the shoe”. When the supply of cards runs low the house reshuffles and resets the count. It is just before this that your count makes the most difference. To know that there are 10 extra high cards is a lot more significant when there are only a couple of decks left than when the shoe is mostly full.
Oh and before you say it, card counting has never been illegal dispite what Hollywood suggests. The casino may stop accepting your bids if you make it too obvious, which is absolutely their right, but you will neither be arrested nor have the heavies take you to a back room.