The basic concept of blackjack counting is that a deck filled with 10s and aces will be to your advantage. While the deck of the dealer is filled with smaller cards but is to the dealer’s advantage. Simply put, when the deck is in your favor bet to the maximum, when it’s with the dealer’s bet minimum.
This is because a deck filled with 10 increases the chance of the dealer getting bust. You on the other hand can just opt to stand. In an opposite manner, a deck filled with smaller cards makes the dealers chance to bust less. If you know the deck is filled with 10s or smaller cards, this can give you the advantage of knowing what strategy to use.
The dealer must then always hit until having a soft 17. To hit with a hand of 10 & 6 and knowing the deck is filled with 10s is a bad idea.
If the deck is filled with aces, there is high chance that you’ll hit blackjack. When the player has blackjack, the pay off odds are 3:2. The dealer will only win on the other hand if he also gets a blackjack. That’s why a deck filled with aces is always to the player’s advantage.
Blackjack counting is not done by memorizing each card that has come out of a 6 deck shoe of cards. If you are able to do that, I'd be in awe: you should be in the world records book or maybe even the loony bin.
Blackjack card counting is done by assigning the different card numbers with different point values. Always remember to pick a system that is easy to remember. This will cause fewer mistakes and you will lose less money.
As stated above, you will assign a point value for each card and you will have to add the value of the cards that have come out. This is called the running count. Based on the plus/minus strategy, here are the values assigned.
2, 3,4,5,6 = +1;
7, 8, 9 = 0;
10, J, Q, K, Ace = -1
To illustrate this more clearly:
The first card dealt is an ace, so we start by having -1. Then 6 is the next card dealt so we add 1. This makes the run count back to zero. Then a 3 and 4 follows, making the run count now 2.
After figuring the run count, you can try to figure the true count. You take the running count you have and divide it with the number of decks remaining from the shoe.
The true counts tell you the appropriate bet size and you can base your strategy from there.