A distinctive ability of a good player is the ability to count cards that have left the game. It is not for nothing that such players are called counters.
While playing blackjack, they carefully monitor the cards used, trying to adjust the probability of the next cards appearing and predict the course of further events. However, we will start by looking at a very simple model based on the fact that cards of different denominations come out of the deck evenly. In other words, we assume that the probability of the appearance of a card of a certain rank (say, an ace or an eight) is 1/13, tens - 4/13 (recall that in addition to the usual tens, this includes pictures).
The hypothesis we have adopted reflects the simple case when the players do not make special calculations, but act only according to common sense, believing that "distortions" are rare. On the other hand, you can imagine an endless deck consisting of an unlimited number of 52-card decks, or the usual “big deck”, where all the cards not participating in the current deal are constantly mixed and shuffled. In such situations, card counting would be meaningless, and our hypothesis would become an immutable fact.
However, this is not so far away. At one time, a lot of counters appeared in the casino, which put the existence of blackjack at risk, but the antidote was found pretty quickly. A third, or even half of the "big deck" began to be excluded from the game using a special cutting card, and the efficiency of card counting decreased significantly. And in many European casinos, mechanisms have already appeared that at any time allow the dealer to mix the played cards with the remaining part of the deck in the game. The cards are shuffled randomly, which effectively means shuffling. As the cards out of the game are constantly being returned to the deck, the shuffle becomes potentially infinite ...
Now we will consider a strategy of the game, which, within the framework of the uniformity hypothesis, allows the player to act optimally. But since the strategy works with this concept in mind, it is called not optimal, but basic. Indeed, enumerators trying to assess the current situation at the table will find an excellent starting point in it. We'll come back to the issue of card counting and adjusting the basic strategy later.
Source: https://stargambling.net/games/blackjack/
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