Blackjack Systems Math

gambling mathsThe game of Blackjack, or twenty-one, is probably the most popular card game played in casinos worldwide. Thanks to its great popularity, Blackjack is among the games that have been reported as the most profitable for casinos around the world.

The games with the dealer shuffling the cards at random and then the players are given the chance to place their bets. The matter is not really materially affected by the number of decks involved in the game, which could generally be 1, 2, 4, 6 or 8. Players can choose the amount of their bet according to the minimum and maximum limits allowed at the table.

Then, the players’ hands are dealt after the players have placed their bets. Over the game, every player uses their skills and personal strategies in order to improve their hand. A last, the dealer reveals their hand and all bets are settled.

Although Blackjack’s rules could slightly vary, the main objective of the game as well as the card’s values are all the same. The player is aimed at making a hand which total value is as close to 21 as possible without surpassing this value, or ideally equalling it. All face cards are worth 10 points, Aces equal either 1 or 10, and the rest of the cards equal the number printed on them.

Dependent Events in the game of Blackjack

A dependent event is considered one that is affected by, or affects, another event.

When it comes to the game of Blackjack, the more cards are drawn from the deck, the larger the chances of drawing other specific cards. If we have to put this in other words, the outcome of drawing a certain card depends on the card that was drawn before that to some extent.

Card-Counting – the Major Myth of Blackjack Gambling

Card-counting has always been one of the most commonly-spread myths related to blackjack. According to the card-counting rule, the player is able to beat the dealer by simply keeping track of the cards that were dealt. However, the situations for the casino customer would vary according to the circumstances.

According to some blackjack experts, the situations would be favourable to the player in case that the so-called high cards, or in other words 10-valued cards and Aces, are predominant in the remainder of the card deck. The situation is considered as unfavourable to the player if there were more small cards (the cards from 2 to 6) in the remainder in comparison to the high cards. The rest of the cards – the 7, 8 and 9-valued ones – are considered neutral.

In addition, various counting-card systems provide the blackjack player with an advantage in case that the deck is well shuffled.

As already mentioned, card-counting has always been considered to offer a slight advantage in card games, especially in the ones played with one deck only. In such cases, the player is considered literally able to destroy the blackjack game if being aware of the deck’s composition as well as the remaining cards’ sequence. The problem is that no player will be able to guess the exact sequence of the cards that remain in the deck, which puts them with the same probability for getting the high cards as the dealer. Things get even more complicated when there are two and more blackjack players at the same table.

All players around the table get both the low and the high cards distributed totally at random among them. When a one-deck game of Blackjack is played head-to-head against the dealer, the player gets a slightly higher chance for making a Blackjack. The same rule is applied to the dealer, but there is a difference in the player’s and the dealer’s pay-off. The player gets 150% for a Blackjack, while the dealer is always paid 1 to 1 when making one.

Unfortunately, the card-counting approach is one of the myths used as a successful means of advertising for casinos. It is certainly attractive to players who believe that counting the cards is what would bring them an advantage to the casino. In addition, it has been statistically proven that counting cards offers up to 2% advantage for the player, which is not such a great margin. The truth is that sometimes the counting-cards strategy can easily eliminate the player’s small potential 2% advantage.

blackjack players in casino


Variance is actually the difference between the expected advantage and the actual results of the player. The term is one of the most commonly-used ones, but it is also greatly mistaken with pure luck, which is not correct.

Standard Deviation (SD)

Standard deviation is normally referred to how far or how often a certain outcome is to deviate from the average. Variance and standard deviation normally stick together. If the player manages to figure out the variance they have in a game of blackjack, and what the standard deviation is in any game in particular at any stakes could be helpful to form a proper assessment.

N-Zero (N0)

N-Zero is not considered very popular among new blackjack players. This is actually the number of hands that are theoretically required before hitting a goal of being ahead by one standard deviation only. Only playing with the same set of rules and betting strategies offer players the chance to get the most accurate evaluation of N-Zero.

Certainty Equivalence (CE)

Certainty Equivalence is a result of taking the expected win rate and adjusting it depending on the level of risk taken in proportion to the current player’s bankroll and how tolerant to risks they are. In other words, the certainty equivalence show players if a certain game is worth playing when compared to their bankroll.

playing casino blackjack

Blackjack Systems

Literally all practical winning strategies for the blackjack player are based on the knowledge of the changing composition of the card deck. A certain point value is assigned to each card.

The point value is chosen to be positive in case that the card out is favourable to the player and is chosen to be negative in case that it is favourable to the casino. The point value’s size, on the other hand, reflects the size of the card’s effect, but it is normally chosen to be a small-digit one for practical purposes. This is when the cumulative point count is considered to be proportional to the expectation of the casino player.

The fractions of each type of card are believed to be determinant for the players strategy and corresponding expectations, which only slightly change with the size of the pack. This is exactly why the better systems are believed to be bringing things back to normal thanks to the fact that they divide the cumulative point count by the total number of the unseen cards remaining in the deck. The truth is that most point count systems are associated with zero cumulative total for the full pack.

The idea on which point count systems are based is to assign point values to each card of the deck. Point values, on the other hand, are proportional to the effects of deleting the so-called small quantity of that card. The best thing a blackjack system could do is find a compromise between simplicity and accuracy.

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