Blackjack Mathematics

Also known as “21”, the object of Blackjack is to accumulate cards whose values add up to a total of as close to 21 as possible, without exceeding this value, and ideally equaling it. The face cards are worth 10 points, while Aces are either worth 1 or 10, depending on the sum of the other cards. Blackjack is known to be a game of skill in that mathematical calculations on the part of the bettor can have a positive impact on the outcome of a bet. This is because Blackjack is a casino game that is based on dependent events.

Dependent Events in Blackjack

A dependent event is one that is influenced by – or influences – another event. (See our independent and dependent events page for more on this). In the case of Blackjack, this means that each time a card is drawn from the deck, the probabilities of drawing other specific cards increases with each time that they are not drawn. So, the outcome of drawing a card is to some extent dependent on what card was drawn before it. If you drew a 5 of hearts, then firstly, that card is guaranteed not to come up again, and secondly, other cards have a higher probability of being drawn since the deck is now smaller.

Probability in Blackjack

Because of this dependant nature of events in Blackjack, the probabilities of drawing certain cards are constantly changing, according to what cards have been drawn previously. The theory of probability involves determining the likelihood of an event.

Card counting in Blackjack

Keeping track of which cards have been dealt means that players can make informed decisions about whether to hit (take another card) or stand (stick with what you’ve got). This card counting tactic creates good opportunities to win. If you have an advantage by having insight into the likelihoods of certain cards being drawn, you can make larger bets and thus increase winnings.

With a good strategy involving card counting, you can get the house advantage in Blackjack down to as little as 0.5%. Without a strategy, expect the house to have an advantage of around 7%. These are approximate figures and can vary according to the particular rules of the game.

Read about the casino game mathematics of other popular casino games or have a read through the Gambling Mathematics Glossary for an overview of the most important concepts related to the mathematics of gambling.