# The Odds of Getting a Blackjack

Blackjack is one of the most popular casino games worldwide, partly because of its simple rules that have remained unchanged for decades and partly because it offers players the opportunity to get a good payoff by playing well. Although some players believe that blackjack is a game of luck, it is possible to increase your chances of winning by practicing optimal strategy and managing your bankroll effectively.

The odds of getting a blackjack are calculated using the probability that the dealer has an ace as his or her first card and the probability that the player gets a picture card or 10 as his or her second card, resulting in a total of 21 in two cards. This combination is called a natural blackjack. If the player has a natural blackjack and the dealer does not, the player wins. Otherwise, the hand is a push, and neither the player nor the dealer wins.

Having the right strategy is important when playing blackjack, as it will help you win more hands than you lose. This is the key to long-term enjoyment of the game, but many players don’t consider their odds of winning or losing before they play. This is a mistake, as the player’s odds can be calculated with a bit of math.

The probability of getting a blackjack is equal to the probability that the player draws an ace and the probability that the dealer draws a ten-card, given that the deck is shuffled before each round. This is called the Fundamental Theorem of Probability, or FTP. This theorem is a result of the law of multiplication, which states that the probability of two independent events can be found by multiplying their respective probabilities.

Another way to determine the odds of winning is to use a concept known as expected value, which can be used in poker and blackjack. This concept is similar to the probability of winning, but it gives a more accurate and useful picture of the overall odds of a hand.

When you are dealt a hand of 12, and the dealer has a 3, it is usually a good idea to hit because the dealer will bust with 28.1% probability, which is more than you can expect from a hit.

However, when you are dealing a hand of 12 against the dealer’s 4, you should stand because it will only improve your odds of winning by a mere 0.2%. If you are not a high roller, this is a very small advantage to gain over the dealer, and it is worth the effort to learn this simple strategy. It will also keep your winning streaks in check, and prevent you from increasing your wagers too much during a losing run, which can easily ruin your experience with the game.