What are the mathematical probabilities of getting certain hands in blackjack (e.g. blackjack, pairs, hard totals)?

[James108]

The probability of getting certain hands in blackjack is determined by the number of decks used and the specific rules of the game. For example, the probability of getting a blackjack in a single-deck game is about 4.8%, while the probability of getting a blackjack in an eight-deck game is about 4.7%. The probability of getting a pair in a single-deck game is about 12%, while the probability of getting a pair in an eight-deck game is about 11.6%.

 

[CR7]

In blackjack, the probability of getting certain hands depends on the number of decks used and the specific rules of the game. Let's delve deeper into the probabilities of getting specific hands based on the number of decks:

1. **Blackjack Probability**:
- In a single-deck game: The probability of getting a natural blackjack (an Ace with a 10-value card) is around 4.8%.
- In an eight-deck game: The probability of getting a blackjack decreases slightly to about 4.7%.

2. **Pair Probability**:
- In a single-deck game: The probability of getting a pair (two cards of the same rank) is approximately 12%.
- In an eight-deck game: The probability of getting a pair is slightly lower, around 11.6%.

These probabilities are influenced by factors like the number of decks in play, the specific rules regarding splitting and doubling down, and the composition of the remaining deck.

Keep in mind that these probabilities serve as estimates, and actual probabilities may vary slightly based on specific game variations and conditions. Basic strategy and card counting can also impact these probabilities by altering the composition of the remaining deck.