What Is the Probability of Being Dealt Blackjack?
Short Answer
The probability of being dealt a natural blackjack is approximately 4.83% with a single deck and 4.75% with six decks — roughly 1 in 21 hands. The probability decreases slightly as the number of decks increases, because the effect of removing an ace or ten from the shoe is smaller in a larger deck.
By The Numbers
Probability of Being Dealt Blackjack by Deck Count
| Number of Decks | Probability | Approximately 1 in |
|---|---|---|
| 1 | 4.827% | 20.7 |
| 2 | 4.780% | 20.9 |
| 4 | 4.756% | 21.0 |
| 6 | 4.749% | 21.1 |
| 8 | 4.745% | 21.1 |
Formula
P = 2 × (A / N) × (T / (N − 1))
Where A = number of aces, T = number of ten-value cards, and N = total cards in the shoe.
Single deck: 2 × (4/52) × (16/51) = 2 × 0.0769 × 0.3137 = 0.04827 ≈ 4.83%
Six decks: 2 × (24/312) × (96/311) = 0.04749 ≈ 4.75%
Why More Decks Lowers the Probability
In a single deck, removing one ace noticeably changes the chance the next card is a ten. In a six-deck shoe, removing one ace barely changes the composition, so the two events are closer to independent — and the small positive correlation that boosts blackjack frequency is reduced.
Detailed Explanation
What counts as a natural blackjack: An ace plus any ten-value card (10, J, Q, K) dealt as the initial two cards. The formula counts both orderings: ace-first and ten-first, which is why the result is multiplied by 2.
Worked example (single deck): There are 4 aces and 16 ten-value cards in 52 cards. The chance the first card is an ace is 4/52, and the chance the second is a ten is 16/51. Doubling for the reverse order: 2 × (4/52) × (16/51) = 128/2,652 ≈ 4.83%.
Dealer blackjack: The dealer has the same probability of being dealt a natural. When the dealer's upcard is an ace, insurance is offered. The probability the dealer has blackjack given an ace upcard is roughly 30.8% in a single-deck game — which is why insurance is a losing bet (it pays 2:1 but the true odds are worse).
Impact on house edge: The 3:2 blackjack payout is one of the player's few advantages. Switching to 6:5 reduces the payout and adds about 1.4% to the house edge, in part because the natural blackjack occurs on ~4.8% of hands.
Limitations & Context
- •Figures assume a fresh shoe; probability shifts slightly as cards are dealt
- •Dealer and player blackjack probabilities are symmetric at the start of a shoe
- •These are per-hand probabilities, not session or bankroll outcomes
- •Probability does not change the negative expected value of the game
- •Card counting does not meaningfully change natural-blackjack frequency