Blackjack is the name of the game. So what are the odds of getting dealt a blackjack? The probability depends on how many decks are played. Of course the essential ingredients to blackjack are an ace and a ten-value card (10, jack, queen, or king). In a single deck game there are 4 aces and 16 ten-value cards. You can get blackjack in one of two orders:
1) A ten-value card followed by an ace
2) An ace followed by a ten-value card
If we add the probabilities of these two events, this will give us the odds of getting blackjack.
The odds of getting a ten-value as your first card is 16/52. 16 ten-value cards divided by the total number of cards in 1 deck. The fraction 16/52 reduces to 4/13. The odds of getting an ace as your second card are 4/51. 4 aces divided by 51 cards remaining. Multiplying 4/13 by 4/51 gives us the odds of getting a ten-value card followed by an ace.
1) 4/13 x 4/51 = 16/663
Looking at the second scenario, the odds of getting an ace as your first card is 4/52 (4 aces divided by 52 cards) which reduces to 1/13. The odds of getting a ten-value as the second card are 16/51. 16 ten-value cards divided by 51 cards remaining.
2) 1/13 x 16/51 = 16/663
Adding the probabilities of the two different orders in which you can get blackjack (16/663 + 16/663) yields the total probability of getting blackjack.
16/663 + 16/663 = 32/663 = 4.827 %
For a 6-deck shoe, the same principles apply but the number of cards changes. In 6 decks, there are 24 aces, 96 ten-value cards, and 312 total cards.
1) Ten-value cards / Cards Remaining x Aces / Cards Remaining
(16 x 6) / (52 x 6) x 24 / (52 x 6) – 1
96 / 312 x 24/311 = 288/12,129
2) Aces / Cards Remaining x Ten-value cards / Cards Remaining
3/39 x 96311 = 288/12,129
The sum of the the two probabilities is 4.749% which means that you’ll get blackjack once out of every 21 hands.