Blackjack: What are the Odds?

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.

Comments

  1. thom waters says:

    Enjoyed the article. One question. Is it possible to determine the probability and odds for getting a total of exactly 21 on your first 3 cards? This would be on any three cards totaling 21. If the probabilities for getting a blackjack mean that you’ll get one every 21 hands, how many hands will it take to get exactly 21 on the first three cards? I’m thinking this might affect how you play double down strategies. Previous cards played must factor into this also. Thanks.

  2. The odds aren’t as bad as I thought. Might give it another go. i just hate turning a fun game into a math problem.

  3. The calculations arent completely correct, they do not take into account that you are not alone playing.
    Say its only you and the dealer, then you would first get one card, then the dealer gets one card face down and then you get another card, meaning that by the time you get your second card the number of cards in the pile is 50 instead of 51 which changes the calculation. But thats the easy part.

    There is also a possiblity that the dealer got the ace/ten you need with his face down card so in order to take this into account, you need to figure out what the chance is that he got your ace/ten and what the odds are in case he has it, combining this and you can figure out what the real chance of a blackjack is.
    Note that it also changes with more players, but it doesnt matter weither their cards are face up or down, but it matters weither someone before you choose to hit/double etc.. making the calculations extreme

  4. Before the cards are dealt, the dealer’s cards are unknown & therefore do not factor into the odds of being dealt blackjack. The number of other players at the table is also irrelevant as their future cards are unknown as well. How player’s play out their hands also has no impact on the probability as these decisions occur after you have already received your two cards. The 4.79% odds of being dealt a blackjack is an average probability, based on no prior information. Of course if you were to keep track of the total number of cards dealt, including the exact number of ten-value cards & aces, you could calculate the precise odds before any given round.

  5. Mike,
    I really enjoy your site here and have found a lot of your information to be very useful. I count and do fairly well…meaning I don’t lose as much as I used to and have started making fair amounts of money when I play. I only play double deck games dealt up on the table…..nothing else. Am I missing out on the other games …..the 6-8 deck games? What are the advantages and disadvantages besides the amount of cards I have to count and concentrate on? My thought would be that my chances are best ( I play alone) because the deck can’t go as drastically one way against me as easily as that seems to happen in multi -deck games. I would appreciate any advice on this. Thank you!!

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