Odds of Being Dealt Blackjack

Posted By: Date: 10/13/2012 at 12:00 am Leave a comment

Sometimes it seems like the dealer is hitting blackjack way more often than should be probable. The same can be said for a player. And of course, the exact opposite rings true at times, where the player or dealer go extenuated periods of time without landing a natural blackjack.  As we all know, blackjack is, in part, a game of luck. Over the very long term, yes, the amount of times a dealer or player gets dealt a blackjack, compared to the times he does not, will fall directly in line with said probabilities. However, there are also streaks of luck ““ both good and bad ““ for everyone; player or dealer.

The exact probabilities of a player or dealer being handed a natural blackjack are 1 in 20.71875, or 4.83%. This means anyone at the table is likely to receive a blackjack one time out of every 20-21 hands.

We achieve this number by doing a lot of math, which brings us to 663 possible hands that can be dealt. Out of these hands, 32 of them can be blackjack. These include A+10, A+J, A+Q, A+K, and the reverse, 10+A, J+A, Q+A, K+A. That’s 8 ways, multiplied by 4 suits, which results in 32 possible blackjack hands. Divide 663 possible hands by 32 blackjack hands and we get 1 in 20.71875, or 4.83%.

An even more fascinating question, which serious blackjack players should be very interested in, is this: What are the chances the dealer has blackjack when his exposed card is an Ace or 10/Face Card?

That is an extremely good question, and since we know the dealer already has half of the hand made, the probability of the dealer making blackjack is a lot more likely than it was before any cards were dealt.

Surprisingly, the odds of the dealer being dealt a blackjack can vary based upon the number of decks in the shoe. One might think that the more decks there are, the more often a blackjack is probable to occur. There are more Aces, more 10’s, more Face Cards to draw from, but the actual chances of hitting a blackjack will decrease ever so slightly with each new deck added to the shoe.

It might seem strange that the odds would change at all just because new decks are being added. Each deck is perfectly similar to the others. The odds of being dealt a blackjack from the start don’t change. Likewise, if you flip a coin, it does not matter what the previous result of the flip was ““ heads or tails. With every new flip, the odds of it landing on heads or tails is always 50/50. Knowing this, how can adding another replicate deck to a blackjack shoe change the probabilities of the dealer having a blackjack?

The reason is because we have to account for all of the other cards, which make up nearly two-thirds of each deck. The more “other”? cards there are, the less likely it becomes that the exact card needed will be dealt. The change in probabilities is extremely slight, but it does exist.

For the dealer, the probability of being dealt a natural blackjack, according to the exposed card, are as follows:

Odds of Dealer Getting Natural Blackjack When Dealer has Ace Showing (Needs 10 or Face Card)

  • 1 Deck of Cards: 31.3726%
  • 2 Decks of Cards: 31.068%
  • 3 Decks of Cards: 30.9677%
  • 4 Decks of Cards: 30.9179%
  • 5 Decks of Cards: 30.888%
  • 6 Decks of Cards: 30.8682%
  • 7 Decks of Cards: 30.854%
  • 8 Decks of Cards: 30.8434%

Odds of Dealer Getting Natural Blackjack When Dealer has 10 or Face Card Showing (Needs Ace)

  • 1 Deck of Cards: 7.84314%
  • 2 Decks of Cards: 7.76699%
  • 3 Decks of Cards: 7.74194%
  • 4 Decks of Cards: 7.72947%
  • 5 Decks of Cards: 7.72201%
  • 6 Decks of Cards: 7.71704%
  • 7 Decks of Cards: 7.7135%
  • 8 Decks of Cards: 7.71084%
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