Odds and Probability in Blackjack
Blackjack is a game that many people take very seriously. Because it is a gambling game where the odds of any particular outcome can be determined somewhat accurately, the odds have been studied extensively. The best players in Blackjack do not make winning any particular hand a priority, but strictly make the best moves based on the probable outcomes. In fact our section on Blackjack strategies is all about keeping the odds as much as possible in favor of the player.
A good player will also understand the mechanics behind the strategies. This is important because it allows the player to more easily remember what to do in infrequent circumstances as well as to apply probability to other appropriate aspects of life. One must first understand the makeup of a deck of cards. Of course, there are 52 cards in a deck, and each numbered card will comprise four of those. This means that if a player were to draw any particular card from the deck that the chances of it being, for example, a seven would be 4 in 52. This can be expressed as a fraction as 4/52. Recalling middleschool math, you will realize that this fraction can be reduced to 1/13.
But in Blackjack of all the possibilities the most likely possibility is that there will be a 10card played. This is because there are 4 cards out of the thirteen in a suit that have that value.
To see how the odds of a particular situation are calculated we will answer the following question: "What are the odds of a dealer going broke if the turned up card is a 6?" Well, let's see:
If the hole card is a 10, the dealer would go broke on any card greater than a 5, which turns out to be 8 cards out of 13, which we can view as 8/13. Using our trusty calculator we can make this fraction into a percentage: 61.5%. The dealer's hole card will be a 10pointer just over 30% of the time. If the hole card were between six and nine the dealer might still go over 21.
To see how the odds of the dealer going bust take a look at the following table:
Dealer's turneddown card

Chances that this is the hole card (a)

Chances of going bust with this card (b)

Total chance of this circumstance
occurring and resulting in a bust
(a X b)

Ace

1/13 = 7.7%

0%

0%

10

4/13 = 30%

8/13 = 61%

32/169 = 18.3%

9

1/13 = 7.7%

7/13 = 53.9%

7/169 = 4.1%

8

1/13 = 7.7%

6/13 = 46.8%

6/169 = 3.5%

7

1/13 = 7.7%

5/13 = 38.5%

5/169 = 2.9%

6

1/13 = 7.7%

4/13 = 38.5%

4/169 = 2.3%

5 or less

4/13 = 38.5%

0/13 = 0%

0/169 = 0%

Total chance of dealer going bust





31%

Now you can begin to see why a player with a score higher than 11 should never take a hit when the dealer turns up a 6. For every time the player with a 12 or more gets a hit, he increases his own likelihood of exceeding 21. Even a 12 has a 4 in 13 or 4/13 chance of busting 21 (about 30.8%). Though taking a card might improve the hand in the cases when the dealer does not bust, the odds are good that the player will bust before the dealer does or not improve his or her hand sufficiently to beat or tie whatever the dealer's next inevitable card will be. The odds in taking a card only get worse as the score gets higher.
Let us say that our player decides that it would be wise to take a card in the above circumstance, that he had an absolute hunch that the dealer's hole card was a three and that the next card from the top of the deck was sure to be a ten. Thus the player must tie or beat 19. The chances of doing this are fairly limited. Only 3 cards will allow the player to do so in one hit, a 7,8, or 9. This gives the player only 3/13 odds which comes out to about 23%. Illustrating why it is better not to play hunches and to stick to the best odds.
It should be understood that the odds above are based on the idea of using an infinite number of decks. The actual percentages will vary based on the number of decks used in play versus cards have already been played, even those currently in the player's hand. We will comment on this later when we go into card counting.
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