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Introduction to Blackjack statistics

If you want to win money at Blackjack, you need to be familiar with the probabilities that govern this card game. You must understand them and master them. In this article, we will introduce you to probability in Blackjack.

The Basic Strategy advantage

There is a relatively simple method for diminishing the house’s advantage. This method is called Basic Strategy. When it is not used, you have a payout rate between 95 and 97%, according to the rules applied to the game. Thanks to this method, this percentage can surpass 99%.

Passing 21 at the same time as the dealer

During a game, it is possible for both you and the dealer to pass 21. The verb “bust” is used in this situation. The probability that you both bust at the same time is 8%. However, if this happens, the bank does not lose money. This is one feature of the game that helps explain the house advantage.

Methods to banish from your repertoire

Certain players recommend methods that, in reality, should be prohibited. For example, certain individuals recommend Standing with a hard 12 to avoid surpassing 21. This technique confers an advantage of 3.91% to the house. Others think that it is advantageous to mimic the way the dealer plays. They draw card after card until they reach a total between 17 and 21 without Doubling or separating pairs (Splitting). This method offers an advantage of 5.48% to the house.

The average value of the dealer’s hand

Since the dealer possesses a codified set of rules, it is simple to calculate the average value of his hand. It is 18.23. In the following table, we show you the final value of each of the dealer’s hands superior or equal to 16.

Final value of the dealer’s hand %
21 natural 4.82%
21 (3 cards or more) 7.36%
20 17.58%
19 13.48%
18 13.81%
17 14.58%
16 28.36%

Probabilities

The probability of ten value cards

In a 52 card deck, you will find 16 ten value cards, that is, cards whose value is ten. Therefore, a deck contains one ten value card per 3.25 cards, that is, approximately one third of the cards. If no ten value card has appeared for seven or eight draws, there is a big chance that the following card will be a ten value card.

The probability of a bust

If your hand surpasses 21, you lose the round. The following table shows you the probability that you will bust when drawing a new card, according to the value of your current hand.

Value of the hand Probability of a bust if you draw a card
21 100%
20 92%
19 85%
18 77%
17 69%
16 62%
15 58%
14 56%
13 39%
12 31%
11 or less 0%

Probability according to the dealer’s first card

In the following table, we show you, on the one hand, the probability that the dealer will pass 21, according to his upcard. In addition, you will also see the advantage that using Basic Strategy grants you, in each case. It is important to note that, when the dealer’s first card is a 5, the probability that he will bust is at its highest. Furthermore, you have the highest advantage. In this situation it can be profitable to increase your bet. You will also notice that the probability that the dealer will bust is significant with a 4, a 5, and a 6. However, with higher cards, the probability decreases.

Dealer’s upcard Probability of a bust for the dealer Advantage of playing with Basic Strategy
2 35.30% 9.8%
3 37.56% 13.4%
4 40.28% 18.0%
5 42.89% 23.2%
6 42.08% 23.9%
7 25.99% 14.3%
8 23.86% 5.4%
9 23.34% -4.3%
Jack, Queen, King 21.43% -16.9%
Ace 11.65% -16.0%

Probability with a deck that is missing one card

If one card is taken out of a deck, the probabilities evolve. This shows the strategic importance of each card. The following table shows the effect of removing one card. You will notice that without the 5, the game will be the most favorable to you. On the other hand, without the Ace, the casino holds the best advantage.

Card% Effect of removing the card
20.40%
30.43%
40.52%
50.67%
60.45%
70.30%
80.01%
9 -0.15%
10-0.51%
Ace-0.59%