The probabilities blackjack

To win consistently at blackjack game, you must understand and master the few following probabilities.

Reduce the casino advantage using basic strategy

The first way to reduce the odds in your favor is to use basic strategy . A player who plays without a strategy can expect grim probabilities, between 3 and 5% in favor of the house according to the rules applied.

Using basic strategy , you can lower the house edge to less than 1% (this advantage varies according to the rules applied by the casino ).

Strategies that block your advantage

Here are some strategies simplistic game totally unfavorable for the player:

  • Never exceed 21 : The player is on a 12 rigid (as counted as 1), this strategy gives an advantage of 3.91% at the casino.
  • Play as the casino : The player plays as the dealer, he draws a card and up to 16 stops on 17 and over, never double or share the cards. The casino has a time advantage of 5.48%.

The average value of the dealer’s hands: 18.23

The average value of the dealer’s hand is of 18.23. Here are the probabilities of the final values ​​of the dealer’s hands, above 16, the dealer is supposed to take up to 16 and stop at 17.

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

Probability of burning all

The player and the dealer has an 8% chance of exceeding all 21.

A third of the cards are “logs”

Sixteen of 52 cards are worth 10 (10, V, D, R) is a log for 3.25 maps: about one third of the cards are the logs.

Player’s advantage over the dealer’s up card

The first column of this table shows the chances of the dealer to jump (over 21), as his first card. Note that the best chance to get out is when the dealer’s upcard is a 5.

The third column shows the player advantage using basic strategy of blackjack, as the dealer’s upcard. The player has the best chance of winning when the dealer has a 5 in the open card. The benefit is negative for the player when the dealer has a 9 or higher.

Dealer’s upcard probability of skipping the dealer Advantage of the player with the 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%
10, J, Q, K 21.43% -16.9%
A 11.65% -36.0%

Effect when you remove the card game

When you look at the odds when removing some cards, we note that some cards have more impact on the probability than others. So, take off 5 of the game has the most impact for the player, so that removing all have had the greatest impact to improve the odds of the casino.

Card removed 1 deck S17 DAS (in%) 6 decks S17 DAS (in%)
A -0.5794 -0.095
2 0.3809 0.0625
3 0.4339 0.0712
4 0.568 0.0931
5 0.7274 0.1193
6 0.4118 0.0675
7 0.2823 0.0463
8 -0.0033 -0.0005
9 -0.1731 -0.0284
10 -0.5121 -0.0840