Black Jack

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How to win at blackjack (21) with gambling expert Michael "Wizard of Odds" Shackleford

Frequently Asked Questions...

What is the probability of getting Black Jack?

How many percent could you get to get a black jack?


Best Answer...

Answer:

As some other answers have indicated, it depends upon the number of decks used.

Also, as some other answers have indicated, they were not accurate because they ignored the fact that after the first card in your hand is dealt that card cannot be received as the second card in your hand.

Given how easy it is to calculate accurate figures, I did.

Following are the percentages for different numbers of decks:

1 Deck =4.826546003%
2 Decks =4.779686333%
3 Decks =4.76426799%
4 Decks =4.756596061%
5 Decks =4.752004752%
6 Decks =4.7489488%
7 Decks =4.746768383%
8 Decks =4.745134384%
9 Decks =4.743864273%
10 Decks = 4.742848673%
100 Decks = 4.734638318%
1,000 Decks = 4.733818846%
10,000 Decks = 4.733736914%
100,000 Decks = 4.733728721%
1,000,000Decks = 4.733727902%
1,000,000,000 Decks = 4.733727811%

Calculation:

If the number of decks is D, the number of cards C = 52D

The percentage of hands that will be blackjacks is

(12,800 x D²) / (C² - C)

FYI: 12,800 = 4 aces x 16 10,J,Q,Ks x 2 x 100 to make it a percentage

Since I have never seen anyone use more than eight decks in a blackjack shoe the calculations for more than eight decks are meaningless, but it did not take any extra effort to calculate them so I figured why not see what they would be.