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#1 2006-11-27 23:41:25

Diego
Guest

statistic/probability percentages on a blackjack ¿?

Hello

First of all sorry for my bad english.

The game is blackjack, in this game the proposit is sum 21, but my question is:

How much is in percentage the probability of have a direct blackjack on a table with 5 players, and one or more have a blackjack with the first 2 cards in a infinite deck (thats is if on your first card you receive a K of hearts, next card can be again K of hearts).

Rules: Cards 2 to 10, equal to the face value of the card.
          Ace can be considered either 11 or 1.
          Picture cards (Jack, Queen, King) are equal to 10 points.

Probability of one player or more have a sum of 21 with two cards¿?

Thanks for all!

#2 2006-11-27 23:47:53

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: statistic/probability percentages on a blackjack ¿?

First, let's find the probability of one specific player being dealt a blackjack.
There are 8 ways that this can happen (ignoring suits): 10A, JA, QA, KA, A10, AJ, AQ, AK.
There are 169 total combinations of cards, so the probability is 8/169.

Now we can extend this to 5 players. The probability of one player not being dealt a blackjack is 1 - 8/169 = 161/169. So the probability of 5 players not being dealt a blackjack is (161/169)^5 ≈0.785.

Therefore, the probability of at least one person being dealt a blackjack is ~ 1-0.785 = 0.215.

Thankyou very much for making it an infinite deck, otherwise it would have been a lot more complicated. smile


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