When playing a game of blackjack, what are the odds that you will be dealt BlackJack on the first deal? Assume you are playing with one opponent and your opponent is the dealer.

Note: 10, jack, queen and king all are worth 10. Aces are worth 11. You have blackjack when the values of both your cards add up to 21. There is only one deck of cards being dealt out.

(In reply to re: Decks? by fwaff)

When the dealer and the ordinary player are both initially dealt blackjack, the dealer wins. So from 128/2652, has to be subtracted the probability that the dealer and the player both have blackjack. The probabilities are the same for each of the four possibilities of order: player-10 dealer-10 player-A dealer-A; player-10 dealer-A player-A dealer-10; player-A dealer-10 player-10 dealer-A; player-A dealer-A player-10 dealer-10, we need compute only one of these and multiply by 4, so we get 4*(16/52)*(4/51)*(15/50)*(3/49) = 11520/6497400 = 96/54145. Subtracting this from the probability that the player gets blackjack(without considering the dealer's hand) we get 128/2652 - 96/54145 = 7552/162435

... which is approx 4.65%

Posted by Charlie on 2003-02-13 03:55:01