Question

Second, in blackjack (Links to an external site.)Links to an external site., calculate the probability of being dealt "blackjack" in the first two cards. Assume the dealer is using one standard deck.

Answer 1

To be dealt a blackjack our two cards needs to be sum 21.

Ace can be taken as value 1 or 11 as player prefers in blackjack. Here if we get ace we take it as 11.

Now we need one more 10 or one of face cards(valued 10 in blackjack) to make sum of 21.

Here dealer is using standard deck.

So there are 2 ways of getting a blackjack.

1)First card Ace second card of 10 value

First card Ace= 4 aces in pack of 52=4/52

Second card of 10 value= 4 cards of each type and 16 face cards in total in 52. But we took away an ace. So 16/51.

Combining=(4/52)*(16/51)=64/2652

2)First card of 10 value second card Ace

First card of 10 value=16/52

Second card Ace=4/51(Since one face card taken)

Combining=(16/52)*(4/51)=64/2652

Probability of being dealt blackjack is adding up both these options=64/2652+64/2652=128/2652=32/663.

So required probability is 32/663=0.0483(approx)