In a game of blackjack, a 2-card hand consisting of an ace and a face card or a 10 is called a blackjack.

Question

In a game of blackjack, a 2-card hand consisting of an ace and a face card or a 10 is called a blackjack. (Round your answers to four decimal places.)

(a) If a player is dealt 2 cards from a standard deck of 52 well-shuffled cards, what is the probability that the player will receive a blackjack?

 

(b) If a player is dealt 2 cards from 2 well shuffled standard decks, what is the probability that the player will receive a blackjack?

Answer 1

1) Combinations of drawing 1 ace * combinations of drawing 1 face cards / all possible 2 card combinations

4C1 * 16C1 / 52C2

4 * 16 / (52 * 51/2)

64/1326

.0483

 

2) Same thing but all the proportions are now doubled.

8C1 * 32C1 / 104C2

8 * 32 / (104*103/2)

256/5356

.0477

 

So we see it makes a very tiny difference in odds, but it does decrease the probability by .006. This explains why casinos typically use multiple decks when dealing blackjack.