In a game of single deck blackjack, what is the likelihood of being dealt a blackjack if three other hands, each with an ace, are also dealt?
1 Answer
Explanation:
Let's first define a few things:
Blackjack uses a standard 52 card deck with 13 ordinal cards (Ace - 10, Jack, Queen, King) with 4 suits (diamonds, hearts, clubs, spades) for a total of
In the game of blackjack, you are dealt two cards initially and if the value totals to 21, it's a blackjack. The value of each Ace can be 11 (or 1 - but that isn't important in this question) and the value of the 10, Jack, Queen, and King is 10.
The question states that there are 4 hands being dealt and that each of the other three hands has an Ace. So our hand needs the 4th Ace. Three cards are spoken for, so we have:
Now to the other card. It needs to have a value of 10. We don't know what any of the other cards are in the other hands and the 4 Aces are now spoken for, so that means the odds of the other card being value 10 is four ordinal cards each with four suits is 16 out of the remaining 48 cards in the deck:
Which gives the total odds as:
