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.
# opponents doesn't come into consideration. Any two given cards that the puzzle author (p.a.) receives makes up a Blackjack.
So, it may be the 2nd or 5th cards( with 2 opponents where p.a. is the dealer).
Or, it may be the 3rd or 9th card (with 5 opponents where opponent is the dealer).
To constitute a Blackjack either the p.a.'a 1st card is worth an ace and the 2nd a 10 or first card is worth a 10 and the second an ace.
Thus, the required probability
= {(4*4)/52}*{(1*4)/51} + {(1*4)/52}*{ (4*4)/51}
= 128/2652
= 32/663
Edited on June 4, 2022, 9:41 am
Puzzle Solution
