What is the probability of being dealt a Blackjack?

Answer 1

When the deck is full, this probability is 4/52 (the probability of getting one of 4 aces) times 16/51 (the probability of getting one of 16 kings, queens, jacks, or tens) times 2 (the number of orders in which you could get these cards: ace first, or ace second). This comes out to 32/663, or about 4.83%. Of course, this probability changes as the game progresses: it decreases when any of the tens, jacks, queens, kings, or aces get discarded, but increases when other cards get discarded. This change is unpredictable, but its expected value is 0; this is a complicated concept to explain, but it means that on average, the probability will go up as much as it goes down. Also, the probability is still 32/663 at any point in the game if you have no information whatsoever about what cards came up before: if you forgot every card you saw, or if you just joined the game.