- Apr 2005
What are the chances of getting 21?
It is true that you have 16 cards representing "10" and 4 representing "11" in a single deck of cards.This is a complicated question but I'll simplify the answer.
If you are talking about getting 21 on the inital deal of two cards then that is a fairly easy calculation. You need to first find the chances of getting a 10 card and then find the chances of getting an 11 card.
out of 52 possible cards there are 4 each of: 10s, Js, Qs, Ks which means you have 16 ways of getting 10 out of 52 cards.
out of 52 possible cards there are only 4 kinds of Ace so 4 out of 52.
Then you multiply the probability of getting each card and you have your answer: (16/52) * (4/52) = 64/2704 = 2.37%
The answer can get more complicated when you start to think about how there is only 51 cards left after you take the first card etc.
Suppose we have n decks perfectly shuffled between subsequent deals in a one player Black Jack game. Let the events be A and B as denoted above.Also, don't forget about the fact that most casinos use multiple decks which makes the odds even worse for you.
with a 52 card deck the probability that a random hand is balckjack is:In his text, "Playing Blackjack as a Business", Lawrence Revere stated that in a single deck game one would get a BLACKJACK once every 20.7 hands
and that for a FOUR-DECK SHOE that would drop to once every 21 hands.
Revere never explained the discrepancy... I believe Peter Griffin in his book, "Theory of Blackjack" explained the 0.3 discrepancy...
..but I don't recall it if he did.
It means to keep track of some of cards that leave the deck by memory. And then being able to compute the necessarily probabilities. Casinos hate it because people who train themselves to do this do have a small advantage, enough to win money.What does it mean to count cards?