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# Copy of "Uh Dealer: We've got a Math Problem"

The Mathematics of Blackjack
by

## Leah Costello

on 28 April 2011

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#### Transcript of Copy of "Uh Dealer: We've got a Math Problem"

The Mathematics of Blackjack Dependent Events in Blackjack "Yes. Pull up a chair" This is because Blackjack is a casino game that is based on dependent events. The object of Blackjack:

Accumulate cards whose values add up to a total of (or as close to) 21 as possible WITHOUT exceeding this value.

Ideally your cards values should equal 21 also known as “21” In Blackjack, mathematical calculations on the part of the bettor can have a positive impact on the outcome of a bet. The face cards are worth 10 points Aces are either worth 1 or 10 points, depending on the sum of the other cards. A dependent event is one that is influenced by – or influences – another event. This means that each time a card is drawn from the deck For example, an Ace of Diamonds. the probabilities of drawing other specific cards Increases with each time that they are not drawn. Therefor the outcome of drawing a card is to some extent dependent on what card was drawn before it. So if you drew an Ace of Diamonds Then firstly, that card is guaranteed not to come up again Other cards have a higher probability of being drawn And secondly, Since the deck is now smaller. Probability in Blackjack to Which leads to the ratio of the number of outcomes in an exhaustive set of equally likely outcomes The chance that a given event will occur. The Mathematics of Probability that produce a given event to the total number of possible outcomes. the probability (P) of event A happening = events represented by algebraic variables For example: drawing a King from a deck of cards is represented as: or or An event that has no chance of occurring For example: drawing five aces from a deck of cards has a probability of zero while an event that is certain to occur For example: drawing a card that is either red or black
from a deck of cards without jokers has a probability of 1 P(A) p(A) Pr(A) Probability Chart (if hand has value of 11 or greater and is taking a hit) Total Hand Value Probability for busting if player hits
21 100%
20 92%
19 85%
18 77%
17 69%
16 62%
15 58%
14 56%
13 39%
12 31%
11 or less 0%
A card is chosen at random from a standard deck of 52 playing cards.

Without replacing it, a second card is chosen.

What is the probability that the first card chosen is a queen and the second card chosen is a jack? Example P(picking a queen) = 4/52 P(jack on 2nd pick after queen on 1st pick) = 4/51 P(queen and jack) = (4/52) x (4/51) = 16/2652 = 4/663 Example for Class
Two cards are chosen at random from a deck of 52 cards
without replacement.
What is the probability of choosing two kings? A)4/663
B)1/221
C)1/69
D)None of the above now lets move on to... Card Coutning The Hi-Lo count is easy to learn ...so lets go with that one. Supposidly, "Any player who can add 1 and 1 together, is a strong candidate for mastering the Hi-Lo counting system" Thanks. First, you'll need to learn the respective value for each card in a deck: 20 small cards (2, 3, 4 , 5, 6) Count +1
12 middle cards (7, 8, 9 ) Count 0