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

20 big cards (10, J, Q, K, A) Count -1 And for those who need a visual.. This is considered a 'balanced system' because if you counted down every single card in a 52 card deck, you would end up with a count of 0. So how do we use the Hi-Lo card counting system? Since each new card is changing the count one way or the other. You are rooting for the under dog, because the more 'small cards' that are played, the higher your odds of winning are. Because, when there are fewer 'small cards' in the deck, you have a better chance of being dealt blackjack, the dealer busting, or just getting strong starting hands. It is an ongoing battle between the high cards and the low cards to control the card count. 1. When you first sit down at a blackjack table, that is using a new full shoe of cards, the count at the table starts at 0. 2. From the initial 0 count, you will be adding 1, subtracting 1, or adding 0, for every single card that is dealt. If you accidentally miss cards that are dealt and your count gets off, you can shift your odds of winning without your knowledge. Keeping track of which cards have been dealt means that players can make informed decisions about whether to hit (take another card) or stand (stick with what you’ve got). How To Use The Hi-Lo Counting System First, keep in mind: BUT BE CAREFUL! For example, a five of Clubs House Advantage With a good strategy involving card counting you can get the house advantage in Blackjack down to as little as 0.5% Without a strategy, expect the house to have an advantage of around 7% And you will reduce your chances of busting from 28% to 17% womp womp. The reason that the house has an advantage in Blackjack is because the player must make his/her play first. And so if the player busts, they immediately lose their bet. This is the only advantage that the dealer has over the player BUT it is a HUGE advantage Ace side count Ace five count back counting

Balanced Count Some terms to know: BUST: to get a total greater than 21 - an automatic loss. Knock out count

Point count Running count

Side count True count Unbalanced Count

Zen Count Hi-Lo Count KO Wizard Ace

Hi-Opt I Hi-Opt II

Omega II HIT: to take another car DRAW: (Same as "hit") taking additional cards in an attempt to get closer to a total of 21 points FACE CARDS: Jacks, queens, kings Number cards are worth their numerical value, regardless of the suit. sTAND: When you don't take anymore cards; To stay Aces: are Aces... NUMBERED CARDS: are cards with numerical ranks 2-10 4 = number of Jacks in deck 51 = Full deck (52) minus the one card (queen) previously chosen 4 = number of queens in a deck 52 = Full deck so lets see that clip again - can you follow it this time?

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

The Mathematics of Blackjack

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