Card Counting - Department of Math and Computer Science

Card Counting
FYF 101 Constructed Pastimes
Anthony Kapolka
Two cards the same?
• dealt first card
• chance of second card matching is
3 / 51 = 5.88%
Second player gets a pair?
• dealt first card
• chance of second card matching is
12/13 x 3/49 + 1/13 x 1/49 = 5.80%
That probablility was conditional
• To compute odds for second player, I
assumed first player had gotten a pair.
• To compute probability both had a pair
multiply the numbers together:
5.88% x 5.80% = 0.34%
Source: youtube.com
Vocabulary
• “cold deck”
• “pocket pairs”
KK was facing AA only 2.44%
• probability
See wikipedia.com: Poker_probability(Texas_hold_’em)
Ranking Hands
Source: http://www.britannica.com/ebc/art-53052/
Computing Odds
Complicated to compute
Easy to Understand:
All
combinations that win
__________________
All combinations
Odds are Dynamic
Source: youtube.com
Probability is no guarantee
over the short term!
Sometimes amazing things happen.
Games against real opponets
involve human factors
Jean Scott plays
video poker for a
0.76% return.
Souce: Discover, May 2000
In Blackjack you play
(alone) against a dealer
with a fixed strategy
Source: Postcard
Vocabulary
• Hard - Soft
• Stand - Hit
• Double
• Split
Source: www.cocopahresort.com/gaming/blackjack_hand.jpg
What is the chance of drawing an ace?
What is the chance of drawing an ace?
4/52
Drawing another ace?
Drawing another ace?
3/51
Drawing another ace?
Drawing another ace?
2/50
Drawing another ace?
1/49
Drawing another ace?
Zero.
This is why card
counting works.
How about with multiple decks?
Basic
Blackjack
Strategy
(See Handout)
A
B
C
Why does the
strategy vary?
Context
Context
Context
opponents hand
cards already played
number of decks
Big cards in deck
favor the players
Big Cards
• Worth 10+ points
• Make blackjack more likely
• Dealer more likely to busts
hands worth 12-16
Big cards in deck
favor the players
Bet More
Small cards in the deck
favor the dealer
Small cards in the deck
favor the dealer
Bet Less
Basic Hi-Lo Counting
• +1 for each card 2, 3, 4, 5, 6
• -1 for each card 10, Jack, Queen, King, Ace
• ignore cards 7, 8, 9.
Positive count favors player
Negative count favors dealer
What’s the count?
Change your strategy
High count means high cards remain.
Bet more when the count is HIGH.
Count / Deck
Multiple deck game?
Divide count by
number of decks played
Change your strategy
Source: Frank Scoblete, Best Blackjack, 1996.
No human factors?
Really??
Let’s play
“Is it okay?”
Card Counting
Okay for you to count cards?
Mid-shoe entry
Count the cards as a spectator.
Start playing
when you like
the count.
Source: www.blackjackadvisor.co.uk
Front Loading
The dealer is sloppy and you
can usually see his hole card.
Dealer Tells
Dealer peeks under 10
Dealer blinks
Dealer deals
Dealer has bust card in the hole
Dealer peeks under 10
Dealer doesn’t blink
Dealer deals
Dealer has pat hand
Reflections
Look for hole card reflections
in the coins in the dealer’s tray,
glasses, or whatever.
Source: weaver.nettblogg.no
Past Posting
Oops Plays
• Hit on 17 when
dealer shows 7-10
• Insure against a 10
• Quadruple down
Quadruple Down
• Place double down hand on table
• Place extra bet on top of original bet
• Dealer either
• tells you new bet goes beside old bet
• reminds you to place new bet
Card Mechanics
Manipulate the cards
during shuffling and dealing.
Source: youtube.com
Marked cards
Cheating has consequences
Source: Brianiac Science Abuse