Card Counting
What is it, how does it work, and can I use it
to pay for college?
(and if it does work, do I even have to go to college?)
Jeff O’Connell
www.ohlone.edu/people/joconnell
Card Counting
Bringing Down the House –
Published 2003
21 – Released 2008
Overview
• The System
• Card Counting - How does it work?
• Card Counting - Does it work?
• The 4 reasons why Mr. O has not, does
not, and will not ever count cards in a
casino.
The System
We flip a coin
Heads, I give you $5.
Tails,
The System
We flip a coin
Heads, I give you $5.
Tails, you give me $8.
Types of Probability:
Theoretical Probability - Use formulas.
The probability of flipping a coin and getting
heads is 1
2
The probability of being dealt a full house in
poker is
3744
1
= 0.00144 »
2598960
700
Types of Probability:
Experimental Probability - Do the experiment.
Weather, Batting Average, etc.
In order for you to win at our game, you need
the experimental probability to be very
different from the theoretical probability.
Say we play 10 times.
What are the chances of you coming out
ahead?
You would need to win at least 7 times.
The probability of flipping a coin 10 times and
getting heads at least 7 is about 17.2%
≈ 1 in 6
Say we play 100 times.
What are the chances of you coming out
ahead?
You would need to win at least 62 times.
The probability of flipping a coin 100 times and
getting heads at least 62 is about 1%
≈ 1 in 100
Say we play 1000 times.
What are the chances of you coming out
ahead?
You would need to win at least 616 times.
The probability of flipping a coin 1000 times and
getting heads at least 616 is about 1.09x10-13
≈ 1 in ∞
The Law of Large Numbers
As the number of trials increases, the
experimental probability will approach
the theoretical probability
So what do we expect to happen with this
game?
If we play 100 times then:
So what do we expect to happen with this
game?
If we play 100 times then:
You win 50 times
You lose 50 times
Total
So what do we expect to happen with this
game?
If we play 100 times then:
You win 50 times
You lose 50 times
Total
50(+$5) +$250
So what do we expect to happen with this
game?
If we play 100 times then:
You win 50 times
50(+$5) +$250
You lose 50 times
50(–$8) –$400
Total
So what do we expect to happen with this
game?
If we play 100 times then:
You win 50 times
50(+$5) +$250
You lose 50 times
50(–$8) –$400
Total
–$150
So what do we expect to happen with this
game?
If we play 100 times then:
You win 50 times
50(+$5) +$250
You lose 50 times
50(–$8) –$400
Total
–$150
-$150
On average you lost
= -$1.50 each time
100
Expected Value is the average loss or gain to
the player in the game.
Roulette has an expected value of –5.26%
($0.0526 for every $1 bet)
Expected Value and the Law of Large Numbers
is how casinos make money!
Blackjack rules:
Card Values • Cards 2 – 9 are valued as indicated.
• 10, J, Q, K are valued at 10.
• Ace can either be valued as 1 or 11.
Each player is trying to get a hand that is
closer to 21 (without going over) than that of
the dealer.
Blackjack rules:
If the player gets closer to 21 (without going
over) than the dealer then the player wins the
amount bet.
If the dealer gets closer to 21 than the player or
the player gets more than 21 then the player
loses their bet.
If the player and dealer get the same value
then the player keeps their bet, called a push.
Blackjack rules:
If the player gets dealt a Blackjack (an ace
and a card valued as 10) the player wins
one and a half times their bet. (If the bet is
$10 the player wins $15.)
Basic Strategy:
Basic Strategy gives the house about a
0.5% edge. ($5 for every $1000 bet.)
The Hi/Low Card Counting System
+1
+1
0
+1
0
–1
The Count of the deck is the sum of all the
+1’s, –1’s, and 0’s.
The True Count of the deck is the count of the
deck divided by the number of decks left. For
example if the count is +16 and there are 4
decks left then the True Count is
16/4 = 4
If the True Count of a deck is over +2 then the
player has about a 1% advantage over the
house ($1 for every $100 bet).
Wanna play some cards?
The 4 reasons why Mr. O has not, does not
and never will count cards in a casino:
1. I am not very good at cards.
2. I am not very good at Math.
3. I don’t think it is worth it.
Card Count
30
20
10
0
1
-10
-20
-30
-40
-50
-60
53
105
157
209
261
True Count
20
15
10
5
0
1
-5
-10
-15
-20
53
105
157
209
261
I found a true count of more than +2, 13% of
the time.
If you have a 1% advantage and bet $100
per hand, you can expect to make an
average of $50 per hour.
The margin of error for this $50 per hour is
about $2800.
So we can expect to make between –$2750
and $2850 per hour.
The 4 reasons why Mr. O has not, does not,
and never will count cards in a casino:
1. I am not very good at cards.
2. I am not very good at Math.
3. I don’t think it is worth it.
4. Lawrence Fishburne.
Thank You!
www.ohlone.edu/people/joconnell