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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

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Card Counting Bringing Down the House – Published 2003 21 – Released 2008

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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.

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The System We flip a coin Heads, I give you $5. Tails,

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The System We flip a coin Heads, I give you $5. Tails, you give me $8.

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Types of Probability: Theoretical Probability - Use formulas. The probability of flipping a coin and getting heads is The probability of being dealt a full house in poker is

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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.

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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

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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

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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 ∞

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The Law of Large Numbers As the number of trials increases, the experimental probability will approach the theoretical probability

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So what do we expect to happen with this game? If we play 100 times then:

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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

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So what do we expect to happen with this game? If we play 100 times then: You win 50 times50(+$5)+$250 You lose 50 times Total

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So what do we expect to happen with this game? If we play 100 times then: You win 50 times50(+$5)+$250 You lose 50 times50(–$8)–$400 Total

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So what do we expect to happen with this game? If we play 100 times then: You win 50 times50(+$5)+$250 You lose 50 times50(–$8)–$400 Total–$150

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So what do we expect to happen with this game? If we play 100 times then: On average you lost each time You win 50 times50(+$5)+$250 You lose 50 times50(–$8)–$400 Total–$150

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Expected Value is the average loss or gain to the player in the game.

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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!

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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.

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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.

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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.)

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Basic Strategy:

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Basic Strategy gives the house about a 0.5% edge. ($5 for every $1000 bet.)

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The Hi/Low Card Counting System

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+1

28 0

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+1 0 –1

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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

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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).

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Wanna play some cards?

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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.

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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.

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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.

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Thank You! www.ohlone.edu/people/joconnell

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