introductory card counting

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Wizard of Odds Introductory Card Counting

Card Counting

Let me say loud and clear that card counting is hard and is not as rewarding as television and the

movies make it outto be. If it were an easy way to make money, then everyone would be doing it.

If you do not know the basic strategy, trying to count cards is highly ill-advised. Experienced card

counters still play by the basic strategy the great majority of the time.There can be no short cut

around learning the basic strategy, those who attempt card counting without a firm foundation in

the basic strategy are making a big mistake.

To be a successful counter you have to be able to countdown a deck fast and memorize largetables of numbers as well as make it look like you're just a casual player.Furthermore, with today's

rules, a realistic advantage the counter will have is only 0.5% to 1.5%. You will not win money

slowly and gradually but your bankroll will go up and down like a roller coaster in the short run.

Only in the long run, over hundreds of hours of playing, can you count on winning.

The underlying principle behind card counting is that a deck rich in tens and aces is good for the

player, a deck rich in small cards is good for the dealer. When the counter knows the odds are in

his favor, he will bet more, and adjust his playing strategy to stand, double, and split in some

plays where basic strategy says to stand. All the options the player has at his disposal favor the

player even more when the deck is ten and ace rich. Here is a list and a brief reason why.

Standing: The player may stand on stiff totals of 12 to 16, and the dealer may not. In ten-rich

shoes, hitting stiff hands becomes more dangerous, favoring the more conservative player

strategy.

Insurance: On average, when the dealer has an ace up, the remaining cards in blackjack will be

30.87% tens (based on a six-deck game), making insurance a bad bet. However, if the probability

gets above 33.33%, it becomes a good bet. Counters know when the remaining cards are ten-rich,

and make powerful insurance bets at those times.

Doubling: Usually, when the player doubles he wants a ten. In ten-rich shoes, the player makes

better double downs, getting closer to 21.

Blackjack: Both player and dealer will see more blackjacks, but the player gets paid 3 to 2, and

the dealer does not.

Surrender: The alternative to surrendering is much worse in ten-rich shoes. If the alternative ishitting, the player is more likely to bust. If the player would otherwise stand, due to the high


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count, the dealer is still more likely to get a 10. While the counter will surrender more in high

counts, the savings will be greater.

Splits: The player is usually splitting high cards and/or off of a weak dealer card. Either way, aten-rich shoe helps the player get higher totals, and increases the probability of the dealer

busting.

I'm working on an in-depth study of how these effects break down. The contribution to each

factor depends on the rules, deck penetration, and bet spread. However, based on average

conditions in a six-deck shoe, my initial results break down the benefits of counting as follows.

WHY CARD COUNTING WORKS

PLAYER OPTION Portion of BenefitSTAND 40%

INSURANCE 34%

DOUBLE 9%

BLACKJACK 7%

SURRENDER 6%

SPLIT 4%

The probability for insurance was taken from Don Schlesinger's "Illustrious 18" list, as found in

Blackjack Attack .The rest of the breakdown is mine.

To gauge the richness of the deck in good cards, the player will keep track of the cards the are

already played. Strategies vary, but all assign a point value to each card. For example, the hi-lo

count assigns a value of +1 to 2, 3, 4, 5, and 6, and -1 to tens and aces. Everything else is 0, or

neutral. At the beginning of a deck or shoe, the count is 0. Then the counter constantly adds and

subtracts from the count, according to the cards played. This running total is called the "running

count." A positive count means that a disproportional number of small cards have already been

played, which means that the deck is rich in large cards. To determine the "true count," divide the

running count by the number of decks left to be played, or in some strategies, the number of half

decks. This will tell you the relative richness of the deck in good cards.

The true count is used in two ways, to determine how much to bet and how to play your hand.

Unless it is obvious, every situation has a line in which you should play one way if the count is

above the line and another if below. For example, a 12 against a 6 may dictate that you stand if

the true count is -1 or greater and hit if the true count is less than -1. The counter will also bet

more when the true count is high, meaning the deck is rich in good cards.
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A problem arises when it comes to treating aces. The player should bet more when the deck is

rich in aces since they add to the probability of getting a blackjack. However, when it comes to

playing your hand, the number of aces left is not nearly as important as the number of tens, so it

is desirable, but not necessary, to distinguish between tens and aces. Some card countingstrategies keep a side count of aces. In the Hi-Opt I and Revere Plus/Minus aces are counted

separately and only considered when making the wager. This is a more accurate and powerful

way to play than assigning a negative value to aces and not keeping a side count, as some

strategies do. Yet, many people feel that for the beginner it is too confusing to keep two counts.

A player is more likely to make mistakes keeping two counts and that costs money. The efficiency

of a strategy that does not keep a side count of aces is only modestly less, but you likely will gain

more from fewer mistakes made. Different experts fall in various places in the spectrum in terms

of what to recommend for the beginner. The Zen Count takes the middle ground and gives aces

a value of -1 and tens -2. Personally, I have tried both and would recommend against a count

that requires a side count of aces to a person ready to take up card counting. The Uston

Advanced Plus/Minus is a good strategy that does not involve an ace side count and can be

found in the bookMillion Dollar Blackjack .How well you know a counting strategy is much

more important than which strategy you know.

Legally speaking, the player may play blackjack any way he wants without cheating or using a

computer, and the casinos may do anything from making conditions unfavorable to barring, in an

effort to stop anyone who they deem has an advantage over the game. Much of the challenge of

card counting is avoiding suspicion that you are anything but a normal non-counting player. The

most obvious indication that somebody is counting is that they make a substantial increase in bet

size after a lot of small cards leave the table. Although the greater the factor by which you can

increase your bet the greater your odds of winning, more than doubling your last bet is a fast

way to arouse "heat"from the dealer and pit boss. Usually when casinos employees realize you are

counting, they will either shuffle the cards whenever you increase your bet, essentially removing

any advantage, or ask you to leave.

This is only scraping the surface of the subject of card counting. I suggest the following pages ofmine.

Hi-Lo Count.

The Ace-Five Count,possibly the easiest way to count cards.

Book review section,for suggestions on good blackjack books.
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The Ace/Five Count

Introduction

Basic strategy blackjack players sometimes ask me for a simple way to overcome the small house

edge in blackjack, with little worry over being recognized as a card counter. This is often done

with the motive of milking the casinos for comps and offers. What follows is, in my opinion, the

easiest card counting strategy to achieve the above goal and still put the odds in the player's

favor.

How It Works

1.

Establish what your minimum and maximum bets will be. Usually the maximum will be 8,16, or 32 times the minimum bet, or any power of 2, but you can use whatever bet spread

you wish.

2. At the beginning of each shoe, start with your minimum bet, and a count of zero.

3. For each five observed, add one to the count.

4. For each ace observed, subtract one from the count.

5. If the count is greater than or equal to two, then double your last bet, up to your

maximum bet.

6. If the count is less than or equal to one, then make the minimum bet.

7.

Use basic strategy for all playing decisions.

This strategy was designed to be most effective on a six- or eight-deck game. I recommend

playing only on games with liberal Strip rules, which are as follows:

4-8 decks

Blackjack pays 3 to 2

Dealer stands on soft 17

Double after split allowed

Late surrender allowed

Re-splitting aces allowed

75%+ penetration

Such games are easy to find in Las Vegas, although sometimes a higher minimum bet is required.

In the low-roller pits, the dealer will usually hit on a soft 17, which is bad, costing the player

0.22%.


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Simulation Results

The following results were provided by Norm Wattenberger using hisCasino Vrit software.

The rules above were used, with six decks, and 75% penetration. In my opinion, Casino Vrit isthe most robust and accurate blackjack simulation software on the market. It can be used to test

just about any card counting strategy under any set of rules and conditions.

ACE/FIVE COUNT STATISTICS

SPREAD Player

Advantage

Average

Initial Bet

SCORE

1-8 0.30% 2.7 3.1

1-16 0.45% 4.2 5.3

1-32 0.57% 7.1 6.5

SCORE is an acronym, coined by Don Schlesinger, for Standardized Comparison Of Risk and

Expectation. It is defined as the advantage squared divided by the variance. The SCORE may also

be interpreted as the expected hourly win per hand for a player with a $10,000 bankroll, who

sizes his bets according to the Kelly Criterion, to achieve a 13.5% risk of ruin. As a basis of

comparison, a Hi-Lo counter, with a 1 to 8 spread, under the same rules, has a SCORE of 8.40,

compared to the 3.1 of the Ace/Five count.

Source: 'Blackjack Attack,' third edition by Don Schlesinger.

Earlier Strategies

After publishing this section, somebody accused me of stealing the idea from Edward Thorp.

Indeed, in 1969 Thorp did discuss a similar strategy in his book 'Beat the Dealer ,' in the fourth

chapter titled "A Winning Strategy." The difference is that Thorp's strategy tracks fives remaining

against total cards remaining. Later, in 1971, Lawrence Revere published a similar strategy as

Thorp's in 'Playing Blackjack as a Business ,' chapter 7 titled "The Revere Five Count Strategy."
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High-Low Card Counting Strategy Introduction

The Hi-Lo Count is the most widely written about, and in my judgment, the most commonly used

card counting strategy. The High-Low was first introduced in 1963 by Harvey Dubner1

. It has sincebeen discussed by just about all the major blackjack writers. In my opinion, the best introductory

treatment is inProfessional Blackjack by Stanford Wong, and the most detailed coverage is in

Blackjack Attack by Don Schlesinger. Following is a brief explanation of how to use the Hi-Lo.

Step 1: Assign a point value to each rank, as follows.

HIGH-LOW POINT VALUES

RANK Value

2 +13 +1

4 +1

5 +1

6 +1

7 0

8 0

9 0

10 -1

J -1

Q -1

K -1

A -1

Step 2: Start with a "Running Count" of zero at the start of the deck/shoe. As cards are revealed,

keep adding or subtracting from the Running Count, according to the point system in step 1. For

example, if the first ten cards to come out of the shoe were 3, 5, K, 7, Q, A, 8, 5, 4, 2, then the

running count would be 1 +1 -1 +0 -1 -1 +0 +1 +1 +1 = +2.

Step 3: Divide the running count by the number of decks remaining, to get what is known as the

"True Count." This is the part that beginning counters hate. You don?t need to be exact. A rough

estimate will do, in my opinion. Let's look at example. The running count is +7 and there are

about 4 decks left. The true count would be 7/4 = 1.75. Round that up to 2, to keep it simple.

The more you play the more you will be comfortable eyeballing this adjustment, without doing

any real division in your head. Usually the right play is obvious. In borderline cases only will you

need to do this True Count conversion.
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Step 4: The greater the true count, the more you should bet. This is where card counting

becomes more art than science. Some blackjack books give rigid rules on how this should be

done. However, the casino managers have read these books too, and the patterns recommended

in earlier books now set off red flags. How you do this should depend on your own style, andhow much heat you are getting. It helps avoid heat to keep the ratio of maximum bet to

minimum bet to a limit, known as the ?Bet Spread.? Only increasing bets after a win, only

decreasing after a loss, and staying the same after a push, makes play look more natural, but at a

cost to profitability.

Step 5: For some hands, you will play according to the True Count and a table of "Index

Numbers," rather than basic strategy. The greater the count, the more inclined you will be to

stand, double, split, take insurance, and surrender. For example, the Index Number for a player 15

against a dealer 10 is +4. This means the player should stand if the True Count is +4 or higher,

otherwise hit.

The following tables are known as the "Illustrious 18" and "Fab 4" respectively.2They appear in

Blackjack Attack by Don Schlesinger, and are republished here with permission. These are the

most important index numbers to remember. Knowing only these will give the counter 80% to

85% of the value of knowing every index number, based on a six-deck game. The difference is

more in single and double-deck games. The lists are given in order of value. If you can?t

memorize all of them, start at the top, and work your way down.

ILLUSTRIOUS 18

ORDER Play Index

1 Insurance +3

2 16 Vs. 10 +0

3 15 Vs. 10 +4

4 10,10 Vs. 5 +5

5 10,10 Vs. 6 +4

6 10 Vs. 10 +4

7 12 Vs. 3 +2

8 12 Vs. 2 +3

9 11 Vs. A +1

10 9 Vs. 2 +1

11 10 Vs. A +4

12 9 Vs. 7 +3

13 16 Vs. 9 +5

14 13 Vs. 2 -1

15 12 Vs. 4 016 12 Vs. 5 -2
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17 12 Vs. 6 -1

18 13 Vs. 3 -2

The player should stand/double/split if the True Count equals or exceeds the Index Number,otherwise hit. The player should take insurance if the True Count is +3 or greater.

FAB 4 SURRENDERS

ORDER Play Index

1 14 Vs. 10 +3

2 15 Vs. 10 +0

3 15 Vs. 9 +2

4 15 Vs. A +1

The player should surrender if the True Count equals or exceeds the Index Number.

A full table of all index numbers can be found in Chapter 3, and Appendix A, ofProfessional

Blackjack by Stanford Wong.

The next table shows some statistics using the High-Low. The blackjack rules this table is based

are liberal Vegas shoe, as follows:

Six decks

Dealer stands on soft 17

Surrender allowed

Double after split allowed

Player may resplit to four hands, including aces

To avoid setting off red flags, the simulation increased the bet after a win only, decreased after a

loss only, and always stayed the same after a push, except resetting to a minimum bet after a

shuffle. The simulation rounded the remaining decks to the nearest half deck, otherwise playing

perfectly.

HIGH-LOW STATISTICS

SPREAD Penetration Index

Numbers

Player

Adv.

Std.

Dev.

Avg.Bet

1 TO 5 4 I18+F4 0.157% 1.50 1.35

1 TO 10 4 I18+F4 0.368% 2.04 1.57

1 TO 15 4 I18+F4 0.578% 2.67 1.73

1 TO 5 4.5 I18+F4 0.300% 1.60 1.41

1 TO 10 4.5 I18+F4 0.587% 2.27 1.681 TO 15 4.5 I18+F4 0.834% 3.06 1.90
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1 TO 5 5 I18+F4 0.469% 1.70 1.47

1 TO 10 5 I18+F4 0.837% 2.52 1.80

1 TO 15 5 I18+F4 1.147% 3.49 2.10

1 TO 5 4.5 All 0.313% 1.61 1.411 TO 10 4.5 All 0.608% 2.29 1.68

1 TO 15 4.5 All 0.862% 3.10 1.91

1 TO 5 5 All 0.494% 1.71 1.47

1 TO 10 5 All 0.857% 2.55 1.81

1 TO 15 5 All 1.182% 3.54 2.11

Explantion of columns

Spread: This is the ratio of the player?s minimum bet to maximum bet. The bigger the range, the

greater the player?s advantage, and bankroll volatility. A wide bet spread also sets off a red flag.

In a six-deck game, I think a 1 to 15 spread is about the most aggressive the player should get.

The simulation played one betting spot only.

Penetration: How many decks played before reaching the cut card. In a six-deck shoe, 4.5 is the

norm.

Index Numbers: I already explained index numbers above. Simulations were run using both the

Illustrious 18 and Fab 4 (I18+F4) above, and with the full table. The difference is not much, which

shows that knowing the top 22 gets you most of the benefit of knowing all of them.

Player Advantage: This is the ratio of net player win to total initial bets. For example, in the last

row, the player could expect to win 1.182% of his total initial bets.

Standard Deviation: This is a term for the volatility per initial bet.

Average Bet: The average final bet per hand, compared to the lowest bet For example, in the last

row, if the player?s minimum bet were $100, his average bet would be $211. This includes

additional money bet due to doubles and splits.

This table was created usingCVCX Blackjack Analyzer by Casino V?rit?. This software produces

hundreds of different statistics for just about any set of rules, betting strategies, and playing

strategies. For the player who wants to run these tests, this software is the best there is, in my

opinion.

Footnotes

1.

Professional Blackjack by Stanford Wong, page 31, 1994 ed.2. Blackjack Attack by Don Schlesinger, page 62, 2004 ed.
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Acknowledgments

Don Schlesinger: For his permission to reprint the Illustrious 18 and Fab 4 tables from his book,

Blackjack Attack .Norman Wattenberger: For his complimentary use ofCVCX Blackjack Analyzer by Casino Vrit.

Further Reading

Card Counting Introduction.

Wizard Ace-Five Count:Very easy and simple card counting strategy.

"21" Movie Review:Truth and fiction about the movie about the MIT card counting team.

Blackjack book reviews.

Main blackjack page.
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