BlackJack School BlackJack Training Author Selzer-McKenzie SelMcKenzie

BlackJack School BlackJack Training
Author D.Selzer-McKenzie
Lesson 1 - Basic Strategy
by the, reprinted with permission.

The foundation of winning at Blackjack is to utilize proper basic strategy in playing the hands. "Proper" means that each decision you make on hitting, standing, doubling or splitting pairs is the correct mathematical play for that hand. There is no room for intuition, gut feelings or guessing when it comes to basic strategy; you must make the "percentage" play each time. Even if you've doubled an 11 against a dealer's 10 five times in a row and lost, when that hand comes up a sixth time you must double. Consistency is a big part of playing a winning game, so resolve right now that you are going to make the proper play, regardless if the dealer rolls his eyes upward or the other players at the table groan quietly when you do it. You are there for the money -- there's no other reason to play blackjack -- and the application of proper basic strategy is going to get that money for you; what others think of your play is not important.
The correct basic strategy for a blackjack game depends upon the rules of the casino where you wi"ll be playing. The strategy which applies to a single deck game in Reno, for example, is quite a bit different than the strategy for an eight-deck game in Atlantic City. I'm going to show you how to learn the basic strategy of your choice; exactly what that strategy is will depend on you. To select a basic strategy, go to the and simply fill in the blanks. Once your strategy is computed, print it out.
Here's what that looks like for a fairly common game: Six decks, double on any first two cards, double after splitting pairs is permitted and the dealer stands on A-6.
Basic Strategy Matrix :
for 6 Decks, S17, DA2, DAS, No surrender
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Splitting Pairs
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Pairs 2 3 4 5 6 7 8 9 T A
(A,A) Y Y Y Y Y Y Y Y Y Y
(T,T) N N N N N N N N N N
(9,9) Y Y Y Y Y N Y Y N N
(8,8) Y Y Y Y Y Y Y Y Y Y
(7,7) Y Y Y Y Y Y N N N N
(6,6) Y Y Y Y Y N N N N N
(5,5) N N N N N N N N N N
(4,4) N N N Y Y N N N N N
(3,3) Y Y Y Y Y Y N N N N
(2,2) Y Y Y Y Y Y N N N N

Key:
• Y = Yes, split the pair
• N = No, don't split the pair
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Soft Totals
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Soft Totals 2 3 4 5 6 7 8 9 T A
(A,9) S S S S S S S S S S
(A,8) S S S S S S S S S S
(A,7) S Ds Ds Ds Ds S S H H H
(A,6) H D D D D H H H H H
(A,5) H H D D D H H H H H
(A,4) H H D D D H H H H H
(A,3) H H H D D H H H H H
(A,2) H H H D D H H H H H

Key:
• H = Hit
• S = Stand
• D = Double; if unable, Hit
• Ds = Double; if unable, Stand
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Hard Totals
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Hard Totals 2 3 4 5 6 7 8 9 T A
17 S S S S S S S S S S
16 S S S S S H H H H H
15 S S S S S H H H H H
14 S S S S S H H H H H
13 S S S S S H H H H H
12 H H S S S H H H H H
11 D D D D D D D D D H
10 D D D D D D D D H H
9 H D D D D H H H H H
8 H H H H H H H H H H

Key:
• H = Hit
• S = Stand
• D = Double; if unable, Hit
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This is the chart that you will eventually know as well as your own name -- but don't worry, you're not going to memorize it in this form. What we are going to do is convert all this into what a "normal" person can understand. I call what's above the "Basic Strategy Matrix" and you'll use it in some of your training. But what we need to do in order to memorize this is to translate the information above into all-inclusive rules. Let's do a few as examples.
Look at the strategy for a player's hand of 9 on the matrix above; it says to double against a 3,4,5 or 6 and hit it against everything else. We can turn that information into a simple rule: "With a hand of 9, double versus 3 through 6, otherwise hit." See how this works? We are going to take each player's starting hand and convert the proper play of that hand into one easy-to-understand rule. Now look at a hand of A-2. Proper basic strategy says to double against 5 and 6 and hit it against everything else, so our rule for A-2 is "Double vs. 5 & 6, otherwise hit." As a bonus, we can group A-2 with A-3 since the play for each is identical. So we end up with a rule like this "A-2 , A-3; double vs. 5 & 6, otherwise hit." One more example; a pair of 3's. When double after split is permitted, proper basic strategy says to split 3's whenever the dealer is showing a 2,3,4,5,6, or 7. Against any other dealer up card, we do not split; we should just hit the hand. Thus, our rule for a pair of 3's becomes "3,3; split vs. 2-7, otherwise hit". Clear on all that? Good. Below is the basic strategy chart for the matrix shown above.
Basic Strategy Decision Chart
for the Basic Strategy Matrix shown above.
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Player's Hand Decisions
5 thru 8 Always Hit
9 Double 3 thru 6, o/w hit
10 Double 2 thru 9, o/w hit
11 Double 2 thru 10, o/w hit
12 Stand 4 thru 6, o/w Hit
13 thru 16 Stand 2 thru 6, o/w Hit
17 or higher Always Stand
A,2 Double vs 5&6, o/w Hit
A,3 Double vs 5&6, o/w Hit
A,4 Double vs 4 thru 6, o/w Hit
A,5 Double vs 4 thru 6, o/w Hit
A,6 Double vs 3 thru 6, o/w Hit
A,7 Double 3 thru 6, Stand vs 2,7,8 Hit vs 9,10, A
A,8-A,9 Always Stand
2,2 Split 2 thru 7, o/w Hit
3,3 Split 2 thru 7, o/w Hit
4,4 Split vs 5 & 6, o/w Hit
5,5 Never Split, treat as "10"
6,6 Split 2 thru 6, o/w Hit
7,7 Split 2 thru 7, o/w Hit
8,8 Always split
9,9 Split 2 thru 9 except 7; o/w Stand
10,10 Never Split
A,A Always Split

Remember The Basic Strategy Decision Chart shown here applies only to the game described earlier; you must produce your own to fit the rules of your favorite casino.
Once you've made your Basic Strategy Chart, we can begin to memorize it. To do that, we will produce a set of "Flashcards". Remember those? You probably learned how to add or subtract using those cards and they will also teach you how to win at Blackjack. You need to make one flashcard for each starting hand by reproducing the information above on a 2" x 2' piece of paper. (Manila file folder material does well for this.) Here's what one looks like...

When you're finished, you'll have a pack of flashcards which will help you to memorize the proper basic strategy for the game you've chosen. Start carrying them with you and as you encounter those "lost" moments we each seem to have in our day -- waiting for a plane, sitting at the dentist's office or even while watching TV, pull your cards out and start reciting the rule for the hand shown. Check your accuracy by flipping over the card and then put it on the bottom of the pack. You'll be amazed at how quickly you begin to learn all these rules.
Homework
I said this was a school, didn't I? Well, you will also have some homework to do before we get together again next week. Here are your assignments
Flashcards: Spend a minimum of one hour each day going through the cards.
Next lesson we'll finish with how to learn basic strategy through a discussion and demonstration of additional training aids and exercises which will give you the means to check your accuracy. It is not necessary for you to have your chosen basic strategy memorized perfectly at that point; all you need to know now is HOW to learn basic strategy. Exactly WHEN you learn it is up to you, since each part of this course is separate and does not depend on you knowing perfectly what came before.


To start at the beginning, visit the page.
Lesson 2 - Learning Basic Strategy
by the, reprinted with permission.

This is a very simple lesson -- I'm going to show you how to memorize your chosen basic strategy perfectly. So perfect, in fact, that you won't have to think about which play is proper; you'll just do it automatically. That skill is developed through a lot of practice; many hours of repetitious exercises which will leave you knowing basic strategy as well as your own name. (I didn't say this was easy, just simple ).
But we can make those hours of practice a little more fun and somewhat interesting -- even challenging -- by using different methods of training. If you're a competitive person the timed exercises will appeal to you; it's a lot of fun to see if you can post a new "personal best" in each of them. But don't worry, you don't have to be a Type A personality to learn perfect basic strategy. Just take your time and do as many exercises in a day as you want and if you keep at it on a regular basis, the knowledge will come. Remember, you are learning a skill here which you will be able to use for the rest of your life. Spending a few dozen hours now may return hundreds of hours of profitable play in the future; seems like a fair trade to me.
Let's get started.
Flashcards - By now, you should have a set of these made up and are using them on a regular basis. Start timing yourself as you go through all of them; a good goal is to recite all the rules perfectly and get through your pack in under two minutes. The time pressure works well in "forcing" you to learn, so record your results so that you can see your progress. If you have a stopwatch, so much the better, because you can use it not only with the flashcards but with many other exercises as well. Don't go out and buy one, though; the approximate time is all we're interested in here, so a wrist watch will do just as well.
Basic Strategy Reconstruction Exercise - Print out the form below and run off a bunch of copies. You will notice that it is just a "blank" of the form we used in Lesson 1 to create the rules for each of the player's starting hands. The object here is to write in the rule for each hand and then check for accuracy. Remember the old saying; "I read and I forget; I do and I remember." That's what this exercise will do for you. Time yourself as you do it and see if you can get under 60 seconds with 100% accuracy.
Player's hand Decisions
5 thru 8 _______________________________
9 _______________________________
10 _______________________________
11 _______________________________
12 _______________________________
13 thru 16 _______________________________
17 or Higher _______________________________
A,2 _______________________________
A,3 _______________________________
A,4 _______________________________
A,5 _______________________________
A,6 _______________________________
A,7 _______________________________
A,8-A,9 _______________________________
2,2 _______________________________
3,3 _______________________________
4,4 _______________________________
5,5 _______________________________
6,6 _______________________________
7,7 _______________________________
8,8 _______________________________
9,9 _______________________________
10,10 _______________________________
A,A _______________________________


Basic Strategy Decision Exercise - Here I've made up a lot of player's starting hands along with a dealer's up card. Use your "Basic Strategy Matrix" from Lesson 1 to make a "correction copy" and mark it as such at the top. Then, just go down the columns of another copy and fill in the proper play. Use your correction copy to check for accuracy. Speed is of the essence here, so work towards a goal of completing this in under two minutes with 100% accuracy.
________________________________________
(Indicate proper play under "Decision")
S=Stand H=Hit P=Split Pairs D=Double
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P D Dec P D Dec P D Dec
8,3 A ____ 2,3,6 4 ____ A,4,2 3 ____
6,6 4 ____ 9,9 7 ____ 7,6 3 ____
5,4 6 ____ 10,3 3 ____ 8,2 A ____
7,7 7 ____ 9,8 7 ____ 8,8 10 ____
9,6 8 ____ A,7 2 ____ 10,7 2 ____
7,5 3 ____ A,4 5 ____ 9,3 3 ____
A,2 5 ____ 6,4 10 ____ 7,4 A ____
3,3 4 ____ A,4 5 ____ 6,3 7 ____
9,2 10 ____ 10,8 6 ____ A,6 5 ____
5,5 9 ____ 6,8 7 ____ A,9 6 ____
A,7 6 ____ 9,7 8 ____ 10,4 5 ____
6,3 4 ____ A,2,5 6 ____ 9,9 9 ____
5,2 2 ____ 3,6 4 ____ 2,4 2 ____
10,2 3 ____ 7,8 9 ____ 6,5 2 ____
9,9 7 ____ 10,3 3 ____ 7,7 2 ____
10,4 9 ____ A,4 4 ____ 3,4 5 ____
6,5 9 ____ 10,5 7 ____ 4,4 6 ____
A,6 2 ____ 5,2 10 ____ A,2,4 6 ____
4,4 6 ____ 8,8 8 ____ 10,2,A 3 ____
10,10 5 ____ A,A 7 ____ 8,2 10 ____
8,6 7 ____ 8,3 10 ____ 6,6 6 ____
7,9 10 ____ 5,5 10 ____ 5,4 2 ____
10,2,A 3 ____ A,5,A 3 ____ A,7 3 ____
A,2,2 6 ____ 2,2 7 ____ 3,3 2 ____
2,6 4 ____ A,5 4 ____ 7,8 7 ____
9,A 6 ____ 6,6 2 ____ 9,9 7 ____
10,6 3 ____ 3,7 9 ____ 2,5,4 2 ____
7,7 6 ____ 3,3 2 ____ 10,4 6 ____
A,A 9 ____ 5,5 9 ____ 9,3 5 ____
2,2 2 ____ A,6 3 ____ A,2 6 ____
9,4 4 ____ 10,6 7 ____ 9,8 7 ____
A,3,4 9 ____ 6,6 3 ____ A,4,A 2 ____
A,4,2 6 ____ 9,4 2 ____ 7,5 3 ____
8,8 10 ____ A,4 10 ____ 2,2 6 ____
5,5 8 ____ 6,4 9 ____ 3,3 7 ____
A,8 6 ____ 8,3 A ____ 6,6 2 ____
5,2 2 ____ 9,9 10 ____ 2,9 10 ____
A,4 6 ____ 7,5 4 ____ 9,7 5 ____
2,3,4,A 6 ____ 7,7 9 ____ 5,4 3 ____
A,A A ____ 9,3 7 ____ 7,4 10 ____
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The Importance of Speed - I stress speed in my classes because the ability to do anything quickly and accurately means you know it well. The play of your hand must be "automatic" because once you learn how to count cards, you'll be too busy counting to think about the proper play. Make sense?
The Card Practice exercises that you will read about next are very visual. You might want to consider our, to enhance the learning experience.
Card Practice #1 - Now, with a copy of your Basic Strategy Matrix next to you, get out a deck of cards and try this exercise. Deal one card up for the dealer and then two cards for your starting hand. Play that hand according to proper basic strategy and, without playing out the dealer's hand, push all the used cards off to the side and do it again. Keep going until the deck is used up, shuffle and repeat. This exercise will get you used to making playing decisions in a casino-style setting. Refer to your Matrix as often as you must in order to assure yourself that you are making the proper play.
Card Practice #2 - Some player hands, like A-7 are difficult to learn. So set up a practice like the one above but leave the player's hand the same and change only the dealer's up card after each round. Continue to hit or double as before. This exercise is particularly good for getting you used to playing "soft" hands (those which contain an Ace) properly. Time is not important here but accuracy is.
Card Practice #3 - This is a variation on the practice above. On this one, keep the dealer's card the same -- say a 6 -- then deal two cards for the player. Play out the hand and then move just the player's cards off to the side. "Stack" your deck a bit by putting in a lot of pairs so you can get used to splitting properly.
Homework
• Spend at least a half-hour each day on your flashcards and time yourself.
• Do a minimum of one "Basic Strategy Reconstruction exercise" each day. Time yourself and record the results along with the date right on the form.
• Do a minimum of one "Basic Strategy Decision exercise" each day and mark both the date and time it took you to complete it on the form.
• Spend at least a half-hour each day doing the 3 card practices. Work on those hands which are the most difficult for you to learn.

Lesson 3 - Counting Cards, The Basics
by the, reprinted with permission.

With this lesson, I'm going to unwrap the veil of mystery which seems to surround the concept of card counting. Here you will discover that you don't have to be a genius to keep track of all the cards in a six-deck shoe; you just have to know a few card-counter secrets.
The first "secret" is that we don't memorize the cards in a deck. Instead, each card is assigned a point-value and all we are really doing is adding those point values together and then converting that information into a usable form. Just what those point values are depends upon which counting system a player decides to use. In this school, I'll be teaching the "High / Low" or "Plus / Minus" system but if you choose to learn another one, everything I'm going to teach still applies.
The other big "secret" about card counting is how we do it at the Blackjack table. I think most people who have flirted with counting can get a good grasp of it at home but once they hit all the distractions of a casino their ability to keep track of the cards, play their hand properly and get a bet into the circle on time breaks down. Remember when I told you that it was a MUST for you to know basic strategy as well as you know your own name? Now you'll begin to see why that's necessary; you don't need more things to think about when you're "on the green".
Pick a System
There are a lot of different card-counting systems available and -- like most things in life -- each has its advantages and its disadvantages. I'll try to sort through the most popular and help you choose one which is right for you. Probably the most important factor in choosing a system is the type of game you'll be playing most of the time. For example, if you play mostly in the Reno/Tahoe area, you should learn a system which performs well against single deck games. If you play in my old stomping grounds, Atlantic City, you'll want to learn a system which is powerful in multi-deck games.
Another important factor in selecting a system is the amount of time you spend playing Blackjack. This is going to surprise you, but a player who intends to spend a lot of time at the tables should learn a very simple system. I say that because, while this really is pretty easy, it does require some concentration and the simpler the system, the easier it is to concentrate for long periods of time. On the other hand, if you're only going to play for 3 or 4 hours a week, a more difficult system may work well for you since a difficult system is usually more powerful and it will optimize the time you spend at the tables. Now, some of you "Type A's" out there are thinking that you'll spend a lot of time at the tables and use a very powerful (and complicated) system to get the most $$$ out of your play. The problem here is that under those circumstances, mistakes begin to creep in and that can cause you to lose your edge. The KISS principle applies: "Keep It Simple, Stupid". If you really want to get the most out of the game, do what I did, learn two counting systems. I use one for multi-deck games and another one for single-decks. It's not that hard and as we go through the lessons on learning how to count, you'll see how the exercises I'll teach you can implement such a strategy.
Card-counting systems are rated by two primary factors: Betting Efficiency (BE) and Playing Efficiency (PE). The anomaly of counting systems is that if you increase the BE you are, for the most part, decreasing the PE at the same time. This happens because of the unusual role an Ace plays in the game. For betting purposes, the Ace is a very powerful card; it's the primary component of a "natural" which pays 3 to 2. But for playing a hand, the Ace is of somewhat limited value. How many times have you doubled an 11 and got an Ace? Now you have a total of 12...exciting, huh? Hit a 14, get an Ace and you've got 15; nothing to shout about, is it? Sure, it's great to double a 10 and get an Ace, but that's one of the very few times when the Ace helps in the play of a hand.
How a counting system treats the Ace determines a lot about the BE and PE of that system. If you need a high Betting Efficiency -- like in a multi-deck game -- then pick a system which counts the Ace as a "big" card; if your game of choice is single-deck, then choose a system which treats the Ace as a "neutral" card (and keep track of the Aces in a "side count", a trick I'll show you later.)
Multi-deck games are beaten primarily by a large betting spread. Simply put, you bet small when the house has the edge and much bigger when you have the edge. A counting system with a high BE factor tells you when to bet big. In a single-deck game, where the house knows a big spread will win the $$$, a high PE lets you bet less and still win. Don't forget; casinos know that their games are vulnerable and they are on the lookout for people who can beat them. A big betting spread is one tipoff they use to detect counters and, depending upon where you play, being detected as a counter may cause your expulsion ("barring") from the casino. Let me stress that what I'm teaching you is entirely legal but not everyone in the casino business feels as I do. There are no laws against card-counting and you can be the best counter in the world, but if the casinos won't let you play your skill is wasted.
To help you decide on a count to use, visit the series of articles called "Counting Systems" on the Blackjack menu page of and look at the systems which are reviewed there. As mentioned earlier, I will be talking specifically about the "High / Low" count, but you can learn any count by the methods I'll use. If you're going to be at single-deck games, the Hi-Opt 1 count is probably the best to begin with; go with the High / Low if multi-decks are what you'll be playing. Since I will be teaching "true count", either of those systems will work well, regardless of where you play. Most "unbalanced" counts don't require you to learn true count, but it's not a big deal, so stick with one of the "balanced" counts. For those who really want to get into it, go with Arnold Snyder's "Zen" count, but you should buy his book, "Blackbelt in Blackjack" to supplement what I'm teaching.
In the next lesson I'll show you how to learn a counting system with the following "point" values:
2, 3, 4, 5, 6 = +1
7, 8, 9 = 0
10, J, Q, K, A = -1
This system has a Betting Efficiency of 97% and a Playing Efficiency of 51%. The best system in the world would rate about 98% BE and 70% PE, so what you'll be learning is easy to use for long periods of time, is good at estimating your edge for betting purposes and is just "OK" at playing the hand properly. (But don't worry; it gets the $$$.) By the way, there's a third rating for counting systems and that's Insurance Efficiency. While basic strategy says to never take insurance, once the proportion of tens in the remaining deck(s) reaches a certain point, it becomes profitable to make the insurance bet. The High / Low counting system has an Insurance Efficiency of .76, which means that about 3/4 of the time you do take insurance (as determined by the "true count"), it will be the correct decision. But...we're getting ahead of ourselves here, so copy your homework assignments and get outta here.
Homework
• Continue working with your flashcards at least a half-hour per day.
• Do at least one "Basic Strategy Reconstruction excercise" each day and continue to work on your speed.
• Do at least one "Basic Strategy Decision excercise" each day and concentrate on getting it done in under 2 minutes.
• Work with the three "Card Exercises" and concentrate on adding up your hand as you play proper basic strategy.
School's out for now. See you here next time.

Lesson 4 - Card Counting - How to Do It
by the, reprinted with permission.

By now you've chosen a counting system that you want to learn and even though it may be different than the Hi / Lo Count which I'm going to discuss here, the methods used to learn it are the same. Just make adjustments where appropriate and you'll do fine, but if you are confused or don't understand something, then.
This entire lesson that you are about to study is very visual. You might want to consider our, to enhance the learning experience.
The Hi / Lo counting system assigns a "point" value to each type of card in a deck. The first step in card counting is to memorize those values. Here they are
Card Point Value
2 +1
3 +1
4 +1
5 +1
6 +1
7 0
8 0
9 0
10 -1
J -1
Q -1
K -1
A -1
A bit of simple math will show you that there are, in a complete deck, an equal number of "plus"-valued cards and "minus"-valued cards. This is called a "balanced" count and since all cards are valued either 1 or 0, this is also a "single-level" count.
The Power of Card Counting
The Hi / Lo count recognizes that the cards 2 through 6 are of greatest value to the dealer, since these cards turn the dealer's "stiff" hands (12 - 16) which s/he must hit into good hands. For example, a 5 turns a dealer's 12-16 into 17-21, consequently it is the most important card for a dealer. On the other hand, an Ace is most important to a player, since it's the key component to a "blackjack" which pays 3 to 2. So, as "little" cards are played, they are no longer available to the dealer and since there are an equal number of plus- and minus-valued cards in the deck, a "plus" count tells us that there are a higher proportion of tens and aces left in the unplayed portion of the deck. This situation is favorable for the player since the chances for a blackjack have increased and doubling or splitting situations stand a better chance of receiving a high card.
Of course, a dealer has the same chance of receiving high cards as you. But remember that the dealer does not receive 3 to 2 for a blackjack, may not double or split and must hit 16 or less. Also, as you will learn in a later lesson, knowing the proportion of 10-valued cards in the decks gives you the knowledge to make profitable insurance bets.
Learning The Point Values
This is the only exercise you will ever need to learn the point values of your counting system. It's the one I use when I'm switching counts for a single-deck game or back again to the one I use for multi-deck games. Just take a deck of cards and begin turning them over one at a time and recite the point value of each card. If a card is a plus-value, I don't say "Plus 1"; I just say "one", because it implies "plus" anyway. If a card is a minus-value, I say "M 1", not "minus 1" because it saves a syllable. For the "neutral" or zero-value cards, I say nothing -- they are completely ignored for counting purposes with the Hi / Lo system.
So, how does this look? Here's a quick example
Ace (M-one)
9
5 (One)
6 (One)
7
King (M-one)
2 (One)
10 (M-one)

Notice that I'm not keeping track of the cards, but merely stating the point value of each. You must practice this until you have the point values firmly implanted in your mind but don't worry, it won't take long.
Single-Card Countdown
If you feel you know the point values of each card in your system of choice by heart, you may now begin to count down a single deck. Simply remove any three cards without looking at them (to check your accuracy) and set them aside. Now turn over cards one at a time and keep a running total of their values. Remember your old algebra classes? If you add +1 to -1 the result is 0. That applies here, so keep it in mind as you go through the deck.
Here's an example:
1st card Ace The count: M-one
2nd King M-two
3rd 10 M-three
4th 6 M-two (make sure you know why)
5th Queen M-three
6th 5 M-two
7th 3 M-one
8th 6 Even (I don't use "zero")
9th 4 One (again, no "plus")
Got it? Good. You're not very fast yet, are you? Well, don't worry about that; we'll work on speed later. When you've completed the deck, the count should be off by the value of the three cards we set aside in the beginning. Look at those cards, check your accuracy, shuffle and begin again. Get into the habit of removing three cards every time you do any counting exercises since they will keep you from fooling yourself when you make a mistake.
For now the key is accuracy; keep at this until you can go through a deck three or four times in a row without mistakes. What you have learned here is called the "running count". Next time we'll work on speeding up your ability to count; can you believe I'll have you zipping through a deck in less than 20 seconds? The babes really love that at parties...
Homework
• Continue testing yourself on basic strategy by doing the Basic Strategy Reconstruction and Basic Strategy Decisions exercises. You won't win if you can't play proper basic strategy.
• Begin learning the point values of your chosen system and when you know them by heart -- and only then -- start doing single-card countdowns of one deck.
See you here next time. Practice!


Lesson 5 - Card Counting - The Tricks
by the, reprinted with permission.

No, I'm not going to teach you card tricks here, but I am going to show you a few interesting ways to practice the count you've decided to learn and then teach you the methods we use to keep track of the cards as they're played at the casino. Developing your speed at counting is an important part of your training, because if you can't count quickly at home, you'll never keep up with the dealer in a casino. Inaccurate counting can cause you to give up any edge you have over the house and it's frustrating to constantly "drop" the count when a faster dealer comes along.
At this point you should have the point values of each card memorized and you might be doing some single-card countdowns of a deck. I'm sure you're slow at it, but that's OK, since accuracy is the most important factor right now. Speed will come as you work your way through the exercises I'll show you this week.
This entire lesson that you are studying is very visual. You might want to consider our, to enhance the learning experience.
Pairs Value Practice
Just as you learned the point value of each card according to the system you wish to use, here you will learn the point value of different PAIRS of cards. This is one of the real "tricks" of the card-counting business: the ability to count cards in pairs. With enough practice, you'll see a hand of Queen, Jack as both a "20" and an M-2. That capability will bring speed to your game. Here are the values of pairs using the Hi / Lo method of counting:
Hand Net Point Value
-2
-2
________________________________________
-1
-1
________________________________________
0
0
________________________________________
+1
+1
________________________________________
+2
+2
________________________________________
Important! Make sure you understand why each pair is valued as shown and don't forget that if you're learning a different count, these pairs may have different values.
If you understand everything above, then start going through a single deck and turn two cards over at a time. DO NOT keep a running count, just recite the value of each pair so you can get used to the adding and subtracting which is required. Do this until you are totally familiar with the values of all possible pairs. Then do it some more.
Laying down a good foundation here will allow you to build your speed quickly later on, so this exercise is time well spent. For you "Type-A's" out there, you might even push this to learning 3-card values. That is a very helpful skill to have, particularly if you intend to play one-on-one with a dealer, since you always see 3 cards at once; your initial pair and the dealer's up card. Most of you will want to begin play at tables with other players since things move slower that way, but like I said -- knowing the 3-card values won't hurt.
Pairs Countdown
Once again, remove three random cards from a single deck and set them aside. (No peeking!) Now, turn over the cards two at a time, keep a running (cumulative) count of the deck and check your accuracy by adding the cards you set aside in at the end. This exercise will be your primary way of practicing card counting.
Gradually, your speed will increase to a point where you will count as quickly as you can turn over the cards. To go even faster, hold the deck in your left hand, face up, and pull the cards -- two at a time -- off the deck with your right hand. (Opposite if you're left-handed). Help the cards along with your thumb and you'll start to build some speed. How fast is "fast"? I go through a deck in 10.5 seconds, but all you need to keep up at an average table with 2 or 3 other players is 20 seconds, though 15 is better (and easy attained if you practice).
Counting at the Table
The method we use to count cards at the table is the real secret of this business. For those games where the cards are dealt face up to the players, the diagram below will show you how we do it. Games where the cards are dealt face down (mostly single deck) require a different methodology and we'll cover that next week.

Most dealers keep their up card face-down until each player has received both cards. The procedure for counting at a table like that is to begin counting when the player at "first base" receives his second card and to count each player's pair as the cards are dealt. End your count with the dealer's up card and then count each player's "hit" cards. Finally, count the dealer's hole card and any cards the dealer may take as a hit.
You can see that this method of counting by pairs allows you to look more natural at the table. Most people think counters track each card as it's dealt, so supervisory people at casinos watch for players who follow every cards as it comes out. My method allows you to look away from the table as the first card is going down and then watch as each hand is made with the second card. That looks a lot more natural, since most players are interested in seeing what hands other players get.
Homework
Besides continuing with your basic strategy practice, start playing some "kitchen table" Blackjack. If you can con someone into dealing to you, great, but if you can't, just deal four player hands out in a manner they use at your favorite casino. Don't assume the role of the dealer; you want to get used to seeing all this from a player's perspective so deal one card to an imaginary first-base player, then to yourself and then to two other imaginary players on your left. Finish with a dealer's card face down across from you and then deal the second player's card. Begin counting as shown above and finish with a dealer's up card. Now, play ALL FOUR player's hands according to proper basic strategy and keep the count. Busy, huh? Don't worry, with practice it will all come to you. When you're done with the first round, do another and then riffle through the few remaining cards to verify that you've kept the count accurately.
This exercise will form the basis for all of our practice -- except speed development -- from here on out. As you'll discover, this type of "overload" makes it very easy to play and keep count at an actual casino game; all you need to do there is just sit back, count and play.


Lesson 6 - Card Counting - Single-deck Play
Every serious counter should have a good knowledge of how to play single-deck Blackjack, even if you spend 90% of your time at multi-deck games, because when you are able to get to a single deck game, it can be very profitable. The primary lure of the game will become more evident as we get into betting strategies, but take my word for it now: any "big" money you'll make at Blackjack will probably come from a single-deck game.
Most of you -- especially those who are close to Atlantic City -- should spend your time practicing instead of playing, all with the idea of taking 5 or 6 trips a year to areas such as Reno or Laughlin. You'll be much better off playing 60 or 70 hours a year at the single-deck games there than you would be playing several hundred hours at the dismal games A.C. is currently offering. Most of my students from the St. Louis area can fly to Reno on a 3 or 4 day trip for under $300, which includes round-trip airfare and hotel, and since they usually make that much in Blackjack profits per day, they often come home with a $1000 or more in net winnings. You "Eastcoasters" can find similar action in Tunica, MS.
This entire lesson that you are studying is very visual. You might want to consider our, to enhance the learning experience.
Counting at the Table
To win at single-deck games, you first need to learn another method of counting at a table where the cards are dealt face down. As you will recall from Lesson 5, there is a very structured approach required for counting in order to make sure you're doing it accurately. I'll never forget the first time I played single-deck; it was in Vegas and I was used to the, then, four-deck game in Atlantic City. On about the second or third hand, the dealer had a "Blackjack" and everybody threw their cards in, face up. Talk about scrambling; my speed training was tested to its limit, but I got the count before the next hand was dealt. That's a situation for which you'll have to be ready and only practice will get you there.
Cards get turned face up for various reasons at a single-deck game, so let's go through a hand and see when you will count them. Begin by counting your two cards, then dealer's up card. Count any hit cards for the players since those will be delivered face up. If a player doubles , s/he will turn his or her first two cards face up, so you'll count them. However, the "double" card will usually be dealt face down, so you won't count it yet. If a player splits a pair, those will be turned face up so count them and then count the "hit" cards as they come out. In a single-deck game, a player signifies a "stand" by placing the cards underneath the bet so you don't see them, consequently you can't count them -- yet. Should a player bust, s/he will toss in his or her first two cards, so count them as you see them. Play ends at the dealer's hand, so count the dealer's hole card as it's turned up and any hit cards for that hand.
Now comes the tricky part. The dealer will begin at the "third base" side and turn over any "hole" cards (as well as double-down cards) from underneath the bet and set them above any other cards in the hand. They will end up as the two cards closest to the dealer; count them as they're exposed. A typical hand will look like this:

As you can see, this player had a hand totaling 7 and took a hit. The dealer has pulled the cards over the top and will now pay it as a winner. Count those two cards as they're exposed, but DO NOT count the King again, since you would have counted it when the player "scratched" for a hit.
This may still be a bit confusing, but once you fit the idea in your mind, you'll quickly get into the scheme of things when you watch a real game in action. You should just stand behind and observe until you're sure you've got the technique, but it won't take long. The ideal way to practice is to have someone deal for you, but make sure they use the procedures shown above.
Developing Your Speed and Endurance
I often use the analogy of a prize fighter when I discuss practicing your counting; a fighter trains for both speed and endurance. They use a "speed bag" for the short, fast jab and a big, heavy bag for the hard punches. A single-deck countdown is your "speed bag"; try to get through it as quickly as possible while maintaining your accuracy. To build your endurance, begin by counting down two decks shuffled together (don't forget to remove 3 cards to check your accuracy). Once you're doing two decks under 40 seconds, go to 6 decks. Shuffle all six together, then break them down to 5 or 6 separate piles on a table top and count them all down as quickly as possible. Your goal here is to do it under 2 minutes; under 1:30 is ideal. The reason why we do so many decks, whether we're training for a single-deck or multi-deck game, is to not only get used to retaining the count for a long period of time, but also to get used to wide swings in the count. The running count for a single deck will seldom go above or below 10, but you'll often get such counts in a six-deck countdown and you need to get used to that. Practicing like this with a lot of distractions around is good. Do it with the kids bugging you, with the TV on, or with Fido barking and you'll develop your ability to keep track while you're in a casino.
A Few More Tricks
Learn to count backward from an odd number by 2's. We can all count "2, 4, 6," etc., but few of us can count "11, 9, 7, 5, 3" very quickly. This is a good exercise to do while you're driving. Start at 25 and take it to M5, over and over again; it will "imprint" in your mind and serve you well at a full table when the count is high and all those 20's and Blackjacks come out. When you get bored, do it backward from an even number just to keep yourself in shape.
When your counting is interrupted for any reason, recite the count to yourself over and over again. Let's say you're practicing at home and little Margaux or your son, Corky (isn't every card counter also a wine fanatic?), has a "life or death" question. If the count at that point is M6, just keep repeating "M6, M6, M6" in your mind as you listen to them. You'll know you're making real progress when you can then TALK to them and remember the count! Practice is what allows that to happen.
Homework
Continue working on your speed with a single-deck countdown, but also work in some two-deck exercises as well. When you can do two decks accurately in under 40 seconds, go to a six-deck countdown.
Important: All I've shown you here also applies to most double-deck games, but you must remember that the basic strategy does change a bit when you're playing a game dealt from less than four decks. See Lesson 1 for how to learn the single-deck basic strategy.
Next we'll begin discussing the only reason for playing Blackjack: Money.
Until then, school's out.

Lesson 7 - Money Management - Part 1
A Sermon
I do a little bit of preaching on the pages of The GameMaster Online every so often, primarily because I hate to think of people handing their money to casinos. I'm not saying I don't lose, because I have my bad days as well, but what I am saying is that the casinos have to fight me for every penny they get. You need to develop that kind of attitude and just the fact that you're reading this now shows me that you're willing to learn, so you've got a good start. Casinos make money because the players allow them to make money. Even if you've learned everything I've taught you up to this point, you're still not ready to play, so forget about it and start building your bankroll towards the day when you WILL be ready. You cannot expect to win at Blackjack if you're betting the rent money. You must have a sum of money set aside which is "extra" -- money which, should you lose it, will not affect your lifestyle in any way. By doing it that way, you'll bet what needs to be bet and play the hands as they need to be played. That's what gets the $$$ at the casino. 'Nuff said.
What is Money Management?
As it applies to playing Blackjack as a card counter, money management is a method of betting which will minimize your losses and maximize your gains. Playing Blackjack carries with it the risk of loss. The advantage a counter has over the casino is small and the fluctuations in a player's bankroll can occur with frightening speed. Proper management of your funds is required in all aspects of the game to give you the best possible chance of reaching that elusive "long term". Some of you will begin your careers as counters with a big win and you'll never look back. Most of you, however, will begin with a loss and it will take more hours of play before you start showing a profit; that's just the reality of the situation. What I'm going to teach you in the next four or five lessons is how to survive at the game until your long term edge begins to have its effect and then show you how to keep the profits you make.
The True Count
The concept of the "true count" is very visual. You might want to consider our to enhance the learning experience.
All of our betting decisions will be made on the basis of what is known as the "true count" or more accurately, the "count per remaining deck". While most of this applies to those who will be playing at multi-deck games, you single-deckers pay attention, too -- you'll need to know this as well. If six small cards come out on the first hand in a game, we will have a running count of 6. For the single-deck players, you will have a true count of just over 6, since there's just a bit less than one deck remaining to be played. If you're at a six-deck game, the count per remaining deck (the true count) is just a bit over 1, since there is just a bit less than 6 decks remaining to be played. See how that works? We are "standardizing" the count by dividing the running count by the total number of remaining decks. Let's try another example to see if you understand the concept. At a single-deck game on the first hand, a running count of 2 (remember, I don't use "+" to indicate a positive number) converts to a true count of 2, when rounded off. In a six-deck game and a running count of 12 after the first hand, the true count converts to 2. Both true counts are 2 , but it takes a much higher running count to achieve that in the six-deck game.
TO DETERMINE THE TRUE COUNT, DIVIDE THE "RUNNING" COUNT BY THE NUMBER OF DECKS REMAINING TO BE PLAYED.
Don't let that statement confuse you. What this means is the number of decks left, whether they'll actually be played or not. In a six-deck game, a deck or more may be cut off by the dealer, but that means nothing when computing true count. The basis for the calculation is the total number of decks in the game which is adjusted by the number of decks which have been played. An example: in a six-deck game where two decks have been played and put into the discard rack off to the side, a running count of 8 translates into a true count of 2 because there are four decks left in the shoe. The dealer may shuffle before all four of those remaining decks have been played, but for true count conversion that doesn't matter.
Take this little test with me to see if you understand the principle.
Deck Remaining Running Count True Count
1. 4 8 2
2. 2 10 5
3. 5 5 1
4. 3 12 4
Estimating the Number of Remaining Decks
The casinos are very nice about providing us a device to determine just how many decks there are remaining to be played in the shoe. No, that device is not the shoe, but the discard tray which can be found on virtually every table where a multi-deck game is played. As cards are used, the dealer places them very neatly in the discard tray where everyone can see them so counters use that, and a bit of subtraction, to determine how many decks are left to be played. At a six-deck game, if there are two decks in the discard tray, there has to be four decks left in the shoe, assuming no cards are on the table. What we strive for is to be accurate to within a half-deck for our estimation. Just exactly how to train for that is one of your homework assignments, so don't worry about it for the moment. What's more important at this point are the mechanics used to calculate the true count by that method. Let's walk through a simple explanation together.
We're at a six-deck game, the running count is M-6 and three decks are in the discard tray. That means three decks remain, so we divide the running count by 3 and our true count is M-2. Yes, this works for negative decks as well -- exactly the same way. Got it? Try this test to see if you do.
Assume we're at a six-deck game. I'm only going to give you the decks in the discard tray, so do the calculation to determine the number of decks left in the shoe.
Decks Played Running Count True Count
1. 2 4 ?
2. 4 8 ?
3. 5 5 ?
4. 1 5 ?
5. 2.5 7 ?
6. 2 0 ?
7. 3.5 M-5 ?
8. 1.5 9 ?
9. 3 M-3 ?
10. 4.5 2 ?
The Answers

1. One (2 decks played, 4 decks remaining, 4 divided by 4 = 1)
2. Four (4 decks played, 2 decks remaining, 8 divided by 2 = 4)
3. Five (You're on your own now, kid.)
4. One
5. Two
6. Zero
7. M-two
8. Two
9.M-one
10. A bit over one (but we always round "down" in order to be conservative, so we'd call this "one".)
I can see some eyes glazing over out there, so we better stop for this week. But don't be discouraged; you can learn this -- it just takes some practice. Speaking of practice, pick up your homework assignment and practice "calibrating" your eyes.
Homework
Estimating the number of decks remaining in a discard tray is really just an exercise in repetitive staring. If you look at a deck of 52 cards long enough, you can tell if 10 or 12 cards have been added to it. So, that's how we calibrate our eyes. Begin with a single deck and look it for a while. Then, put another deck on top of it and look at that for a while. Now, put a third deck on top and look at that for a while. Finally, pull one deck off -- don't count the cards -- just estimate how much a deck is, pull it off and then count it to see how close you were. Now, put that deck back on top and pull off two decks, count them for accuracy and put them back on top. Now, build your stack up to five decks and pull off a deck and a half, then three decks and so on. You'll be amazed at how quickly you've begun to recognize how many decks are in a pile. A nice variation to this exercise is to have a friend set up piles of various sizes (within a half-deck accuracy) while you're out of the room and then you come in and recite the size of each pile.
Keep at it, because you've got to be accurate at this. Your money will be riding on it.
See you here next week when we discuss how to bet by using the true count.

Lesson 8 - Money Management - Part 2
A Few Words on Single Deck
In the previous lesson, I taught you how to figure the "true count" for a multi-deck game, but I want to emphasize that the concept of true count also applies to single-deck games as well. The conversion is done a bit differently, but the result is the same; you end up with a standardized count per remaining deck. If you see just one card in a single-deck game, a 5 for example, you now have a "running count" of 1 and a true count of one. That, of course, is because there's only one deck in the game to begin with and we determine the true count by dividing the running count by the number of remaining decks. If, after playing several hands the running count is 6 and there's three-fourths of a deck left to be played, we must divide the running count by .75 in order to determine the true count. In this instance, the true count is 8. If we were at the halfway point of the deck, the true count would be 6 divided by .50 = 12. Got the concept of that? In a single-deck game, you have to divide by fractions, and that isn't easy to do, so all you single-deck counters need to practice this in order to figure it properly when you play.
Betting With the True Count
For each increase of 1 in the true count as figured by the Hi / Lo counting method, the player's advantage increases by about .5% in the average Blackjack game. If the casino has an edge over the basic strategy player of .40% (6 decks, double on any first two cards, double after splitting pairs, dealer stands on A-6), it takes a true count of just about 1 in order to get "even" with the house. Being even means that the player who utilizes proper basic strategy will win as much as s/he loses -- in the long run -- at a true count of one. A true count of 2 gives the counter an edge of .5% over the house; a true count of 3 gives the player an edge of 1% and so forth.
It is the edge that a player has on the upcoming hand which determines their bet. Counters bet only a small portion of their capital on any given hand, because while they will win in the long run, they could lose any one hand. By betting an amount which is in proportion to their advantage (called the "Kelly Criterion"), they are maximizing their potential while minimizing the risk. A lot of people misinterpret the Kelly Criterion by assuming that the amount bet is in direct proportion to the advantage. They think that if you have a 1% edge, you should bet 1% of your "bankroll" and that is incorrect. What they are forgetting is the doubling and pair splitting which goes on in the course of a game and that increases the risk or "variance" of a hand. For a game with rules like those listed above, the optimum bet is 76% of the player's advantage. Here's a table of optimum bets which will work well for most multi-deck games:
True Count Advantage % Optimum Bet
-1 or lower -1.00% or more 0%
0 -0.50% 0%
1 0% 0%
2 0.5%x76% .38%
3 1.0%x76% .76%
4 1.5%x76% 1.14%
5 2.0%x76% 1.52%
6 2.5%x76% 1.90%
7 3.0%x76% 2.28%
By using this table, you can determine the optimal bet for any bankroll; just multiply the figure in the last column by the amount of the bankroll. Thus, for a bankroll of $3000, the optimal bet for a true count of 2 is .0038 X $3000 = $11.40.
Some Practical Considerations
First and foremost, it isn't practical to bet in units of less than $1, so a betting schedule must be rounded off. Secondly, it is more appropriate to bet in units of $5 so that you'll look like the average gambler, plus it cuts down on the calculations you need to make. Further, it is impossible to refigure your optimal bet while seated at the table, even though it should be recalculated as the bankroll varies up and down. Finally, it just isn't possible to play only at shoes where the true count is 2 or higher; you will sometimes have to make bets when the house has an edge. All of this rounding and negative-deck play cuts into your win rate, but by knowing the conditions which can cost you money, steps can be taken to minimize their impact on your earnings.
The Betting Spread
A single-deck game with decent rules in which thirty-six cards or more are used before a shuffle can be beaten by a 1 to 4 spread. A two-deck game in which seventy cards or more are used before the shuffle can usually be beaten by a 1 to 6 spread. A game with four decks or more will require a spread of 1 to 12 in order to get an edge. We'll discuss the evaluation of games in a later lesson, but I wanted to lay the foundation for your money management by giving you an idea of what it takes to play winning Blackjack. The spread is expressed in betting units, so if you play with $5 chips, you'd be spreading from $5 to $60 in a six-deck game. Since a counter should have a bankroll consisting of a minimum of 50 top bets, a spread like this will require a bankroll of $3000.
With a $3000 bankroll, a betting schedule could look like this:
True Count Player's Bet Optimum Bet
0 or lower $5 $0
1 $5 $0
2 $10 $11.20
3 $20 $22.80
4 $40 $34.20
5 $50 $45.60
6 $60 $57.00
A betting schedule like this allows you to "parlay" your bets as the count rises, thus making you look more like a "gambler".
YOU WILL SAVE A LOT OF MONEY AND FIND MORE PROFITABLE SITUATIONS IF YOU LEAVE A TABLE WHEN THE COUNT HAS GONE DOWN TO A TRUE OF - 1. BUT LEAVE ONLY AFTER LOSING A HAND; NO GAMBLER WOULD LEAVE A TABLE AFTER A WIN.
So, have I got your brain spinning? If so, just hang in there as I'll be wrapping all this up in a nice, easy-to-understand package in the coming weeks. As always, get your homework, then you're outta here.

Lesson 9 - Money Management - Part 3
Expectation and Standard Deviation
If you flip a coin 100 times, your expectation is to receive 50 heads and 50 tails. But the reality may well be different; the measurement of that reality is called "standard deviation".
Standard deviation is a mathematical term used to predict the outcome of a situation. In our coin-flipping exercise, we expect 50 heads and 50 tails to occur, but two-thirds of the time the actual result will be somewhere between 45 and 55 either way. That is, a result of 55 heads and 45 tails or something in between is not unusual; it will happen 68.3% of the time. That measurement is for 1 standard deviation from the expectation and if we were to run hundreds of 'trials' of 100 flips, we could plot our results on a bell curve and the vast majority of results would fall between 55 and 45 either way. What would be unusual would be to have a lot of trials where the result was actually 50-50! Got that concept in your mind? Good. You'll need to understand this in order to survive the mental turmoil caused by the losses which are inevitable in this game.
Nothing has caused counters to give up Blackjack more than a lack of understanding about normal, everyday standard deviation. Counters who have trained hard unrealistically expect to win each time they play, so when they have several losing sessions, they forget what they've learned. Next thing you know, they're over betting their bankroll and fail to play their hands properly and when they wake from the daze, their money is gone.
PATIENCE AND SKILL WIN -- HUNCHES AND WISHING WILL NOT WIN. PRAYER DOES NOT WORK AT BLACKJACK.
So, what can you expect -- what's the worst which can happen? Well, you can lose all your money, but if you establish a bankroll of at least 50 'top' bets, play proper basic strategy at all times and don't over bet, you stand a good chance of making some $$$ at Blackjack -- if the game at your local casino is a game which can be beaten. Did I ever say this was easy?
The table below illustrates the possible results from varying hours of play at a fairly typical game. Shown with the expectation are the possible dollar results as measured by 1 standard deviation (68.3% of the time) and 2 standard deviations which covers what will happen 95% of the time. Three standard deviations cover what will happen 99.7% of the time.
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Expected Win / Standard Deviation
Assumptions: $12 average bet, 50 hands per hour,
1.25% average advantage.
Results
Time Expected Win 68.3% of the time 95% of the time
3 hours $22.50 +$240 to -$168 +$435 to -$373
12 hours $144.00 +$552 to - $264 +$961 to -$673
48 hours $360.00 +$1393 to -$242 +2,212 to -$1,059
90 hours $675.00 +$2,300 to -$40 +$3,320 to -$1,160
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Let's talk about this a bit. If you were to play several hundred 'sessions' of 3 hours each, the average win for those sessions would be about $22.50. (This comes from using a $5 to $60 betting spread which we discussed in previous lessons). But few sessions would result in a win of exactly $22.50; about two-thirds would be somewhere between a win of $240 and a loss of $168. Most of the other sessions could see you winning as much as $435 or losing as much as $373 and a few would see wins or losses even bigger than that! Do you see now why it takes a bankroll of $3000 to support a $5 to $60 betting spread? In order to be successful, you must be able to absorb losses which are many times that of your 'expectation'. These fluctuations are real; they will happen to you at one time or another and if you're not prepared for them, you'll either get frustrated and quit or lose your cool and blow your bankroll.
Now look at the results for 90 hours of play. Most of you will be -- at worst -- about breakeven after that many hours. A few might be up by $2300, but some of you could be down by $1160 or more. Boy, I'd hate to hear the names you'll be calling the old GameMaster then! But it can happen and it won't be unusual if it does, so ask yourself right now if you can deal with playing a disciplined game for 90 hours, still be at a loss and continue playing and betting as I've shown you. It's sad, but most of you won't be able to deal with that and you'll be another victim of standard deviation. That's why I'm not afraid of the casinos going out of business, even if every player in the world learns how to count cards -- few have the patience to stick it out. I don't want to be overly-negative, but that's the reality. However, if you do stick it out, the percentages will eventually begin working in your favor. As I tell all my students, "the money comes in 'chunks' at Blackjack". This is not a slow, consistent way to make money; your bankroll will, at times, resemble a roller coaster and it's difficult to deal with that from an emotional point of view.
Just try to understand the concept of standard deviation and continue 'calibrating' your eyes by doing deck estimation exercises with six decks. As I've said before, you need to be accurate within a half-deck for computing the true count.

Lesson 10 - The Proper Mental Attitude
I always stress the idea of 'expectation' as it applies to casino gaming because understanding the concept will help you stop gambling and hopefully turn you into an investor at the tables. By definition, an investor expects to make a profit so you cannot be an investor if you play at games where there is a negative expectation. If you bet $10 on the Pass line at craps, you'll either win $10 or lose $10, but your 'expectation' is to lose 14 cents on every hand. That's because the house has a built-in edge of 1.4% on that bet and if you play it frequently, your average loss will work out to be 14 cents per decision. In the short term you might win a lot of money, but play it long enough and the house edge will eventually have its effect. Since the average craps table produces about 60 decisions an hour, the cost per hour of betting $10 on the pass line will work out to be -- in the long run -- about 60 X 14 cents = $8.40.
Now let's look at this concept from the point of view of a positive expectation situation like card counting at Blackjack. If your average bet is $12 and the average advantage you have over the house is 1.25%, your expectation is to win $12 X .0125 = $.15 per hand. Yes, that's 15 cents per hand. At a rate of 60 hands an hour, you can expect to make -- in the long run -- about 60 X 15 cents = $9.00 an hour. But, if you can increase the number of hands you play per hour to, say, 80 hands, you've raised your expectation to 80 X 15 cents = $12.00 an hour. The only other way to make more money is to either raise the size of your average bet or increase your edge over the casino. The bet size is just a function of your bankroll (and your ability to continue 'fooling' the casino into believing you are just another gambler and not a card counter) and the advantage is mostly a function of the casino's rules for their Blackjack game. I will address both these issues in future lessons, so for now let's focus on increasing the number of hands you play in an hour.
More Hands Mean More Money
If you are the only player at a six-deck game, you can play at a rate of about 200 hands an hour. With all else remaining equal, that will raise your expectation to 200 X 15 cents = $30 an hour -- a very healthy increase. The problem here is that I want you to get up and walk away whenever the true count drops below M1, so 200 hands an hour is possible only if you get one of those shoes where the count stays positive AND if you are fast enough to keep the count while your playing at this rate. Moving when the deck goes bad is a must, since it's cheaper to not play at all rather than play at a game where the house has an edge over you.
But 200 hands an hour is a worthy goal, so continue practicing with your single-deck countdown in an effort to build your speed to a point where you can go through a deck in under 20 seconds. When you can do that and compute the true count and play perfect basic strategy, you should play one-on-one whenever possible. That may mean that you'll have to go to the casino at 2 AM on a Monday, but it will be worth it. Just remember that increasing your rate of play will increase your hourly standard deviation, so don't be surprised if you lose $400 or more in an hour's play; your risk hasn't increased but you have -- in effect -- 'compressed' your time factor. Dealers often tell me that a player "can't win" one-on-one, but they're wrong. Their misconception in this regard comes from the fact that because more hands are being played, the swings are bigger and dealers usually remember the big losers and forget the big winners. As an investor, it is in your best interest to play as many hands an hour as possible, since your expectation is to win 15 cents a hand.
THE GOAL OF THE PROFESSIONAL PLAYER IS TO PUT IN AS MUCH QUALITY PLAYING TIME AS POSSIBLE; WIN OR LOSS AMOUNTS ARE SECONDARY. BY PLAYING AND BETTING CORRECTLY, THE $$$ WILL COME WITH TIME.
A Winning Attitude
As I've said before, the wins at Blackjack come in 'chunks', so you shouldn't be concerned when you have a losing session, nor should you feel invincible when you win. A proper mental attitude eliminates the highs and lows of the game (thus making it very boring -- at least in my opinion) but it enables you to play a solid , unemotional game. When I have a losing session (on average, 35% of the time), I just go away knowing that the casino will take good care of the money and I'll eventually come back and get it. 600 hands of play means I've 'earned' 600 times my expectation per hand so I just need to keep going to work and my paycheck will eventually reflect my earnings. To put it simply, if you are playing a winning game, it isn't a matter of 'if' you will win, merely a matter of 'when'.
So let the ice-water begin to flow in your veins -- as one author put it, "steely blue eyes will do." Emotion has no place in card-counting; accuracy and patience are the only requirements for getting the $$$.
Homework
Get an old deck of cards and a marker pen. For those of you playing at 6-deck games, write the number "1/2" on the back of one card, "1" on the next card, "1 1/2" on the third card and continue up to 5 by increments of one-half. Now , number the backs of 20 more cards individually from 1 to 20. Shuffle both piles (separately) face up so you can't see the numbers and turn over the top card from the first pile. This will represent the number of decks in the discard tray. For example, if it's the "2 1/2" card, it represents 2 1/2 decks in the discard tray, so that must mean there are 3 1/2 decks left in the shoe. Now begin turning over the cards from the second pile. These represent the running count and we want to practice computing the true count, so if the first card is "8", the true count is 8 divided by 3 1/2 = 2 (remember, we round down to be conservative). Keep going through the running count cards while the 'decks' card remains the same. When you've gone through all the running count cards, change the 'decks' card and do it again.
This exercise will help speed your ability to compute the true count accurately. Those of you who will be playing single deck just need to make a card for 1/4, 1/2, and 3/4 decks and running-count cards from 1 to 10, but you will practice the same way.
I usually demonstrate this, instead of writing it out (), so if it's confusing, please don't hesitate to e-mail me and I'll explain it further. As you do this exercise, concentrate on accuracy and remember to be conservative in computing the true count.

Lesson 11 - Evaluating Games
While almost all Blackjack games are ultimately beatable, the rewards to be gained from marginal situations do not adequately compensate you for your time and risk. Therefore, you must evaluate a game in several ways before playing it. Two primary areas of concern are the house rules of the game, including the number of decks used and the placement of the cut-card, what we call "penetration."
Many rule changes require a change in your basic strategy, so don't forget about the " Rule changes may also affect your betting schedule, so if you have any doubts about what to do,
Effect of Rule Variations on the Player's Edge
(Assume 6 decks, double on any first two cards, no double after splitting, resplit all pairs, except Aces, insurance is available and the dealer stands on Ace-6. This yields a -.54% advantage to the player.)
Changes which help the player Change in the edge
Double after split +.14%
Resplit Aces +.07%
Early surrender vs. all +.70%
Early surrender vs 10 0nly +.30%
Late surrender +.08%
Single Deck +.50%
Two Decks +.20%
Four Decks +.05%
Changes which hurt the player Changes in edge
Dealer hits A-6 -.20%
Double only on 11 -.46%
Double only on 10,11 -.09%
Double only 9, 10,11 -.09%
No resplitting pairs -.04%
No insurance (if you are counting cards) -.40%
To determine the casino's edge over you at the beginning of a shoe, just add or subtract the rules variations from the 'base' game listed above. For example, if you play a double deck game which has the same rules as the base game, the casino advantage is computed as follows.
Base game -.54%
Two Decks +.20%
_____________________
Player edge -.34%
Effect of Deck Penetration
How far the dealer goes into the deck(s) before shuffling can have a major effect on your winnings. The reason is that with a shallow penetration, the 'high' counts which enable you to bet more occur less often in decks where the shuffle comes early. The table below shows how often counts will occur on a percentage basis at varying degrees of penetration.
Percent Occurrence at...
True Count 50% 65% 75% 85% penetration
+1 15 15 13 13
+2 8 7 8 8
+3 3 4 4 5
+4 1.5 2.5 3 4
+5 1 1 2 2
+6 .5 1 2 2
+7 0 .5 1 1.5
+8 0 0 .5 1
+9 0 0 0 .5
+10 0 0 0 .5
Let's examine what I'm trying to say here. If you play at a game with only 50% penetration, out of every 100 hands, only 29 will have, on average, a true count of 1 or better. Since it requires a true count of 1 to get even with the house, only 14 will be hands on which you have an advantage. Now look at the stats for a game with 85% penetration. Here, about 37.5% of the hands will be at breakeven or better and almost a quarter will be hands on which you have an advantage.
YOU ARE WASTING YOUR TIME AND MONEY IF YOU PLAY AT A GAME WITH LESS THAN 65% PENETRATION.
Even if a game doesn't offer the best rules, it can still be beaten if good penetration is available. Remember that you should leave a game when the count drops below a true of minus 1 so that you spend most of your playing time making bets in what I call the 'profit zone.'
Homework
Calculate the player starting advantage for the following:
• Single deck, double only on 10 and 11 and the dealer hits A-6. Resplits (except Aces) are permitted and insurance is available.
• Six decks, dealer stands on A-6, double any first two cards, double after split is allowed, resplitting permitted, including Aces and insurance is available.
• Two decks, double on any first two cards, no resplitting of pairs, no double after split allowed, late surrender and insurance is available.
I'll post the correct answers to this quiz in the next lesson.

Lesson 12 - Casino Playing Tactics
What Are Casino Playing Tactics?
It's a sad fact of life that casino personnel, especially floor supervisors and pit bosses do not like card counters playing at their Blackjack games. They know the game can be beaten by a skilled player, so depending upon how deep their paranoia runs, their reaction to a player who wins and is suspected of being a counter may vary from close scrutiny ('heat') to outright barring of that player. Consequently, a skillful player must hide his or her abilities and appear as just another 'loser' while winning at the game. Proper casino playing tactics help to disguise your skills, thus allowing you to continue to play.
A Casino 'Profile' of a Counter
Casino supervisors believe they have card counters profiled and can spot them by their actions. While the list is long, here are some of their prejudices:
1. Card counters are usually young, white males (probably with beards) who dress too casually for the amount of money they throw around.
2. Card counters 'scout' the tables in a pit, looking for a good count before sitting down.
3. A counter will change $200-300 into chips but then only bet $5 or $10 on the first hand.
4. Counters don't talk to anyone; they stare at the discard tray and rescan the table, checking on the count.
5. Counters don't smoke or drink alcohol.
6. A counter thinks a while before placing his bet.
7. A counter doesn't hesitate before playing a 'stiff' hand.
8. A counter never takes insurance with a minimum bet out, but does take insurance when a big bet is out, regardless of his hand.
9. A counter varies his bet beyond a 'parlay'.
10. Counters don't tip the dealers.
11. A counter pulls back a big bet and lowers it on a 'push' or when the shoe ends.
12. A counter always makes a minimum bet on the first hand of a newly-shuffled shoe.
Card Counter Camouflage
To make money at Blackjack, you must maintain your welcome at the casinos. But even though you may feel that there's a big red 'C' on your forehead the first few times that you play as a counter, it really isn't there and if you avoid a few of the 'newbie' mistakes, the casino supervisors probably won't pay any attention to you at all.
If you are playing for high stakes, you'll be noticed whether you win OR lose; high-stakes players are always noticed. But, if you are starting with the $5 to $60 spread which I recommend, you probably won't be noticed at all. How often you play at a particular casino has a lot to do with this. Remember that most casinos have at least two shifts, so try to spread your play around between casinos and shifts. AVOID PLAYING FROM ONE SHIFT TO ANOTHER. Keep your sessions fairly short and it will take them a long time to even begin to figure out what you're doing.
The real key to fooling the casino personnel is to appear as though you are just another gambler. Here are some techniques which I use.
1. Dress appropriately for your betting level. A 'high-roller' should look like a prosperous person not, as one author put it, "like an out-of-work substitute school teacher." If you go to a local casino on the day shift during the week, dress like a business person who's playing hooky from the office. Do NOT dress like a tourist (a very effective disguise) if they are going to see you again next week.
2. When you enter a casino, walk directly to a table where the dealer is shuffling and sit down. Talk to the dealer, or at least say "hi".
3. If you are playing a $5 minimum bet, buy in for less than $100, but more than $40. Do not use terms like 'red' or 'green'; 'nickels' or 'quarters'. Call the chips $5 or $25 chips.
4. Do not order anything from the cocktail servers; they are too slow and waiting for a drink may cause you to play at a negative deck while you're waiting. Instead, order non-alcoholic drinks at the bar (O'Doul's, orange juice, anything with a lime) and carry it around with you.
5. Try to always have a bet in your betting circle. Remember, only counters think about how much to bet; gamblers just put something out there. If you busted your hand or got a Blackjack, place your next bet as the dealer is playing his hand. With practice, your bet will be the correct amount, but it won't appear as though you had to think a lot about how much to put out.
6. Gamblers NEVER leave a table after a win. If the count has dropped below -1, continue playing at the minimum bet until you lose a hand.
7. Hesitate before hitting a 'stiff' hand. Talking to the cards helps.
8. Occasionally, insure your Blackjack against the dealer's Ace when you have the minimum bet out. Do not ask for 'even money'; go through the motions like you don't know how it all works. This will also make the dealer slow down on her insurance calls in the future which will give you extra time to calculate the true count. It's best to do this 'minimum' insurance bet when a floor supervisor is looking.
9. If you are going to tip the dealer (something which you should do sparingly), wait until the count is high and you have a big bet out. Placing a bet for the dealer at that time will make it look like you want her to help you win.
10. Once or twice in each session, start off a new shoe with a bet of 2 or 3 times the minimum.
11. Do not vary from proper basic strategy as a form of camouflage; most casino personnel wouldn't know good play anyway. In fact, perfect basic strategy players look like idiots -- hitting a 12 against a 2 or 3 or doubling an A-7 against a 4 is nuts! (To them.)
12. Do not talk to others at the table about your abilities; do not help others to play their hands properly. Never admit that you've understood a book about Blackjack. Do not appear confident, but don't act like a loser when you're obviously winning -- gamblers love to win!
13. I can't bring myself to wear one, but a 'fanny pack' has got to be one of the most disarming items a counter can wear. With that and a pair of glasses on, damn few supervisors will ever think you're this cold-blooded, card counting, steely-eyed destroyer of casinos. But I guess if my usual act ever starts to wear thin, I'll get one and put it on. I'd rather be rich than cool.
Homework
Here are the answers for last week's assignment.
Calculate the casino's starting advantage for the following games:
• Single deck, double only 10 or 11, dealer hits A-6. Answer: .33%
• Six decks, double on any first two cards, dealer stands on A-6, resplit pairs, incl. Aces, double after split allowed. Answer: .33%
• Two decks, double on any first two cards, no resplit of pairs, no double after split, dealer stands on A-6, late surrender. Answer: .30% (I didn't specify if the dealer stands or hits on A-6; this figure is for a game where s/he stands.)

Lesson 13 - The Advanced Course - Part 1
The most powerful (legal) means of overcoming the casino's edge in Blackjack is to vary your bets according to the true count. Additional gains of .2 to .3% are available to those who also vary the play of their hands according to the true count. You undoubtedly have had situations where the count was sky-high and just knew that hitting that 12 against the dealer's 3 was going to get you a face card. There is a point, as measured by true count, where standing with a 12 against a 3 is more profitable than hitting. This is called a 'basic strategy variation' and you'll learn a lot of them in this series.
Basic Strategy Variations
Modifying the play of your hand according to the true count will occur about 10% of the time. Should the count drop, you will double less, hit 'stiff' hands more and split pairs less often. As the count goes up, you will double more often, hit 'stiffs' less and split pairs more. For each basic strategy play, there is only one variation. For example, the variation for the hand 10, 6 versus 10 is to stand instead of hit; you would never double and you obviously may not split. Another example is 5,4 versus 2. Basic strategy says to hit, but if the count is high enough, you would double this hand. A good example on the minus side is A-2 versus 5; basic strategy says to double, but if the count is below 0, you should just hit. The easy way to remember something like that is "Double Ace-2 vs. 5 at 0 or higher." Broken down into the 'shorthand' of a flashcard it is A-2 vs. 5 = 0. (Yes, we'll be going back to our old friends, the flashcards.)
The Power of Basic Strategy Variations
The value of any variation is determined by how often it will, on average, be used. If you play 100,000 hands of Blackjack a year ( about 20 hours a week, year round), you can expect to see a hand of 16 vs. 10 about 3500 times (3.5%). That's actually the number 1 non-insurance situation. Any variation here has considerable value, simply because you'll be using it relatively often. Conversely, you will receive 9,9 vs. 2 only 43 times in that 100,000-hand sample, so the variation here is of little value, because you'll rarely use it. The frequency of hands allows us to prioritize the learning of basic strategy variations.
One of the most important variations from basic strategy is the insurance bet. Since the dealer will show an Ace as an up card about 7.5% of the time, knowing when it's profitable to take insurance is very important. If you are playing at a six deck game, insurance is worthwhile when the true count is 3 or higher. You should always make the insurance bet at that point, regardless of what cards you're holding, since it has no relationship with your hand. The High/Low counting system has an 'Insurance Efficiency' of 80% which means that 8 out of 10 times you'll be doing the right thing when you make an insurance bet based on the true count.
As I mentioned earlier, considerable value is gained by learning those variations which involve starting hands of 12-16 vs. any up card, since those are the hands you'll see most often. In fact, fully 54% of all your hands will be 'stiff' at some point in the playing. This is a good place to make an important point: basic strategy variations apply not just to your starting hands, but also to hands composed of 3 or more cards. You will stand on A, 2, 10, 3 versus 10 if the count is 0 or higher, as well as a hand of 10, 6. Doubling (or not doubling) is next in importance and splitting/not splitting pairs is least important.
The Value of Basic Strategy Variations
It's safe to say that utilizing these variations will increase your winnings by 10% in the six-deck game. But there's a major side-benefit to them as well. By using these variations, you'll look more like a 'gambler' in the casino. Hitting 16 against 10 some of the time and standing on it at other times is typical gambler behavior. For those casino supervisors who know proper basic strategy (damn few!), seeing you double A,7 versus 2 is crazy, just as standing with 15 against a 10 is 'chicken'. Yet, all of those are -- at certain counts -- the correct play.
If you play at a single-deck game, the value of variations to basic strategy soars to 25% or more. If you spend any time at those games, you must learn them.
In the next lesson, I'll show you how to learn these variations

Lesson 14 - The Advanced Course - Part 2
Basic Strategy Variations: Hit or Stand?
The most common decision any player makes at Blackjack is whether to hit or stand, consequently this will be the most common basic strategy variation and you should learn all the important ones. The first is with a hand of 16 against a dealer's up card of 10. You should stand if the count is over 0 and hit if it is 0 or lower. This means that if the running count is 1 or higher, stand. Since the 'decision' number is 0, it's not necessary to calculate the true count -- the running count will do in this situation. Don't get confused here. Almost all basic strategy variations rely on the true count, but for those where the decision number is 0, the running count will suffice.
The next most important hand is 15 against a dealer's 10. The decision number is a true count of 4, if you are playing at a game of four decks or more. This variation and the others can be easily learned if you make a set of flashcards. They needn't be fancy or sophisticated; merely accurate. Cut some 2'" squares from manila folders and they'll work just fine. A typical flashcard should look like this

If you imagine the 10 and 16 placed on the centerline of a 2" X 2" square, the 0 is offset so your left thumb covers the number. As you go through the stack, recite "sixtten versus 10, stand at zero" (or higher). For a hand of 15 vs. 10, a card will look like this

When you come to this card, you'll recite "15 versus 10; stand at 4".
As time goes on, you won't need to remind yourself that you should stand with the 15 against 10, so you'll recite "15 versus 10 is 4".
Got the idea? If you don't, pleaseand I'll get back to you as soon as possible.
Here are the numbers you'll need to learn. These may vary a bit from numbers you'll see published in books like Stanford Wong's "Professional Blackjack" because the ones I use are specifically for a six-deck game where the dealer stands on A-6 and a few have been modified based upon the theory of 'risk averse' play which was developed about 15 years ago. These numbers work well; they have been proven in thousands of hours of actual casino play by me and my students. Do NOT use them for single-deck games, however. Single-deck play requires different numbers and will be covered in a future lesson.
________________________________________
Basic Strategy Variations: 6 Decks, Dealer Stands on A-6
12 vs. 2 Stand at 3 or higher
12 vs. 3 Stand at 2 or higher
12 vs. 4 Stand at 0 or higher (Yes, if the running count is at all minus, you hit 12 against a 4.It drives the other players at the table crazy!!!)
12 vs. 5 Stand at -1 or higher (This means you hit if the count is LOWER than -1).
13 vs. 2 Stand at -1 or higher
14 vs. Ace Stand at 9 or higher
15 vs. 7 Stand at 10 or higher
15 vs. 8 Stand at 10 or higher
15 vs. 9 Stand at 8 or higher
15 vs. 10 Stand at 4 or higher
15 vs. Ace Stand at 5 or higher
16 vs. 7 Stand at 9 or higher
16 vs. 8 Stand at 7 or higher
16 vs. 9 Stand at 5 or higher
16 vs. 10 Hit at 0 or lower
16 vs. Ace Stand at 3 or higher
________________________________________
And to finish it off, one weird play: Stand with A-7 against Ace at 1 or higher.
Homework
Make up a set of flashcards and begin learning these variations.

Lesson 15 - The Advanced Course - Part 3
Basic Strategy Variations: Double?
The opportunity to double your bet in return for agreeing to accept only one more card is a very powerful option for the player, if it's utilized correctly. I can't tell you how often I see players double hands like 7 or 8 against a dealer's up card of 6 and then bemoan their fate when they lose. Yes, the dealer is very vulnerable with a 6 showing, but placing an extra bet changes the mathematics of the hand, so all doubles must be well-considered. For example, in a six-deck game where the dealer stands on A-6, doubling a hand of 8 against the dealer's 6 has a total return of 10.3% whereas just hitting the hand returns 12.3% and the risk is lower!
That said, there comes a time when it is worthwhile to double an 8 against a dealer's 6 and that's when there's a higher proportion than normal of 10s left in the deck. That point is determined, of course, by the true count. As the true count gets more positive, it becomes more profitable to double. Conversely, as the count goes negative, it becomes a better play to hit some hands, rather than double.
Just as you're using flashcards to learn the hit/stand variations, make up, a set for doubling. Here are the numbers you need:
Basic Strategy Variations Six decks, dealer stands on A-6
Soft Doubling
A-2 vs. 4 Double at 7. (Got this? Basic strategy says to HIT A-2 against a 4, but if the true count is 7 or higher, you should double.)
A-2 vs. 5 Double at 0. (Don't get confused here. Basic strategy says DOUBLE A-2 against a 5, but if the count is at all negative, just hit it; double only when the count is 0 or higher.)
A-2 vs. 6 Double at -2. (or higher. As long as the count remains above -2, you'll double; once it goes lower than -2, you'll just hit --- then hopefully leave the table if the count doesn't improve.)
A-3 vs. 4 Double at 6.
A-3 vs. 5 Double at -2.
A-4 vs. 4 Double at 0.
A-7 vs. 2 Double at 2.
A-8 vs. 4 Double at 5.
A-8 vs. 5 Double at 2.
A-8 vs. 6 Double at 1.
A-9 vs. 5 Double at 6.
A-9 vs. 6 Double at 5.
Hard Doubling
8 vs. 5 Double at 6.
8 vs. 6 Double at 3.
9 vs. 2 Double at 2.
9 vs. 3 Double at -1.
9 vs. 7 Double at 6.
10 vs. 9 Double at -2.
11 vs. A Double at 1.


Lesson 16 - The Advanced Course - Part 4
Basic Strategy Variations: To Split or Not To Split
The primary factor to consider when splitting pairs is whether or not your casino of choice allows doubling after splitting (DAS). If DAS is allowed, you must have the proper basic strategy memorized. I see players make a lot of errors in splitting pairs, primarily with a hand of 8, 8. Most know that a pair of 8s should be split against all up cards, but most stand when they hold them against a dealer's 10. The cost of that mistake isn't huge, simply because a hand of 8,8 is fairly rare. But by standing, a player has an expectation of -.537% and by splitting (if DAS is allowed), an expectation of -.483% is realized. So, the extra money which is put to risk does -- in the long run -- give a better return. Think of it this way. Would you rather stand with a 16 against a 10 or hit an 8 against a 10? By splitting, you get to hit an 8. Incidentally, the numbers also indicate that splitting is best when DAS isn't allowed, though there isn't as big a difference.
As the true count goes up, you'll split more and as it goes down, you'll split less. One play which is justified by a high count is the splitting of 10s. For example, there may come a time when it's worthwhile to split a pair of face cards against a 6. I counsel my students to avoid that play since it draws such a negative reaction from other players at the table. I don't really care what the others at a table think of my play, but if the floor personnel are alerted to what I've done, their initial suspicion may be that I'm a counter. If they've seen me playing good basic strategy and suddenly I have a big bet out and I do something like splitting 10s against a 6, they're going to think I'm either very stupid or very smart. I guess it all relates to the image your projecting in the casino; if it's one of a 'wild man', then go for it. But if you're quiet, polite and a non-drinker, I'd advise against making the play.
All other splitting situations should be followed to the letter; especially that of splitting 4s against a 5 or 6 (if DAS is allowed). Most people don't have the pairs part of basic strategy memorized perfectly, so they won't know what's right or wrong when you do it and most think it's wrong to split 4s. Nothing quite like making the right play and looking like a dummy when you do it!
As you go through the numbers on splitting pairs, you'll see that some don't agree with those published by Stanford Wong and other authors. As I've explained before, some have been modified as a result of Friedman's study on risk-averse play, and I feel they take no advantage from you yet do lower your risk somewhat.
________________________________________
Basic Strategy Variations:
Double after split allowed.
3,3 vs. 2 Hit at 0 or lower. (Instead of splitting.)
4,4 vs. 5 Hit at 0 or lower.
4,4 vs. 6 Hit at -2 or lower.
6,6 vs. 2 Hit at -2 or lower.
8,8 vs. 10 Stand at 8. (If the count is really high, you do stand instead of hit.)


Lesson 17 - The Advanced Course - Part 5
Basic Strategy Variations: Test Yourself
By putting my classes up on the internet, I know I'm reaching a much larger audience than I ever had while teaching classes in person, but I do miss the ability to see how you all are doing in learning the material. In my 'in-person' classes, I always tested my students to gauge their progress and thus determine how effective my teaching methods are. We can't do that here, but I want you to test yourself with the methods I'm going to show you, if for no reason other than the fact that it will build your confidence when you see how much you really know. Much like we did when learning proper basic strategy, you should first complete one copy of the test directly from the material I taught in order to give yourself an answer sheet to use when correcting subsequent tests.
This test just asks you to 'fill in the blanks' with the correct index number from -2 to +10. Print as many copies of this as you'd like.
Advanced Course Practice Matrix
Dealer's Up Card 2 3 4 5 6 7 8 9 10 A
Player's Hand A,2 H H __ __ __ H H H H H
Player's Hand A,3 H H __ __ D H H H H H
Player's Hand A,4 H H __ D D H H H H H
Player's Hand A,5 H H H D D D H H H H
Player's Hand A,6 H D D D D H H H H H
Player's Hand A,7 __ D D D D S S H H __
Player's Hand A,8 S S __ __ __ S S S S S
Player's Hand A,9 S S S __ __ S S S S S
Player's Hand 8 H H H __ __ H H H H H
Player's Hand 9 __ __ D D D __ H H H H
Player's Hand 10 D D D D D D D __ H H
Player's Hand 11 D D D D D D D D D __
Player's Hand 12 __ __ __ __ S H H H H H
Player's Hand 13 __ S S S S H H H H H
Player's Hand 14 S S S S S H H H H __
Player's Hand 15 S S S S S __ __ __ __ __
Player's Hand 16 S S S S S __ __ __ __ __
Player's Hand 17 or more S S S S S S S S S S
Player's Hand 2,2 P P P P P P H H H H
Player's Hand 3,3 __ P P P P P H H H H
Player's Hand 4,4 H H H __ __ H H H H H
Player's Hand 5,5 NEVER SPLIT; TREAT AS '10'
Player's Hand 6,6 __ P P P P H H H H H
Player's Hand 7,7 P P P P P P H H H H
Player's Hand 8,8 P P P P P P P P __ P
Player's Hand 9,9 P P P P P __ P P S __
Player's Hand 10,10 S S S S S S S S S S
Player's Hand A,A P P P P P P P P P P
THIS MATRIX ASSUMES DOUBLE AFTER SPLIT IS PERMITTED AND ALSO ASSUMES THAT YOU DON'T CHOOSE TO SPLIT 10s.

Lesson 18 - Advanced Single-Deck Blackjack - Part 1
While much of card-counting is a science -- the science of mathematics -- it all takes on something of an art form when playing at a single-deck game. True count conversion is difficult to do quickly, large bet spreads (over 4 to 1) are difficult to obtain and it's hard to keep an accurate count at a game which is dealt face-down when you're used to counting where all the cards are face up. Despite that, I really urge you to learn how to play single deck and, instead of banging your head against the multiple-deck games in your area, save your money and take 2 or 3 trips to Reno each year. No, I'm not in the employ of the Reno Chamber of Commerce, but I can tell you that it's a great place to make $$$ at the Blackjack tables, it's relatively inexpensive and typically very easy to get to from all over the United States. Sure their rules, for the most part, suck (only double on 10 and 11, no double after split and the dealer hits A-6) and that gives the casinos the same .5% edge off the top that you're fighting now, but it takes just one +1 card to get you even with the house and that's the real appeal of single-deck. I should mention that some casinos in Reno (as well as in Tahoe and Laughlin) allow double on any first two cards, so the casino edge is dropped to about .2% and that's a very beatable game.
The key to evaluating good single-deck play is how many cards you'll see before a shuffle. If you can find a game with 60% penetration and get away with a 5 to 1 betting spread, it's fairly easy to obtain a long term winning rate of 1.5% of all the money you bet, just by playing basic strategy and varying your bets according to the count. If you also modify the play of your hand according to the true count, a win rate which approaches 2% is possible. That's serious money Blackjack fans, so the effort is worth it.
Which Counting System?
I use two different systems for counting cards; the Hi/Lo for multi-deck play and the 'Hi-Opt 1' system for single deck play. The latter counts 3-6 as +1; 7,8,9 and ace as 0 with 10s as -1. Since there are only four aces to track in a single deck game, I find omitting the ace in the count improves the play of the hand, yet I can still 'adjust' the count for betting purposes. Let's talk about a side count of aces for a moment. We expect to see one ace per quarter-deck played in a normal distribution, but of course that doesn't always happen. For example, if a quarter deck has been played and no aces have come out, the remaining deck is 'rich' one ace. I can -- for betting purposes -- temporarily add +1 to the count, yet for playing purposes the true count without adjustment is correct. Got that concept? If a quarter-deck has been played and 2 aces have come out, the remaining deck is 'poor' by one ace, so I would lower the count by 1 (that is, 'add' a minus 1 to the count ) just for betting purposes, since my opportunity to receive a natural has decreased. This is a very powerful addition to your game, but my advice is to just use it in single-deck play because an ace adjustment is very taxing, mentally.
If you want to learn the Hi-Opt count, use the same techniques I showed you for learning the Hi/Lo count. All of my advanced techniques will, however, be based upon the Hi/Lo system, since that seems to be the method most of you are using.
The most difficult aspect of single-deck play is computing the true count. First you must 'calibrate' your eyeballs for measuring the number of cards which have been played. Today most casinos have the dealer place the discards in a rack to the side; unlike the 'old' days when they put the discards underneath, so deck estimation is easier. The really tough part is the division which is required. In a multideck game, we're almost always dividing one whole number (the running count) by another number which is at least 1. Admittedly, some people have a problem of dividing 17 by 2.5 qucikly, but it doesn't take long to get used to. In single deck, you're always dividing by a fraction or decimal and that's not easy. For example, if you're at a single-deck game and a quarter-deck has been played, with a running count of 3, the true count is 3 divided by .75 = 4. That's actually an easy example. Try dividing a running count of 5 by .5. The answer is, of course 10, but how many of you wanted to say 2.5 or 1? Only practice will make this an automatic process.

Lesson 19 - Advanced Single-Deck Blackjack - Part 2
Basic Strategy Variations
Casinos that offer single-deck Blackjack games are very aware that it can easily be beaten by a counter who uses a big bet spread, so trying to play the game with a 1-12 spread like I recommend for 6-deck games will likely get you a one-way ticket out of the casino, pronto. That's not to say you're going to get "backed-off" if you bet more than 5 chips on a hand, but I think it's fair to say making $$$ at a good SD game requires a bigger bag of tricks than needed against a 6-deck game, so altering the play of your hand according to the count is a logical place to start.
If you know how to count cards, you can use the count to tell you how much to bet on each hand, but you can also use the count to help you play each hand more accurately, too. If you've studied my course up to this point, you know one of the key factors in playing a winning game of Blackjack is to leave the table when the True Count drops to -1 or lower, but that tactic isn't very practical at a single-deck game, because only a few rounds of hands are dealt before the shuffle.
Consequently, you have to sit through a lot more "negative" decks, but the good thing is that a shuffle is never too far away. Yet, at the same time, we all know the casino's edge increases as the count drops, so we want to neutralize the effects of that as much as possible. Because you'll be sitting through many more negative counts at a single-deck game, what we need to do is learn the plays for hands like hitting 12 against a dealer's 5 and so forth. We also want to avoid doubling and splitting pairs in low counts and we'll hit instead. But we don't want to guess at important plays like that, so we'll need to learn Basic Strategy variations for "lower" numbers, like -2, -3 and so forth. A realistic range for most single-deck games is a True Count of -6 to +6 and that will cover 85% of all the hands you'll ever play, assuming 63% penetration which is about as good as it gets. In a later lesson, I'll talk about the importance of penetration, but for now, trust me on this.
Some players prefer to learn just the indices for the most common hands, with the idea that they'll get a hand like A, 4 against a 5 less than 100 times in every 100,000 hands of play, but they'll have a 16 against 10 much more often. In his book, in the 2nd edition, Don Schlesinger devoted a chapter to what he calls "The Illustrious 18" that are, in his opinion, the most important Basic Strategy variations. I'm not big on reproducing other authors' original works, so I'll refer you to the book for a complete listing if you feel you'd rather not memorize all of the variations I've listed here. Another idea worth considering is to not learn the indices below -2, with the rationale that you'll likely be betting the minimum in such a count, so any playing mistakes will, in the long run, cost you very little. Or, you might want to learn only the indices where you'll be placing extra bets on the table, as in doubles and splits, with the idea that, if I'm going to be putting more $$$ on the table, I'm sure as hell going to play the hand correctly.
But I'm of the opinion that if something about this game can be learned, it should be learned. (Okay, I know I'm a fanatic for this stuff, but what can I do?) If single deck games will be where you'll spend most of your time, then it's probably worth the effort to memorize the 90-odd indices presented here. But if this isn't your primary game, a range of -2 to +6 with some judicious editing will probably suffice. Don't forget that some of these indices are similar to those for a multi-deck game, so you won't be starting from scratch. Learn those numbers you think are important for where and how you play.
Rather than talk you through each hand's variation, as I did in the multi-deck section, what I've done here is produce a Basic Strategy Matrix that shows an "index" number for each appropriate play. Don't worry if you have a problem understanding it, because I'll explain it all at the bottom.
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Basic Strategy Variations Matrix
Single Deck, H17, Da2, no das, no surrender

Using the Matrix
(GM Note: The Basic Strategy for this game is available from BlackjackInfo.com: The general rule for understanding the Basic Strategy Variations Matrix is this: If the number in a slot is 0 or a minus, then that play is a Basic Strategy move that you should make as long as the count is higher than the number shown. For example, with A, 6 vs. 2, you will double as long as the count is 0 or higher. If the count is minus, just hit. In the case of 9 vs. 4, you'll double as long as the count is -2 or higher (remember that -1 is "higher" than -2). For a hand of 9,9 vs. Ace, you'll stand as long as the count is 0 or less. If the count is higher than 0, you split the 9s. The exceptions to this general rule have been noted, but you have any questions.
It's a lot easier to use the matrix if you've memorized the Basic Strategy for this game but if you haven't yet done that, you really should learn it before you get into this advanced mode of play. For each player hand and dealer's up card combination you will see either a specific action, such as hit, stand, double, etc., or a number. The number is an "action point" based upon the True Count and it keys the variation. As to what the proper variation is for a situation may get a little confusing, but if you study the hand in question, you can usually figure it out. A good example of this is A, 7 versus a dealer's 2. In the matrix, you'll see the number 1 in that spot, so do you hit or stand or do something else? Well, "something else" is the answer, so you should double, just as you do with A,7 vs. 3, 4, 5, and 6. Logic plays a role here, so if a play sounds illogical, it's probably the wrong one. Would you really hit A,7 against a 2? Of course, you might stand, but that's already the Basic Strategy play, so doubling is all that's left. Consequently, what this is telling you is that you should double A,7 against a dealer's up card of 2 when the True Count is 1 or more. If the True Count is less than 1, use the Basic Strategy play, which is to stand. Against a 3, Basic Strategy says to double A,7. But the index for that is -1, so that's telling you to double A,7 vs. 3 only if the True Count is -1 or higher. If it's not, then you should stand.
Let's talk about another variation that may cause some confusion: 8, 8 vs. 10. The notation in that box is "Stand@6", so if the True Count is 6 or more, you will not split the 8s, but stand instead. Another hand that draws a lot of questions is 7, 7 vs. 10. Yes, Basic Strategy is correct when it says to stand with 7, 7 vs. 10 in a single-deck game, mostly because the dealer either has a good hand, like a 20 or s/he is "stiff" and we're hoping for a dealer bust. Because you already have 2 of the four 7s in the deck in your hand, the odds are greatly reduced that you can beat a dealer's 20 by catching another 7, so the mathematics work out that you're better off standing and praying. But it's a close call, so if the count is below 0, you should hit. This means that if the running count is -1 or lower, you should hit 7,7 versus a 10, not split. If the count is 0 or higher, stand.
Now, take a look at the Hard Totals section, where I have 2 different types of 16s: a 10,6 and a 9,7. In the 10, 6 row there's a "4" under the dealer's 10 and a "0" in the 9,7 row. This is what's called a "composition-dependent" play and I included it for several good reasons. First of all, 16 vs.10 is a relatively common hand and you can see by the numbers that there's quit a difference between how the two 16s should be played. What the variations matrix's saying is that you should stand with 9,7 at 0 or higher, but stand with 10,6 only when the True Count is 4 or more. This is quite a departure from what we do with a 16 vs. 10 in a multi-deck game, where we stand only when the count is more than 0 (i.e., a running count of 1). Just a side note here: there's a lot of confusion about this play in my multi-deck section, but what I do is stand with 16 vs.10 when the running count is 1 or more, otherwise I hit it. What you do when the count is exactly 0 doesn't really matter because the expected value is the same for either play. The same is true for a hand of 9,7 vs. 10 in a single-deck game.
Anyway, why would we stand with 10,6 vs.10 only when the True Count is at 4 or more? It all has to do with the total number of 10s in a single deck, which is sixteen and you already have one of them in your hand and the dealer is showing one as his up card. That's two less 10s that can bust you and two less 10s the dealer can have in "the hole", so it sways the decision away from standing toward hitting more aggressively. Look, a hand of 16 is never going to be great, regardless of how you play it, so all we're really doing is trying to minimize the damage. Hitting 10, 6 vs. 10 until the True Count is 4 or more helps with that process.
In the row for 6,6 you'll see a notation under the dealer's card of 7 like this: Split@<0 and that means, "split a pair of 6s versus 7, if the count is below 0."
I don't want you to leave without me telling you the most important variation of all, which is the Insurance bet. You hopefully know that proper Basic Strategy tells us to never take insurance (even when you have a 'natural' and the dealer's up card is an Ace, in spite of what everybody else tells you), but in a single-deck game, the insurance bet becomes profitable at a True Count of 1.4 or higher.

Lesson 20 - A Field Trip with the GameMaster
On February 1, 1997 the Station Casino St. Charles which is located on the banks of the Missouri River in a western suburb of St. Louis began offering a handful of tables of double deck Blackjack. The rules are the same as their six-deck game: dealer hits A-6, double on any first two cards, resplit pairs up to 4 times (and, effective March 3, resplit Aces as well) and double after split. Most of the tables are $25-$500, but there are usually one or two with a $10 minimum. The casino has an edge of .35% over the basic strategy player and the game is cut at the 75% penetration point and it's dealt from a shoe (a Missouri Gaming Commission rule) with all cards face up.
Basic Strategy Variations
I have never played double deck before for any length of time, so I knew I'd have to do some homework to get ready. The basic strategy for double deck is the same for 4 or 6 decks, so there was not a lot there which I needed to work on. However, unlike the 6-deck games where I get up when the true count is -1 or lower, I knew I'd have to play through all the double deck shoes, so I'd need to learn more of the 'minus' indexes in the basic strategy variations. For example, in a six-deck game, I'd be long gone before I'd have to play a 13 against a dealer's 5 in a highly negative count. But, one should hit a 13 vs. 5 at -4 and I needed to learn that. I added all the plays from -3 to -6 to my pack of flashcards which covers -2 to +10 and began to learn all the basic strategy variations from -6 to +10.
Money Management
Next I had to work out a betting schedule. I always like to use an example of a betting schedule based on a $3000 bankroll so, even though I actually use a multiple of that, I'll break everything down to that size so you can see how it will work with a minimum bankroll. The casino has a starting edge of .35% now that resplit of Aces is allowed; it was .40% and since each increase of 1 in the true count is worth .5%, at a true count of 1 I'd have a small edge over the casino. Since I'd be playing at a $10 table, I'd be over betting somewhat until the true hit 2, but there was no choice in the matter. Because double after split is allowed, my optimum bet would be 76% of my advantage. If this is confusing to you, reread the section on money management which begins at Lesson 7. Here's a table I use to calculate the optimum bet:
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True Count Advantage Optimum Bet
0 or lower (.35+) 0
1 .15% X .76 .00114
2 .65% X .76 .00494
3 1.15% X .76 .00874
4 1.65% X .76 .01254
5 2.15% X .76 .01634
6 2.65% X .76 .02014
7 3.15% X .76 .02394
8 3.65% X .76 .02774
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Following me on this? At the beginning of a shoe, the casino has an advantage of .35% because of the rules of their game and the fact that they're dealing from 2 decks. If the count goes minus, their edge will increase and the OPTIMUM bet in that situation is $0. That's not the PRACTICAL bet, however, since it's a $10 minimum table, so I have to bet that amount. As the count goes up, I can bet the prescribed percentage of my bankroll as indicated. For example, with a $3000 bankroll, my optimum bet at a true count of 3 is .00874 X $3000 = $26.22. Here's how the chart looks for a $3000 bankroll:
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True Count % Optimum Bet Optimum Bet
0 or lower 0 $ 0
1 .00114 X $3000 $ 3.42
2 .00494 X $3000 $ 14.82
3 .00874 X $3000 $ 26.22
4 .01254 X $3000 $ 37.62
5 .01634 X $3000 $ 49.02
6 .02014 X $3000 $ 60.42
7 .02394 X $3000 $ 71.82
8 .02774 X $3000 $ 83.22
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That's the theoretical, not the practical. As I stated before, I must bet at least $10 and I really feel strongly about the fact that the top bet should not exceed 2% of the total bankroll, so I end up with a $10-60 spread until the bankroll gets bigger. A 1 to 6 spread can beat this game, but there's a nice little trick I can use to get more money on the table without increasing my risk too much: play 2 hands in positive situations. Here we go with more math, but stick with me; it's important.
Since I would, whenever appropriate, play 2 hands, I'd need a table for the optimum bets for those situations. The rule here is that 56% of the advantage times the bankroll is the optimum bet for each of two hands. In other words, if it's correct for me to bet $25 on one hand, I would be over betting if I bet $25 on each of two hands at the same true count. Because of covariance (the relationship of two hands to one another), the optimum bet must be reduced. Since I must bet at least $10 on each hand (Casino Station St. Charles doesn't have that silly rule that a player must bet twice the minimum on each hand when playing more than one; many do, so check), it's practical for me to spread to two hands of play only when the true count is at 2 or more. Here's how that chart looks:
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True Count % Advantage Optimum Bet for Two Hands
2 0.65% X .56 .00364
3 1.15% X .56 .00644
4 1.65% X .56 .00924
5 2.15% X .56 .01204
6 2.65% X .56 .01484
7 3.15% X .56 .01764
8 3.65% X .56 .02044
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Factoring this with a $3000 bankroll gives us the optimum bet for each of two simultaneous hands at different positive counts:
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True Count % Optimum Bet Optimum Bet for Two Hands
2 .00364 X $3000 $ 10.92
3 .00644 X $3000 $ 19.32
4 .00924 X $3000 $ 27.72
5 .01204 X $3000 $ 36.12
6 .01484 X $3000 $ 44.52
7 .01764 X $3000 $ 52.92
8 .02044 X $3000 $ 61.32
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At Last! The Betting Schedule
Obviously I cannot place a bet of $10.92 so I'll have to round things off in order to arrive at a practical betting schedule. In doing that, I keep several things in mind. First, I want a schedule which will allow me to 'parlay' winning bets as the count goes up. For example, if the bet for a true count of 2 is $20, it would be great if the bet for a true count of 3 was twice that; it makes me look like a 'gambler' to just add my winnings to the original bet. Of course I'd only be doing it because the count has gone up, but it's something to keep in mind as I design the schedule. Another 'nice-to-have' thing is a schedule which allows me to bet some multiple of the true count. For example, "$10 times the true" would mean that at a true of 2 my bet would be $20, at a true of 4 it'd be $40, etc. Another point to keep in mind is that we have a bit of a 'fudge' factor built into counts above 2.4 in a double deck game. Why 2.4? Well, that's the true count at which one should take insurance in a double deck game and that option is so valuable that it adds to our advantage. While the advantage goes up about .5% with each increase of 1 in the true count, above 2.4 the advantage increase is more like .58%. So our 'real' advantage at a true of 7 is more like 4% than the 3.65% which I show on the charts above. This gives us a cushion for rounding up a bit.
So, here's the betting schedule I worked out for a $3000 bankroll. Bear in mind that as the bankroll increases (or decreases), the schedule must be changed in order to keep the risk of 'gambler's ruin' about the same. I will modify the schedule at $1000 increments; that is, if I win $1000, I'll refigure the betting schedule by remultiplying all the percentages by $4000. On the other hand, if I choose to spend my profits, I'll just continue to operate with the original schedule. In the unlikely event that I hit a big losing streak (how's that for positive thinking?) I really couldn't downsize the bets very much. As long as the bank remains above $2000, I'll stick with this schedule. If it should go below $2000, I'd quit until I could build the bank up again.
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Betting Schedule $3000 Bank - Double Deck
(DOA; DAS; RSA; Dlr hits A-6)
True Count Bet: One hand Two Hands
0 or lower $10 N.A.
1 $10 N.A.
2 $15 $10
3 $25 $20
4 $40 $30
5 $50 $40
6 or higher $60 $50
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Notice that I top out at one hand of $60 or 2 hands of $50, regardless of how high the count gets. I'll stick with that until the bankroll increases and I get a 'feel' for just how the floor supervisors at the casino react to such a spread. The 'pit critters' know that counters vary their bets widely, so I'm going to be conservative for a while since this is my 'home'. If I was playing this game somewhere else -- where they wouldn't see me for months at a time -- I'd be more aggressive. The single-hand schedule is not an easy one to memorize; it's not a straight parlay and it's not a simple multiple of the true count. I'm going to be screwing around a lot with $5 and $25 chips and precise betting is another indicator of a card counter, so I may find myself 'pushing' the count; that is, over betting a bit on a true of 2 or 3. I'll have to watch that, since my reaction will be to bet $20 on a true of 2 and $30 on a true of 3. With that, the schedule is $10 times the true, but a bank of $4000 is required to justify those bets. I'll just have to see how it goes.
Playing Two Hands
Whether or not one should play one or two hands is more a factor of opportunity than strategy. If there is no space available at the table for a second hand, I obviously must play only one. Neither am I going to play two hands when the true count is below 2, nor am I going to play two hands if I'm alone with the dealer. The reason for that last rule is twofold: First, by playing a second hand, more cards are used and -- since I only go to two hands on positive counts -- I'll be 'eating' good cards. That's okay, but when head-to-head with the dealer, my two hands represent an increase in the total bet of about 150% but I'm also using up 150% more of the cards. Second, the game has a high maximum bet, well above my maximum so I don't need to spread to two hands in order to get more money on the table. So, whenever I'm alone and the table limit is above my top bet, I'll always play one hand.
If there is at least one other player besides me at the table, I'll then spread to two hands whenever possible. In that case I do want to 'eat' the good cards; why give the opportunities to others when I can get them for myself? Mercenary, perhaps but this IS about money, you know.
Lots of gamblers play two hands, so the maneuver won't draw a lot of attention to you unless you make a big deal about it. First, most casinos allow two hands only if they are located in two adjacent betting circles. If you're sitting at 'first base', don't try to place a second bet at the empty spot on third base. Also, I don't ask people to move to the next spot over in order to accommodate my second hand and I never refuse to allow someone else to sit down and play in the spot I was using for my second hand. You have to look indifferent about the idea of a second hand -- just like a gambler would. One neat trick is to spread to two hands when a new player joins the table (assuming of course that the count justifies it); gamblers seem to think that doing so 'keeps the cards in proper order' when someone is jumping in and out. Naturally it's BS, but anything that makes me look more like a gambler is welcomed.
Practice Makes Perfect
Next I had to set up a regimen of practice to get used to playing a double-deck game. I already own several decks of cards from the casino, so I can use them to 'calibrate' my eyes for estimating the number of decks left to be played. I did this to a half-deck accuracy and can consistently cut 26 cards from two decks shuffled together. I accomplished this simply by breaking the pack into four parts over and over again and counting the segments when I was done. Just looking at a half-deck, a full deck and a deck and a half gets you used to estimating the number of cards remaining to be played. It's hard to describe until you try it for yourself, but I think you know what I mean. I also did some mental calculations of dividing various running counts by 1.5 and .5, etc. to get used to figuring the true count.
I further practiced by counting down two decks to check my accuracy; I can do it in 22 seconds which is more than ample for casino conditions.
But the practice I did most was with a program called "Blackjack Professor" which I set up to reproduce the conditions and rules for the game at Station Casino St. Charles. Whenever I had a spare hour or so I played the game, which is dealt on a head-to-head basis with no other players, utilizing my betting schedule and the other techniques which I use in the casino. For example, if I had $10 bet and the count jumped up considerably, as it will near the end of a shoe, I would not come out with a $40 bet on the next hand, since I wouldn't likely do that at the casino. I'd bet $20 instead and then go to $40 on the next hand, if there was a next hand. Conversely, if I 'pushed' a hand and the count had dropped dramatically, I'd leave the bet out there, just as I would do in the casino. By doing all that, I felt my results from practice would be similar to what I could expect in the casino. Here are the results of 6 different sessions on the computer. Remember, I played each hand according to the basic strategy variations and I bet according to the schedule above, though I never spread to 2 hands because I was always alone at the table. The earnings per hour are based on a rate of 60 hands an hour, a much more realistic figure than the 300 hands an hour I was able to play on my computer.
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Session # of hands % won $ won $/hour % advantage
1 276 48.03% 65.00 $14.13 1.60%
2 596 47.42% 135.00 $13.59 1.39%
3 566 45.05% 272.50 $28.89 2.99%
4 472 43.54% (345.00) ($43.86) (4.43%)
5 1773 46.36% (940.00) ($31.81) (3.03%)
6 920 51.14% 1302.50 $84.95 8.35%
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This totals to 4603 hands which represents about 76 hours of casino time and a profit of $490 or $6.44 an hour. From the program, I was able to extrapolate that my average bet size is about $14, so my overall advantage for these 6 sessions works out to be about .76% which is about half of what I would expect in a bigger sample size. My big losing session saw me reach a low of about $1050 which is not surprising. The lesson to learn from these simulations is that "the money in Blackjack comes in chunks." To anticipate a steady income from this game is a big mistake; you can easily see how wild the swings are.
Actual Play
All the above is theoretical; what matters are real results from actual casino play. To date I've played 7 sessions and here are the results, based on a $10 to $60 spread:
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Session 1 2.5 hours ($110)
Session 2 1.5 hours ($410)
Session 3 2.0 hours $240
Session 4 2.0 hours $250
Session 5 3.0 hours $355
Session 6 3.0 hours $205
Session 7 2.5 hours ($260)
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These actual playing sessions total 16.5 hours of play and a profit of $270 for an hourly income of $16.36. I must add that the first two sessions were played before I had fully developed my betting schedule and before I had put in a lot of practice time. I will freely admit that those two losses were a 'wake-up' call that I needed to spend some time practicing the double-deck game, even though double deck is MUCH more closely related to 6 decks than it is to single deck. Once I got 'in the groove', my results are about as I expected. If we ignore those first two sessions, I've won $790 in 12.5 hours for an hourly rate of $63.20. That number cannot be sustained, but it's very typical of how this whole thing works. Over the coming months, I'll probably win about 65% of my sessions and lose or break even in the rest. The hourly income will drop to a more realistic $20 or so, assuming I don't increase the bank size. That's not enough to retire on, but it is a nice part time job.
I hope the thought processes which I've tried to show in this lesson give you an insight into how to structure a plan for your own play. I guess the only 'sage' advice I have at this point is that you must practice a lot more than you play to be successful at this game.
Our next set of lessons deals with the Double Deck game.

Lesson 21 - Beating the Double Deck Game - Part 1
At first glance, it would seem only logical that a smart player will do better at a game that uses fewer decks, but that's not always the case when you compare double-deck games with six-deck games. A lot of variables come into play, not the least of which are the rules of the games, the minimum bet size required and the amount of scrutiny the games get from casino supervisory personnel. If you do not count cards, it's very likely that you'll be better off avoiding the double-deck games out there. I know some of you may be surprised by that comment, but I make it based upon the fact that many casinos have less liberal rules on their double-deck games, yet they require higher minimum bets. As a result, the casino's overall edge may be similar to that of their six-deck game, but you'll have to bet more on every hand for the privilege of playing. Because a non-counter cannot get a long-term edge over the casino, you'll just be betting more on a consistent basis and the casino will eventually get your $$$.
Now don't get me wrong here; if the rules are the same, a game using two decks will have a lower casino edge than one that uses six-decks, yet the strategies are almost identical. If the minimum bets are the same (or are at least within your comfort level), then go with the 2-decker. That's a key point, by the way. The proper Basic Strategy for a double-deck game closely resembles that of a four- or six-deck game, much more so than a single-deck game. The few differences between a two-deck and six-deck game with the same rules (dealer hits or stands on soft 17, double after split is allowed, etc.) lie mainly in splitting pairs and, since pairs are the rarest hands you'll get, the impact is negligible. I might be wrong about this, so check, but I do believe that the only change is to split a pair of 7s against a dealer's 8 in a double-deck game. In a six-decker, you don't do that. Not a hand you're going to see everyday, either way.
Note from the BlackjackInfo.com editor:
There are indeed only a handful of changes in strategy between the 6-deck and the 2-deck game. In a 2-deck S17 game: Split 77v8, Split 66v7, and Double 9v2. If the game is H17, also double A3v4.
My point is that you can move back and forth between DD and 6D games and not worry that you're playing improperly, but the big question is whether or not you should. We've already covered the non-counter situation, so let's turn our attention to those of you who do count. Even in this situation, the double-deck game isn't necessarily the hands-down choice and I'll show you why as we go along.
For whatever reason, many casinos treat their double-deck games as "premium" games, so they have higher minimum bets, may have less liberal rules, less favorable penetration and are usually watched more closely by the "pit critters", as we lovingly call them here. Some casinos seem to think that counters are showing up in droves at their DD games and carting off chips by the box load, but that's not necessarily the case. I know of some games that are very easy to beat, but they are few and far in-between. The reality is that beating the double-decker takes extra effort and some sharp play by the counter. But you came here for answers and I have them.
The primary advantage to playing a double-deck game is the volatility of the count. Unlike a 4- or 6-deck game, the running count, which is converted to the True Count (count per remaining deck) in a DD game can rise or fall quickly, but it's gone almost as fast, due to the shuffle. That's obviously good when the count is negative, but no fun at all when the count is "up". Things happen quickly in a DD game and the wise counter takes advantage, but it requires good skills at converting to the True Count and almost needs some ability to anticipate what's going to happen, while remembering that we never make guesses when counting.
The Key: Penetration
Because a DD game uses only 104 cards, versus the 312 of a 6D game, just a few extra cards of penetration can make a big difference in how well you can do at the game. In my Blackjack School lessons, I tell you that you're wasting your time if you play at a 6-deck game where less than 65% of the cards are dealt before the shuffle. In a DD situation, 65% penetration is very acceptable, 75% is fantastic and 80% or more is phenomenal. What you'll more likely find is penetration in the 50% range. Yep, they put together two decks and then use only one of them! I hate it when that happens.
But penetration is really important, so it's something you need to become familiar with. If you play a DD game where the dealer hits A-6, you may double on any first two cards, double after split, etc. and you use a 1-8 betting "spread" (I'll explain it later on) and the casino deals only 50% of the cards, your long-term edge as determined by simulations that I ran on Statistical Blackjack Analyzer will be about 0.64%. If the penetration deepens to 60%, the player advantage goes up to 0.95% and at 75% penetration it's 1.47%. That's not bad, you know.
Let's recap this so it stays with you:
Impact of Penetration
on a Double-Deck Game
Percent Penetration Theoretical Player Edge
50% 0.64%
60% 0.95%
66% 1.14%
75% 1.47%
A "trick" I stress in my lessons is to leave the table when the True Count drops to -1 or lower, if at all possible. That can be fairly easy to do in 6-deck games and not so easy to do in DD games. Therefore, you have to pretty well accept the fact that you'll be playing in all counts, which makes the penetration factor even more important. We call this "play all" and the figures above were calculated under those conditions. By the way, you need to remember that simulation software plays Blackjack perfectly and we humans don't. That's why I use the term, "theoretical" player edge; that's about as good as it will ever be, but figure 10% less for purposes of reality.
Getting Started
If you have never played DD games as a counter, you need to do some basic planning first. While they aren't a world apart from 6D games, here are some differences to consider:
• Many, though not all, DD games are dealt facedown and that requires you to count the cards in a different way.
• Because it will be difficult to leave the table when the count drops, you'll need to learn more "negative" Basic Strategy variations.
• Many DD games require the dealer to hit soft 17 (I'm going to assume that throughout this series), so there are some Basic Strategy changes needed. You can get them at www.blackjackinfo.com
• With penetration being such a crucial factor, you should first check your local game to see if it's even worth the trouble. Verify the rules while you're there.
So, start doing your homework on this and I'll be back next time with a plan for how to bet in this game.

Lesson 22 - Beating the Double Deck Game - Part 2
Inlesson 21), I tried to demonstrate that the real key to winning at this game is finding one where the casino deals more than 50% into the decks before shuffling. Admittedly, you can make a few $$$ in a game where only one deck of the two is dealt, but it's certainly not easy and your earnings really are limited. Shallow penetration can be overcome, somewhat, by using a bigger bet spread (like $5-$60 instead of $5-$40, for example) but please notice that I said "somewhat".
A bigger (or wider, if you prefer) bet spread - the ratio between your minimum and maximum bets - creates its own set of problems that you have to consider. First of all, many DD games have higher minimum bets, so you may find yourself at a $10 table and the 1-12 spread will require you to make a $120 "top" bet. That will require a pretty hefty bankroll, far more than the $3000 minimum I recommend in my Blackjack School lessons for the $5 minimum bet, six-deck game. The second and probably the biggest problem is that the casinos aren't stupid. They know their games can be beaten by card counters who use big bet spreads and I think it's fair to say that most aren't going to allow you to spread $10-$120 for long periods of time, unless they are just totally convinced you're some sort of wild-assed gambler. Hey, some people can pull that off; I know, because I've done it and I've seen it done by others.
But, surprisingly, there isn't that much to gain in overall advantage by going from a 1-8 spread to a 1-12 spread in our "core" game, which is 2 decks, the dealer hits A-6, you may double on any first two cards, including after splitting pairs and no surrender is allowed. Even if you can find a game where 60 cards of the 104 are dealt (57% penetration) a 1-8 bet spread that consists of betting one unit at a True Count (TC) of 1 or less, two units at 2, four units at 3, six units at 4 and eight units at a TC of 5 or more will yield an overall "initial bet" advantage of only 0.58%. A 1-12 spread where a TC of four has us betting 8 units, ten units at 5 and twelve units of 6 or more under the same conditions has an initial bet advantage of 0.81%. That tiny extra edge is hardly worth the cost of the added risk of ruin and the extra scrutiny you'll get from the "pit critters" while using it.
The reason for the small gain is simple: The penetration is just so shallow that you'll seldom be making a 10- or 12-unit bet, but you need them to make up for all the minimum bets you'll be making at counts where the casino has the edge over you. We lessen the impact of that quite a bit in the six-deck games by leaving the table when the TC drops to -1 or lower, but we pretty much agree that tactic isn't as feasible in a double-deck game and you'll generally have to play through all the counts, negative and positive. It's costly. Sure, you could "ramp" your bets more quickly so the top bet is out at a TC of, say, 4, but that'll have you bouncing bets all over the place and it's sure to draw a lot of attention, if not "heat". I think I can show you a better way to go and, a little later on, I'll show you a tactic that can really make you some $$$ at even this mediocre game.
Betting With the True Count
For each increase of 1 in the true count as figured by the Hi/Lo counting method, the player's advantage increases by about .5% in the average Blackjack game. If the casino has an edge over the basic strategy player of .41% (2 decks, double on any first two cards, double after splitting pairs, dealer hits on A-6 and surrender is not available), it takes a True Count (TC) of just about 1 in order to get "even" with the house. Being even means that the player who utilizes proper basic strategy will win as much as s/he loses - in the long run - at a True Count of one. A TC of 2 gives the counter an edge of .5% over the house; a TC 3 gives the player an edge of 1% and so forth. These are conservative numbers because beyond a TC of about 2.4 (the point at which you should make the insurance bet) in a double-deck game, the value of each increase of 1 in TC is actually worth a little more than 0.5%.
It is the edge that a player has on the upcoming hand that determines their bet. Counters bet only a small portion of their capital on any one hand, because while they will win in the long run, they could lose any given hand. By betting an amount that is in proportion to their advantage (called the "Kelly Criterion"), they are maximizing their potential. A lot of people misinterpret the Kelly Criterion by assuming that the amount bet is in direct proportion to the advantage. They think that if you have a 1% edge, you should bet 1% of your "bankroll" and that is incorrect. What they are forgetting is the doubling and pair splitting that goes on in the course of a game, which increases the risk or "variance" of a hand. For a game with rules like those listed above, the optimum bet is 76% of the player's advantage. Here's a table of optimum bets that will work well for a game where the casino has a 0.41% advantage over the Basic Strategy player:
True Count Advantage % Optimum Bet
-1 or lower -0.91% or more 0%
0 -0.41% 0%
1 0.09% x 76% 0.07%
2 0.59% x 76% 0.45%
3 1.09% x 76% 0.83%
4 1.59% x 76% 1.21%
5 2.09% x 76% 1.59%
6 2.59% x 76% 1.97%
7 3.09% x 76% 2.35%
8 3.59% x 76% 2.73%
9 4.09% x 76% 3.10%
10 4.59% x 76% 3.49%
By using this table, you can determine the optimal bet for any bankroll; just multiply the figure in the last column by the amount of the bankroll. Thus, for a bankroll of $5000, the optimal bet for a true count of 2 is .0045 X $5000 = $22.50.
Some Practical Considerations
First and foremost, it isn't practical to bet in units of less than $1, so a betting schedule must be rounded off. Secondly, it is more appropriate to bet in units of $5 or $10 so that you'll look like the average gambler, plus it cuts down on the calculations you need to make. Further, it is impossible to refigure your optimal bet while seated at the table, even though it should be recalculated as the bankroll varies up and down. Finally, it just isn't possible to play only at games where the true count is 2 or higher so you will have to make a lot of bets when the house has an edge. All of this rounding and negative-deck play cuts into your win rate, but by knowing the conditions that can cost you money, steps can be taken to minimize their impact on your earnings.
The Betting Spread
The most effective 1-8 betting spread would be to bet one unit whenever the casino has the edge and 8 units when the counter has the edge. That concept, however, presents two problems. First and foremost, the "pit critters" are going to know you're a counter after about ten minutes of play and they'll likely ask you to leave. An even bigger problem is that you'd be making your maximum bet when you had a tiny advantage of only 0.09%. Such a small edge virtually guarantees that you'll lose many of those hands so you could hit a losing streak that would wipe you out if your top bet were, say, one-fiftieth of your bankroll. But, if you can get away with it (as I know some players in Europe can), you have to make sure your bankroll is much bigger than just 50 times your maximum bet. A bankroll of 200-300 max bets would be more appropriate in that case.
A more practical answer to both of the problems presented above is to "ramp" your bets, which is another way of saying gradually increase them. If your minimum bet is $10, then a 1-8 spread will make your top bet $80, no matter how high the count gets. Depending upon when you'd like to get your top bet on the table, that is, at which True Count, it's then a simple matter to calculate just what size your total bankroll should be. Let's say you wanted to bet $80 at a TC of 5 or more. The optimum bet for that count is 1.59% of your total bankroll, so if you divide $80 by 0.0159, you get $5031 as the proper bankroll. Now remember, you won't be making every $80 bet at that count because it's your "top" bet and some will be made at a higher advantage, but $5000 is a good number and one that I'll recommend.
Just a quick note here: That $5000 represents the total amount you should be willing to commit to this adventure, but it's not what you'll carry with you on a trip to the casino. For most trips, a "session" bankroll of 20 top bets or $1600 should suffice, but there will be a time when even that's not enough. We'll talk about that later. With a $5000 bankroll, the betting schedule could look like this:
True Count Player's Bet Optimum Bet
0 or lower $10 $0
1 $10 $3.50
2 $25 $22.50
3 $40 $41.50
4 $60 $60.50
5 $80 $79.50
6 $80 $98.50
7 $80 $117.50
8 $80 $136.50
9 $80 $155.00
10 $80 $174.50
Please notice that "Optimum Bet" means the best bet for that count, were you able to make it. Because our top bet is purposely capped $80, this schedule uses it at a count of 5 or more. But, if you're able to get away with a higher bet, the $5000 bankroll supports the bets shown: $100 at a TC of 6 and so on. If you do that, though, your "session" bankroll should be bigger than the $1600 previously recommended.
The Bet Schedule Examined
First of all, I hate this schedule for a lot of reasons. The main one is that it's a dead giveaway to any "pit critters" (PCs) that know the generally accepted bet spread needed to beat a double-deck game is 1-8. And here you are, playing away, hour after hour with a minimum bet of $10 and you never bet over... what? $80! Well, duh. Gosh, is 80 eight times 10? Even the thickest PC knows that. Don't forget that they're "hawking" these games anyway, so we don't want to make it easy for them. I'm firmly convinced that a lot of counters are getting 86'd at good DD games because they're betting $25 at a minimum and $200 at a maximum; 8 to 1, the magic number for a DD game. We need to change that for our game.
The other reason I hate this betting schedule is, it's "clunky". By that I mean it requires some fairly precise bet levels and precision betting is another sign of a counter. This one goes from $10 to $25, which is fine if you're playing at a $10 table. I don't have a problem with that. But then it goes to $40, which is three red chips on a green chip. It actually makes you look like you're betting more than if you were to just go to two greens ($50). After the $40, you go to $60, which isn't too bad, because it's a 50% "parlay" if you won the previous hand and the dealer didn't color you up to all green when s/he paid you on the last hand. But the dealer will constantly be taking away reds and giving you greens in an attempt to make you bet more per hand, not to mention trying to eliminate the difficulties s/he's having in continually breaking down your bet if you're at a casino where they have to separate the colors before paying you. Clunky! Precise, to be sure, but it will definitely slow down your game and actually help the casino to toss you out. You don't need that. But what's the alternative? Let's look at some possibilities.
The Betting Schedule Simulated
To test this betting schedule and to find some alternatives to it, I ran a series of simulations on Statistical Blackjack Analyzer (SBA) using the rules of our "core" game: 2 decks, double on any first two cards, double after splitting pairs, dealer hits on A-6 and surrender is not available. What got changed from simulation to simulation will be shown in the explanation for each.
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Simulation #1 - Basic Strategy for the play of the hands, Player's Bet as shown in the schedule above according to the Hi/Lo count, never left the table regardless of how low the count got ("play all"). Penetration was 60/104.
Simulation #1: Results
Initial Bet Advantage: 0.59%
SCORE: 13.31
Estim. Payoff per 100,000 rounds played is $10,325.65,
with an estimated standard deviation of $8950.40.
Average st. dev. per round: $28.30
Av. std. per round per unit: 1.13153
Average bet per round: $17.42
Comments on Simulation #1 -
This will serve as our "baseline" game and it's easy to see you'd really be wasting your time at it. The primary reason is the shallow penetration, just as I showed you in Part 1. The SCORE is a measurement called "Standardized Comparison Of Risk and Expectation" that was developed by Don Schlesinger and others and is thoroughly explained in his book, nd edition, which every serious card counter should own. For our purposes here, it's an effective way of comparing the value of each game or bet schedule or whatever that we will be examining: the higher the SCORE, the more $$$ you'll make. As a side note, a SCORE of 40-50 ought to be the minimum one should look for in the games they'll be playing.
The other numbers are pretty much self-explanatory (yeah, right!) and are calculated by the SBA software. I'm basically tossing them in for the "math boyz and girlz" out there, but the 100,000 rounds of play number is one you need to understand. This number has caused more card counters to quit the game, convinced that it cannot be beat, than any other factor out there. What it says is this: Were you to play 100,000 hands of this game (at 100 hands per hour that's 1000 hours of play!) your expectation is to win roughly $10,000. However, that $10,000 result can fall within one, two or even three standard deviations from a reality point of view, so if you experienced a one standard deviation event to the loss side of the ledger, your result would be a profit of $10,000 minus $8950 or $1050! That's about a buck an hour. Should you be really unlucky (about a 1 in 50 shot), you'd actually end the 100,000 hands of play with a loss of your entire $5000 bankroll, plus a couple of grand extra, should you care to toss it into the pot. And this could happen even if you play each hand perfectly, never over-bet, don't lose count at the table, etc. Some people use stats like this to justify their idea, "It's all luck, not skill" and they couldn't be more wrong. But don't get me started. We have some way to go before we rest this night and, as "The Duke" would say: "We're burnin' daylight, Pilgrim." Plus, I'll talk about "risk of ruin" later.
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Simulation #2 - Everything is the same, except the most important Basic Strategy variations are used to play the hands (These are the "Illustrious 18" that are explained in "Blackjack Attack" 2nd edition, the most important being taking insurance at a TC of 2.4).
Simulation #2: Results
Initial Bet Advantage: 0.92%
SCORE: 30.51
Estim. Payoff per 100,000 rounds played is $16,048.10,
with an estimated standard deviation of $9187.70.
Average st. dev. per round: $29.05
Av. std. per round per unit: 1.13153
Average bet per round: $17.42
Comments on Simulation #2 -
You can quickly see that the average bet remains the same, but the potential profit has increased by nearly 60% and that's due to making better plays with the cards you're dealt. It should point out that you cannot expect to get a big advantage at this game playing only Basic Strategy and by just varying your bets according to the count, like you can in a six-deck game. While the "Illustrious 18" will get most of the $$$ for you, it's a series of variations that are based upon "high" counts and it ignores low-count plays such as hitting 12 against a dealer's 4 and others like that. I agree with the concept because you'll be betting minimums in those situations, consequently the potential gains aren't all that big, but later on I'll show you what you can do with variations in the -6 to +10 range and then you can learn what you'd like.
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Simulation #3 - In this one, I want to "de-clunk" the original betting schedule presented above by making it less precise and by using as few $5 chips as possible. We can't get around using "reds" if we're at a $10 table because nothing will kill you quicker than betting $25 in negative counts and then spreading only to $80 or so in positive counts, so the minimum bet has really got to be the minimum: $10, period. But what will happen if we ramp-up a little faster by betting $50 at 3, $75 at 4 and topping out somewhere between $80 and $100 at 5? This will require a bigger bankroll if our average bet is $90 at a TC of 5, about $6000. What I'm suggesting here is that you not bet the same amount each time the count's at 5 or more. In some places, the dealer will call out, "checks play" if you bet $100 or more and that will attract some attention, but in a lot of places that won't happen and, in fact at $100 per hand, you may be the small bettor at the table! Only you know your local game, but keep it in mind and check what they do the next time you go. Another approach is to play two hands as the count goes up, but so many casinos now have a "no mid-shoe entry" rule that precludes it, I'm reluctant to add it into what is already a very long lesson. Plus, I've already covered that in the series, "Playing Multiple Hands", which is archived at f you think that's how you'd like to proceed.
Here's the schedule I used for this simulation, otherwise everything is like #2:
True Count Player's Bet Optimum Bet
0 or lower $10 $0
1 $15 $3.50
2 $25 $22.50
3 $50 $41.50
4 $75 $60.50
5 $90 $79.50
6 $90 $98.50
7 $90 $117.50
8 $90 $136.50
9 $90 $155.00
10 $90 $174.50
I made the top bet $90, but remember that it's an average; sometimes you'll bet $80 and other times you'll bet $100. Our "risk of ruin" has gone up, no doubt, but let's see if it's justified.
Simulation #3: Results
Initial Bet Advantage: 1.02%
SCORE: 35.33
Estim. Payoff per 100,000 rounds played is $19,845.70,
with an estimated standard deviation of $10,557.60.
Average st. dev. per round: $33.39
Av. std. per round per unit: 1.15907
Average bet per round: $19.40
Comments on Simulation #3 -
Hey, not bad! We've just about doubled the estimated profit and it would take a two standard deviation event to put us at a loss, but even then it would be only (!!) $2000 or so. It's obvious that this is a better betting schedule, but can you pull it off? You're now using a 1-10 spread at least part of the time and that'll require either a good "act" or short playing sessions. Basically, we're dragging a $20/hour profit out of the game (assuming 100 hands per hour) and to some people that's a nice return on a $6000 investment. To others it's a pittance and I understand that; we all want different things.
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Before I let you go, I want to show you what this simulation looks like if you are able to avoid playing when the TC drops to -3. It's tough to do, I know, but definitely worthwhile, if at all possible. Develop an overactive bladder or any other trick to avoid playing the negative decks and you can make some nice $$$ at this game!
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Simulation #4 - Everything is the same as # 3, except you leave when the count drops to -3 or lower.
Simulation #4: Results
Initial Bet Advantage: 1.40%
SCORE: 67.41
Estim. Payoff per 100,000 rounds played is $29,929.60,
with an estimated standard deviation of $11,527.45.
Average st. dev. per round: $36.45
Av. std. per round per unit: 1.1583
Average bet per round: $21.43
Comments on Simulation #4 -
Wow! This puppy makes you want to run out and find a game, doesn't it? But hold on, pardner. First of all, you need to remember that it's going to take you longer to play 100,000 hands because you'll be away from the table quite a bit. How often? Well, SBA can tell us that because it keeps track of the "dropouts" and they are considerable. This simulation played 10,946,376 "shoes" and it left 4,912,246 when the count dropped. That's just about 45% of the time, which is a big number. So, it'll likely take you twice as long to play the 100,000 hands and that'll cut the hourly win to $15, if you consider an "hour" to be time in the casino. If you consider it to be time on the table, it's another matter. But who's going to figure it that way?
You actually make more per hour under the conditions of Simulation #3 because you're "on the green" almost all the time but you make more per hand played when you use the tactics of Simulation #4. Like so many other things in life, you pays yer money and you takes yer choice.
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Here's some homework. Decide on a betting "schedule" you'd like to use, then make up a set of flashcards to help you memorize it. Just put the various True Counts on the front (1 or lower, 2, etc.) and then put the proper bet on the back. Go through them until you know what you should be betting for each count.
In the next (and last lesson on Double Deck) we'll wrap up with basic strategy variations.

Lesson 23 - Beating the Double Deck Game - Part 3
Double Deck Basic Strategy Variations
Beating the double-deck Blackjack game requires that you first find a game that offers decent penetration and a minimum bet that will allow you to spread your bets from 1 to 8, yet still stay within reasonable money management principles based upon your total bankroll. Another "arrow in your quiver", so to speak is to vary the play of your hand according to the count.
If you know how to count cards, you can use the count to tell you how much to bet on each hand, but you can use the count to help you play each hand more accurately, too. If you've studied my course up to this point, you know one of the key factors in playing a winning game of Blackjack is to leave the table when the True Count drops to -1 or lower, but that tactic isn't very practical at most double-deck games because fewer rounds of hands are dealt before the shuffle, as compared to a six-deck game.
Consequently, you have to sit through a lot more "negative" decks, but the good thing is that a shuffle is never too far away. Yet, at the same time, we all know the casino's edge increases as the count drops, so we want to neutralize the effects of that as much as possible. Because you'll likely be sitting through many more negative counts at a double-deck game, what we need to do is learn the plays for hands like hitting 12 against a dealer's 5 and so forth. We also want to avoid doubling and splitting pairs in low counts and we'll hit instead. But we don't want to guess at important plays like that, so we'll need to learn Basic Strategy variations for "lower" numbers, like -2, -3 and so forth. A realistic range for most double-deck games is a True Count of -6 to +6 and that will cover 85% of all the hands you'll ever play, assuming 50-60% penetration.
Some players prefer to learn just the indices for the most common hands, with the idea that they'll get a hand like A, 4 against a 5 less than 100 times in every 100,000 hands of play, but they'll have a 16 against 10 much more often. In his book, "Blackjack Attack" in the 2nd edition, Don Schlesinger devoted a chapter to what he calls "The Illustrious 18" that are, in his opinion, the most important Basic Strategy variations. I'm not big on reproducing other authors' original works, so I'll refer you to the book for a complete listing if you feel you'd rather not memorize all of the variations I've listed here. Another idea worth considering is to not learn the indices below -2, with the rationale that you'll likely be betting the minimum in such a count, so any playing mistakes will, in the long run, cost you very little. Or, you might want to learn only the indices where you'll be placing extra bets on the table, as in doubles and splits, with the idea that, if I'm going to be putting more $$$ on the table, I'm sure as hell going to play the hand correctly.
But I'm of the opinion that if something about this game can be learned, it should be learned. (Okay, I know I'm a fanatic for this stuff, but what can I do?) If double-deck games will be where you'll spend most of your time, then it's probably worth the effort to memorize all the indices presented here. But if this isn't your primary game, a range of -2 to +6 with some judicious editing will probably suffice. Don't forget that most of these indices are similar to those for a six-deck game, so you won't be starting from scratch. Learn those numbers you think are important for where and how you play.
Rather than talk you through each hand's variation, as I did in the multi-deck section, what I've done here is produce a Basic Strategy Matrix that shows an "index" number for each appropriate play. Don't worry if you have a problem understanding it, because I'll explain it all at the bottom.
Basic Strategy Variations Matrix
Double Deck, H17, Da2, no das, no surrender

Using the Matrix
(GM Note: The Basic Strategy for this game is available from BlackjackInfo.com: t's a lot easier to use this matrix if you've memorized the Basic Strategy for this game and if you haven't yet done that, you really should learn it before you get into this advanced mode of play. For each player hand and dealer's up card combination you will see either a specific action, such as hit, stand, double, etc., or a number. The number is an "action point" based upon the True Count and it keys the variation. As to what the proper variation is for a situation may get a little confusing, but if you study the hand in question, you can usually figure it out. A good example of this is A,7 versus a dealer's 2. In the matrix, you'll see the number 2 in that spot, so do you hit or stand or do something else? Well, "something else" is the answer, so you should double, just as you do with A,7 vs. 3, 4, 5, and 6. Logic plays a role here, so if a play sounds illogical, it's probably the wrong one. Would you really hit A,7 against a 2? Of course, you might stand, but that's already the Basic Strategy play, so doubling is all that's left. Consequently, what this is telling you is that you should double A,7 against a dealer's up card of 2 when the True Count is 2 or more. If the True Count is less than 2, use the Basic Strategy play, which is to stand. Against a 3, Basic Strategy says to double A,7. But the index for that is -2, so that's telling you to double A,7 vs. 3 only if the True Count is -2 or higher. If it's not, then you should stand. Let's talk about another variation that may cause some confusion: 8, 8 vs. 10. The notation in that box is "Stand@6", so if the True Count is 6 or more, you will not split the 8s, but stand instead.
The general rule for understanding the Basic Strategy Variations Matrix is this: If the number in a slot is 0 or a minus, then that play is a Basic Strategy move that you should make as long as the count is higher than the number shown. For example, with A,4 vs. 4, you will double as long as the count is 0 or higher. If the count is minus, just hit. In the case of 9 vs. 4, you'll double as long as the count is -3 or higher (remember that -1 is "higher" than -2).
I don't want you to leave without me telling you the most important variation of all, which is the Insurance bet. You hopefully know that proper Basic Strategy tells us to never take insurance (even when you have a 'natural' and the dealer's up card is an Ace, in spite of what everybody else tells you), but in a double-deck game, the insurance bet becomes profitable at a True Count of 2 (actually 2.4 if you can achieve that degree of accuracy) or higher.
Learning the Basic Strategy Variations
Once you've chosen the Basic Strategy variations you want to learn, you should make a set of flash cards for them. Exactly how to do that is explained in Lesson 14 of "The GameMaster's Blackjack School" and I cannot over-emphasize their value. Make up a set and carry them with you, or at least study them intently before each playing session if double-deck Blackjack isn't your "primary" game.

Lesson 24 - Understanding the Surrender Option
I can well remember the good ol' days in Atlantic City when casino gaming first began there. The one casino that was open at the time (Resorts International) had to offer a Blackjack game where the rules were established by the Casino Control Commission and that included a weird rule called 'surrender'. At least we thought it was weird until we figured out what a huge advantage it gave to the player who used it correctly!
Most players dubbed surrender as a sucker bet. One time at a table, some other player summed it all up when he declared: "Surrendering is nuts! Why give up half your bet when you could just as easily win the hand?" To a degree, he was right. What I mean by that is it's true that a player could win or lose any one given hand, but he didn't carry the thought far enough. If you play thousands of hands, giving up 50% of the bet on some of them is actually the cheaper alternative to playing it out.
For those of you who aren't familiar with surrender, it's a player option that some casinos offer. When allowed, you may elect to give up half the amount you've bet rather than play out the hand. For the mathematically inclined, you can see that for those hands where your expectation is to lose more than 50% of the time, surrender is a good deal. There are two types of surrender: early and late. Those terms refer to whether or not a dealer checks to see if s/he has a blackjack (when an Ace or 10 is showing) before you may make the surrender decision. In A.C., the type of surrender was 'early' which meant that you could give up half your bet before the dealer knew if s/he had a 'natural'. That came about simply because state regulations didn't allow 'peeking', so a dealer didn't know what his hand was until all the players had made their playing decisions.
These days, the most common form of surrender is the 'late' version where the dealer checks for a natural and, if s/he doesn't have it, then you may surrender. This is worth a lot less, since if the dealer does have a natural, s/he takes your bet before you can surrender. But, in spite of that restriction, surrender can still be of some value to you, if you use it properly.
Let me show you an example; assume a 6-deck game with double after split allowed and the dealer must stand on A-6. If I have a hand of 9, 7 and the dealer is showing a 10, my 'expectation' is to lose 53.7% of all the money I bet in that situation. If I surrender, I'll lose 50% of all the money bet in that situation. A modest improvement, but better nonetheless.
So this makes figuring the basic strategy for surrender very simple. If the expectation is to lose more than 50%, surrender. For a multi-deck game, here are the rules for late surrender:
Player's hand of 9,7 or 10,6: Surrender against a dealer's 9, 10, Ace
Player's hand of 8, 8: Surrender against a dealer's 10
(Though it's virtually a toss-up; split if DAS is allowed.)
Player's hand of 15: Surrender against a dealer's 10
(Note If the dealer hits A-6, surrender against an Ace, also.)
Late surrender adds to the player's edge by a modest .1%, but I like it when I have a big bet out there and I get a 10 for my first card, as expected, and then get the last 6 in the deck as my next card. Who hasn't done that before?
If you count cards, the surrender option is an even better deal as the count goes up. If you've read and studied my lessons up to this point, you know that in a 'high' count situation, the proportion of 10s and faces (and Aces) in the remaining deck(s) versus 'little' cards is much greater, so the odds of getting such a card have increased considerably. This is where the value of surrender goes up.
Most surrender available these days is 'late' surrender, which means that the dealer checks the hole card if s/he is showing an Ace or 10. If s/he has a 'natural', your entire bet is lost and surrender isn't an option. Knowing that the dealer doesn't have a Blackjack makes surrender, to some people, a stupid play, but let's examine the situation a bit closer. Just what kind of hand can the dealer get with a face card showing? First of all, the dealer is going to bust only 23% of the time when s/he is showing a 10 or face as an up card. Secondly, s/he is going to end with a total of 20 or 21 41% of the time! And you think you're going to beat her with your 16? When the dealer is showing an Ace, and does NOT have a Blackjack, s/he still is going to end with a total of 19 or more 46% of the time and will bust only 17% of the time. That's why surrender is valid, even if the dealer doesn't have a Blackjack.
Now, as the count goes up, both you and the dealer have a better chance of getting 10s and Aces. Thus, it's more likely that you'll get a 10 card if you hit. So, if you have a hand of 15 and the dealer is showing a 9, s/he has a better chance of having a 10 in the hole and it's more likely that you'll hit with a 10. Time to bail! When the true count is 2 or more, surrender your 15s against a dealer's 9. Against an Ace, surrender 15 at a true of 2 or more, if the dealer stands on A-6. If the dealer is required to hit A-6, surrendering 15 is a basic strategy move. Another good one to remember is to surrender 14 against a 10 at a true of 3 or more.
The use of surrender is, from my experience, interesting from a 'camouflage' point of view. As you are hopefully aware, we card-counters prefer to keep our skills concealed since, for some sick reason, casino personnel don't like counters. Surrendering is actually a fairly sophisticated playing technique, so it's fair to say that the 'average' gambler doesn't use it. Yet, I want to look like an avaerage gambler in order to conceal my abilty to beat the game. But I use surrender when it's offered and it really helps when the count is high, I have a big bet out there and I surrender a 15 against a 9 (or a 13 against a 10 - true of 8), because it makes me look like a 'chicken.' Most casino personnel think surrender is a 'sucker' play anyway, so when they see you giving up half a $200 bet, they think you'll never make any $$$ at the game. That's just what I want them to think.
This is the final lesson of my Blackjack School, at least for the time being. However, I'm always coming up with new ways to beat the game and I usually write a new article on the topic once a month. So, to stay in touch, be sure to visit our original site, a regular basis.

BlackJack School BlackJack Training Author Selzer-McKenzie SelMcKenzie