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Blackjack Counting Systems

I teach the Hi/Lo system of counting because it’s easy to learn, easy to use and relatively effective at most games, particularly multi-deck games where a large bet spread can be attained. But I recognize that Hi/Lo has its limitations and the games available to you may be better exploited by a different system. In this series, I’ll examine a lot of the different counting systems so that you can make up your own mind regarding which is the best to use.

I find, by using the training methods I’ve learned, that it’s fairly easy to learn a new counting method; in fact, I use a different system when I play single-deck games and I have few problems in keeping my count straight after just an hour or two of ‘refresher’ practice. I will say, however, that on any particular trip, I stick to one or the other. I never try to play some single-deck, then a bit of multi-deck and then move back to single-deck, unless I use the same ‘system’. But, to keep it simple, I just play one or the other, so when in the Reno/Tahoe area, I stick to single-deck; the same is true in Mississippi, whereas I play all multi-deck in Las Vegas. Remember that double-deck games have a lot more in common with six decks than one deck, so I treat those as multi-deck games.

How Counting Systems Work

Let me give you just a bit of the thinking behind counting systems so you’ll understand how, and why, they work. All the systems, in one way or another, recognize the importance of the different cards to the player. For example, the most important card to a player is the Ace, because it’s part of a ‘blackjack’ or ‘natural’, as we prefer to call it. The bonus that a natural pays is of paramount importance; it’s worth about 2.3% to the player. In other words, if a game pays only even-money for a natural, the casino gains an additional edge of 2.3% on the player, over and above the edge they may already have because of the other rules (dealer hits A-6, six decks, etc.) Therefore, the removal of an Ace from a deck or decks of cards has a measurable impact on a player’s edge. As an extreme example, if all 4 Aces are removed from a single-deck game, the casino will have a huge edge which is virtually impossible to overcome. So, the “effect of removal” for Aces is significant and can be quantified. The same is true for the 5; it’s the most important card for the dealer, since it makes all those 12-16 hands which the dealer MUST hit into 17-21. Remove all the 5s from a single-deck game and the player has a nice 2+% edge over the casino. So, the “effect of removal” for 5s is also significant and can be measured. Thus, the first thing a counting system does is give us a way to calculate our advantage or disadvantage over the casino as cards are played or ‘removed’.

Another role of a good counting system is to give us some idea on how to play the hand. Or, more correctly, when to deviate from the proper playing strategy. To use the example above, if we were in a single-deck game and all the 5s had been played, would you hit a 16 against a dealer’s 10? Well, you might, but the play of that hand has been affected by the removal of the 5s. So, obviously, we have an “effect of removal” when it comes to playing the hand, as well as figuring our advantage. But this is, as you can imagine, less precise because the values are constantly changing. The value of a 5 when we have a 16 to hit is very high, but the value of the 5 when we have a 9 to double is very low. All we can do is basically average the impact of a 5 when playing a hand and hope for the best. You can see where this leads: if a counting system is good for betting purposes, it’s not as good for playing purpose and vice-versa.

Before we leave the theory part, we need to address one more area and that’s the insurance bet. This is really simple and all our analysis is based upon one question: Is the dealer’s hole card a 10? The odds on that are easily figured and, if we keep track of the proportion of 10s to other cards, we can make ‘perfect’ insurance decisions. (I say ‘perfect’, because we won’t be right all the time, but in the long run we’ll show a profit from the bet if we use a “ten-count”). The ability to make accurate insurance bets is very important to a counter, in fact, it’s the single-most important basic strategy variation, since it accounts for a full third of all the gains we’ll make by varying basic strategy. (Depending upon the basic game, our bet spread and other variables, we can expect to add about 0.2 to 0.4% to our average edge by varying from basic strategy according to the count.) How well a counting system ‘predicts’ the 10 in the hole is an important consideration. A system which is very accurate for the insurance bet is, surprisingly, pretty good at making playing decisions, but it’s downright poor at indicating our edge over the casino.

The Three Ratings

All counting systems or methods can be rated in three ways for how they treat the factors mentioned above. The first rating is a system’s “betting efficiency”, which indicates how accurately the count measures your edge over the casino. For example, if the rules of a casino indicates that they have a 0.5% edge over the player who uses proper Basic Strategy, a counting method with 100% betting efficiency would precisely measure the edge (or lack thereof) for the player, IF the player was keeping the count accurately and figuring the true count correctly. Of course, some sort of money management program would still be necessary, because even though a player may have an edge, it doesn’t necessarily follow that s/he is going to win the hand.

The second rating is the “playing efficiency” which measures how well the system guides us in making basic strategy variations except the insurance decision, which is treated separately; and that’s the third rating; “insurance efficiency”. All of these ratings are shown as averages, since there are times when a system can be very accurate and, at other times, it can be very inaccurate. The Hi/Lo system, for example, is very accurate when it’s indicating you should double 11 versus an Ace, (82%), but quite inaccurate when telling us to stand with 16 versus 9 (53%).

The Best of the Best

The best count for the insurance bet is 100% accurate, as is the best count for betting. The best count for playing purposes is about 70% accurate, but unfortunately, no count currently exists which can offer all this in one package. So, you have to decide which will work best for you. If you play a lot of single-deck with a 1-4 spread, then a system with a good playing efficiency will probably be best, if you have the opportunity to spread from 1-12 betting ‘units’, then you’ll want something with a strong betting efficiency and, if you often play with a friend or spouse at the same table, you should have him or her learn the best insurance count and work out a signaling system to share information.

The Series

What I’ll do here, over time, is try to examine the various counting systems out there in a rational order. Not only will I give you their 3 ratings, but will discuss their pros and cons as well as their strengths and weaknesses. Numbers alone don’t tell the story; if you play for many hours at a stretch, a difficult system isn’t going to be very effective if you’re making a lot of mistakes, for example. We generally classify counting systems on ‘levels’. The Hi/Lo is a ‘one-level’ system, because all the point values are +1, 0 or -1. A ‘two-level’ system uses +2, +1, 0 -1, -2 and a three-level system counts one or more cards as 3, etc. You get the idea. I’ll also address unbalanced systems which do not require a conversion to true count and we’ll take a look at some ‘theoretical’ systems as well. (How about one where the Ace is +51 and the 10 is -180; not practical for a human, perhaps, but not too difficult for a computer).

Just so you know, the Hi/Lo has a betting efficiency of 97%, a playing efficiency of 51% and an insurance efficiency of about 80%.

Single-Level Counting Systems


The term “single-level” refers to counting sytems where the point values assigned to the cards are either 1,0 or -1. This type of system is what made card-counting popular, mostly because it made the task feasible for the average human being. What I will do here is examine the two primary types of single-level systems which exist: Ace-included and Ace-deleted. What this refers to is how the Ace is treated by the point system. The Ace plays a unique role in the game of Blackjack, because it’s valued as a ‘high’ card for betting purposes and as a ‘low’ card for playing purposes. It’s obviously the key component of a blackjack or ‘natural’, but if one hits a 14 and gets an Ace, it’s now a low card. Knowing that the deck(s) remaining to be played have an abundance of Aces in it is very useful from a betting point of view, but of little value if one has to hit a 12, so many counting systems developed in two ways: those that treated the Ace as a ‘neutral’ card (point value of 0) and those that treated it as a high card (point value of -1 or more). This has considerable impact on the playing, betting and insurance efficiency of a system. (If all that is ‘greek’ to you, please reread the first chapter of this series.)

Some History

The first truly succesful counting system required the player to keep track of the ratio of tens to non-tens and that was difficult to master. This was the famous Thorp “Ten Count” which was detailed in his 1962 book, “Beat the Dealer”. (He was actually preceded by Alan Wilson who created the “Wilson Count” in 1958, but didn’t publish it until 1965). Once Thorp’s method was published, several scientists and mathematicians began developing ‘point’ count systems based upon his work. The most notable was Harvey Dubner who, in 1963, created a crude version of what he called the “High-Low” point system. Julian Braun of IBM Corp. perfected Dubner’s system into what we call today the Hi/Lo or Plus/Minus system.

Braun’s work was noticed by a college professor who uses the pseudonym “Lance Humble” and he contracted with Braun to perfect a system which had been published by Charles Einstein in his 1968 book, “How to Win at Blackjack”. The Einstein count did not assign a point value to the Ace and his didn’t count the 2,7,8, or 9 either, so the count remained ‘balanced’. (There is an equal number of high and low cards in a complete deck. I’ll cover ‘unbalanced’ counts later.) Braun’s development of this Ace-neutral count resulted in the Hi-Opt 1 count which was originally sold privately (for $200!!), then published in a book called “The World’s Greatest Blackjack Book” in 1980.

The Hi/Lo was refined by Stanford Wong in his 1975 book, “Professional Blackjack”, but even more importantly, Wong gave the reader the information needed to actually put it all into use. Jerry Patterson took Wong’s information in 1978 and created the first really good ‘school’ where the average person could learn all this stuff. Just to complete this brief history, Jerry Patterson is the one who taught me how to count cards; I was a student in his second-ever class.

How Effective is a Single-Level System?

Of course, it all depends upon how you define “effective”. If you go strictly by the ‘numbers’, then the best you can get from a single-level count is a 97% betting efficiency, a 63% playing efficiency and a 100% insurance efficiency (more on that later), though no one system provides all that. But effectiveness can also be measured in other ways: ease of learning and ease of use come to mind, for example. The single-level systems are rated very high in those categories, so your choice really boils down to what kind of game you play, whether or not you’re a pro, how much you bet and other factors. I’ll say this with great confidence, though: No category of counting systems has removed more $$$ from casinos than the single-level counts.

The Primary Single-Level Systems

I have chosen 4 single-level systems to examine here. There are others, but my criterion was that there had to be available, at a reasonable cost, all the information a prospective user may need to effectively learn and use the system. This basically means that there has to be a book or software program currently in print which will give you the basic strategy variations, side-count information, etc.

The Hi/Lo

Point Values: 2-6 = +1; 7,8,9 = 0; 10, A = -1
Betting Efficiency: 97%
Playing Efficiency: 51%
Insurance Efficiency: 79%

Most Effective: In games where a minimum 1-8 bet spread can be achieved.
Good Points: Easy to learn; easy to use for long playing sessions
Bad Points: Not accurate in identifying opportunities to vary from basic strategy
The Book to Buy: “Professional Blackjack” (1994 edition) by Stanford Wong

Uston Advanced Plus/Minus

Point Values: 3-7 = +1; 2,8,9 = 0; 10, A = -1
Betting Efficiency: 95%
Playing Efficiency: 54.7%
Insurance Efficiency: 79%

Most Effective: In games where a minimum 1-8 bet spread can be achieved.
Good Points: Easy to learn; easy to use for long playing sessions.
Bad Points: Not accurate in identifying opportunities to vary from basic strategy.
The Book to Buy: “Million Dollar Blackjack” by Ken Uston

Hi-Opt 1

Point Values: 3-6 = +1; 2,7,8,9,A = 0; 10 = -1
Betting Efficiency: 88%
Playing Efficiency: 61.5%
Insurance Efficiency: 85%

Most Effective: In games where a large bet spread cannot be achieved, especially single-deck.
Good Points: Easy to learn, adapts well to multi-parameter counting. Plus, if you are being observed by a casino employee and that person is counting with the Hi/Lo, s/he may be confused by your count.
Bad Points: Requires a side count of Aces to be really effective; that’s difficult to do in multi-deck games.
The Book to Buy: “The World’s Greatest Blackjack Book” by Humble & Cooper

The Canfield Expert Count

Point Values: 3-7 = +1; 2,8,A = 0; 9,10= -1
Betting Efficiency: 86%
Playing Efficiency: 62.3%
Insurance Efficiency: 85%

Most Effective: In games where a large bet spread cannot be achieved, especially single-deck.
Good Points: Easy to learn. Plus, if you are being observed by a casino employee and that person is counting with the Hi/Lo, s/he may be confused by your count.
Bad Points: Requires a side count of Aces to be really effective; that’s difficult to do in multi-deck games. Also, I’m not totally certain that the book is still available.
The Book to Buy: “Blackjack Your Way to Riches” by Richard Canfield

The Insurance Count

I threw this in because, while at first glance it doesn’t appear to be a single-level count, it basically is. The value of this count lies in using it with a playing partner where you both sit at the same table. One person uses a conventional count for betting and playing purposes and the other uses this count for insurance bets.

Point Values: 2,3,4,5,6,7,8,9,A = +4; 10 = -9
Betting Efficiency: 72%
Playing Efficiency: 62.1%
Insurance Efficiency: 100%

Most Effective: For insurance bets in single- and multi-deck games.
Good Points: Fully exploits the insurance bet which is the singlemost important basic strategy variation.
Bad Points: While it can be used on its own as a ‘conventional’ count, its betting efficiency is lacking. So, it really requires a second player.
The Book to Buy: None; just insure when the true count is 16 or higher.

Just so you know where I’m heading with this, here’s a list of forthcoming chapters listed in the order in which they’ll appear:

Second-Level Counts
Third- and Higher-Level Counts
Computer-Level Counts
Multi-Parameter Counts
Unbalanced Counts

I’ll probably toss in a final chapter covering any counts or counting methods which don’t get covered by the above.

Level-Two Counting Systems


The term “level-two” refers to counting systems where the point values assigned to the cards are either 1,2, 0, -1 or -2. This type of system recognizes that even within a category of cards (‘low’ cards for example), some cards have more of an impact than others. Fives are the prime example; they help the dealer most when s/he has a hand of 12 to 16, so if there are none left in the deck, it’s likely that the dealer won’t do as well. Threes are less important, but in many single-level systems, a 3 and a 5 receive the same weighting. Level-two and higher systems differentiate between 3s and 5s, as you’ll see.

What I’ll do here is examine the two primary types of level-two systems which exist: Ace-included and Ace-deleted. What this refers to is how the Ace is treated by the point system. The Ace plays a unique role in the game of Blackjack, because it’s valued as a ‘high’ card for betting purposes and as a ‘low’ card for playing purposes. It’s obviously the key component of a blackjack or ‘natural’, but if one hits a 14 and gets an Ace, it’s acting as a low card. Knowing that the deck(s) remaining to be played have an abundance of Aces in it is very useful from a betting point of view, but of little value if one has to hit a 12, so many counting systems developed in two ways those that treated the Ace as a ‘neutral’ card (point value of 0) and those that treated it as a high card (point value of -1 or more). This has considerable impact on the playing, betting and insurance efficiency of a system. (If all that is ‘greek’ to you, please read the first chapter of this series.)

How Effective is a Level-Two System?

Only incremental gains are available by using a level-two count in place of the better level-one systems. For example, the best level-one system detailed in the previous installment of this series has a Playing Efficiency of 62.3% and the best level-two system which we’ll review here has a P.E. of just over 67%. What does this mean? If one could play at a single-deck game with 100% accuracy and the dealer routinely dealt out half the cards, a strategy gain of about 0.95% could be effected at that point. With a counting system offering 67% efficiency, the gain would be 0.95 X 67% = 0.64% whereas the best single-level count (without a side-count of Aces) would produce an edge of 0.95 X 62.3% = 0.59%. Is a 0.05% gain worth it? Well, if your average bet is $10, it’s a difference of a half-cent. If your average bet is $200, it’s a dime. Level-two counts have Betting Efficiencies very similar to level-one counts, so there’s no discernible difference between the two in that regard and, as you’ll see, their Insurance Efficiencies are similar as well. The biggest gain that most level-two counts demonstrate is when they are compared to the single-level Hi/Lo system which was, for the most part, the first single-level count most people learned. In this comparison, the level-two systems offer Playing Efficiencies which are almost 25% higher and that’s what gave them their boost in popularity. But, as better single-level counts were developed, the differences narrowed to what we have today.

From a personal point of view, I still think that the Hi/Lo is most effective against multi-deck games where one can get a decent bet spread, but I use the Hi-Opt 1 (a single-level count) with a side-count of Aces for single-deck play. If I played only single-deck games, I’d probably go with one of the level-two counts that I’ll examined here.

The Primary Level-Two Systems

I have chosen 2 level-two systems to examine here. There are others, but my criterion was that there had to be available, at a reasonable cost, all the information a prospective user may need to effectively learn and use the system. This basically means that there has to be a book or software program currently in print which will give you the basic strategy variations, side-count information, etc.

The Zen Count

Point Values: 4,5,6 = +2; 2,3,7 = +1; 8,9 = 0; A = -1; 10 = -2
Betting Efficiency: 96%
Playing Efficiency: 64%
Insurance Efficiency: 85%

Most Effective: In virtually all games.
Good Points: Easy to learn; easy to use for long playing sessions
Bad Points: The true count is figured at the half-deck level and that’s not easy to do in multi-deck games.
The Book to Buy: “Blackbelt in Blackjack” by Arnold Snyder

Comments: If you’re looking for a good, relatively easy to use system, this may fit the bill. Since the Ace is included in the count, this is basically a beefed-up Hi/Lo and yet it’s powerful in a single-deck game. The book has a lot of good, additional information, including a complete explanation of the first ‘unbalanced’ count which will be reviewed in a later installment.

The Omega II Count

Point Values: 4,5,6 = +2; 2,3,7 = +1; 8, A= 0; 9 = -1; 10 = -2
Betting Efficiency: 92%
Playing Efficiency: 67%
Insurance Efficiency: 82%

Most Effective: In single-deck games where it’s difficult to achieve a big bet spread
Good Points: Very high Playing Efficiency, even without an Ace side-count.
Bad Points: Fairly low betting efficiency unless the Ace side-count is used.
The Book to Buy: “Blackjack for Blood” by Bryce Carlson

Comments: This count can be brought up to a 98+% Betting Efficiency by incorporating an Ace side-count. That’s pretty easy to do in a single-deck game, but very difficult in a multi-deck game. The book is a worthwhile investment, even if you don’t use the count.

Just so you know where I’m heading with this, here’s a list of forthcoming chapters listed in the order in which they’ll appear:

Third- and Higher-Level Counts
Computer-Level Counts
Multi-Parameter Counts
Unbalanced Counts

I’ll probably toss in a final chapter covering any counts or counting methods which don’t get covered by the above.

Level-Three (and higher) Counting Systems


In this installment, we’ll examine card-counting systems that push the limits of mental ability; the systems which try to replicate the power of a computer yet are still used by a solitary counter whose ability to add and subtract quickly and accurately in his or her own mind makes it all work. The term ‘level-three’ refers to a counting system that assigns a value of 3 (plus or minus) to one or more of the cards which it tracks. One of the counts which exists goes so far as to assign a point value of 4 to one of the cards, so it would be considered a ‘level-four’ counting system. My primary criterion for choosing the counts to examine has been that a reasonably-priced book had to be available in case you wanted to learn the count yourself. That being the case, I’m going to examine two level-three systems and not cover the “Revere Advanced Point Count which is a level-four system, but is sold for $200 or so.

As you’ll see, the gains made by these counts in their ‘efficiencies’ are just incremental when compared with level-two systems, so I really question the value of taking on the extra work involved. Sure, they can be learned, but the big question is how accurately they can be used in actual casino playing conditions? That decision is up to you, naturally, so let’s proceed.

How Effective is a Level-Three (or higher) System?

In spite of the fact that one of these systems here counts the Ace as a value of -1 and the other counts it as 0, neither of these offer much improvement over the betting efficiency of the level-one Hi/Lo system. If the majority of your play is at multi-deck games (double-deck or more), the betting efficiency of a system needs to be your primary concern, since these games are beaten mostly by a large bet spread. But, if you’re fortunate enough to play a lot of single-deck games where a narrow bet spread of 1-4 is about all that’s practical to use, then the Playing Efficiencies available from at least one of these counts will probably impress you. If a dealer routinely uses half the cards in a single-deck before shuffling, a strategy gain of 0.95% is available through perfect play; that is, play where each hitting, standing, doubling, etc. decision is made knowing the exact composition of the remaining cards. No mentally-based counting system offers 100% playing efficiency, but something on the order of 69% can be achieved by a level-three count whereas the best level-one system is in the 62% range and the best level-two system hovers around 67%. Is it worth it? If you bet $100 or more per hand, it probably is, but the key is accuracy. Sure, you can check your accuracy at home and it will probably be pretty good, but how can you check it under actual playing conditions in a ‘real-life’ casino with all the distractions they offer?

I have to say that I used to use one of the systems here in a multi-deck game venue but went back to the simplicity of the Hi/Lo when I found that my mental alertness fell off after only an hour or so of play. But, that’s just me, so whatever count you choose, I wish you the very best.

The Primary Level-Three Counts

The two systems here meet the criteria mentioned above but you’ll find that they are considerably different in their overall efficiencies. That’s mostly because one assigns a point value to the Ace and the other doesn’t. Remember, in order to get the most out of a system that doesn’t assign a point value to the Ace, there has to be a side-count of them. This is pretty simple in a single-deck game, but, I can assure you, very, very difficult to do in a six-deck game.

The Uston Advanced Point Count

Point Values: 2, 8 = +1; 3, 4, 6, 7 = +2; 5 = +3; 9 = -1; 10 = -3; Ace = 0
Betting Efficiency: 98%
Playing Efficiency: 69%
Insurance Efficiency: 91%

Most Effective: In single-deck games
Good Points: This count offers the highest combined efficiencies of all the counts we’ve covered to this point.
Bad Points: Difficult to learn and hard to use accurately in multi-deck games.
The Book to Buy: “Million Dollar Blackjack” by Ken Uston

Comments: If you can’t bring a computer into the casino with you, this is the next-best thing. But, it does require a sidecount of Aces to extract this power and true count adjustments are at the half-deck level which isn’t easy. And bear in mind that all cards except the Ace have a point value; you’ll be very busy at a full table when the cards start flying.

Stanford Wong’s Halves Count

Point Values: 2, 7 = +0.5; 3, 4, 6 = +1; 5 = +1.5; 8 = 0; 9 = -0.5; 10s and Ace = -1
Betting Efficiency: 99%
Playing Efficiency: 57%
Insurance Efficiency: 73%

Most Effective: In multi-deck games where a large bet spread can be obtained
Good Points: This is actually a lot easier to learn than it looks.
Bad Points: The Insurance Efficiency is quite low.
The Book to Buy: “Professional Blackjack” by Stanford Wong

Comments: Yes, this looks like something other than a level-three count, but if you double all the point values, you’ll see it is. I learned this count after I mastered the Hi/Lo and used it to great effect in really good multi-deck games but for me, it was tiring to use.

Just so you know where I’m heading with this, here’s a list of forthcoming chapters listed in the order in which they’ll appear:

Computer-Level Counts
Multi-Parameter Counts
Unbalanced Counts

I’ll probably toss in a final chapter covering any counts or counting methods which don’t get covered by the above.

Computer-Level Counting Systems


The “father” of card counting was Professor Edward O. Thorp whose book, “Beat The Dealer” was initially published in 1962. In the revised edition of 1966, he presented not only his original “ten-count” system, but added his “simple point count” system and a “complete point count” system which evolved into the High-Low or Plus-Minus Count. But most people forget that he had developed an “ultimate” point count system in the first edition of his book. Thorp knew his stuff and he was aware of how powerful a counting system could be, if one could add and subtract like a computer. That wasn’t a very practical idea back in 1962 and he certainly didn’t envision the Internet or Web casinos, but here we are.

You are probably reading this at a computer which is so powerful that, if you had it back in 1945, you would have probably been burned as a witch. Well, maybe not, but when you consider that the Internet was initially based upon computers with 25K (“K”, not megs) of memory, what we have at our fingertips today is astounding. But, Las Vegas has never looked kindly upon the use of computers at the gaming tables; in fact, it’s now illegal to use one. That wasn’t always the case, though. Back in 1960, a man named Robert Bamford developed a Blackjack-playing “black box” which he used, openly and at some profit, in the casinos until they began shuffling the deck after every hand. Concealed computers followed in the ’70s, the most famous being “George” which was used by a team formed by Ken Uston. With George, that team made over $150,000 in December of 1977.

So, what’s the name of your computer? It doesn’t have to be “George” for you to use it to play very accurate, if not perfect, Blackjack. Of course, you’re not going to carry it into your favorite casino, but if you play Blackjack on the Web, you can do so with great accuracy. If you’ve read the previous installments of this series, you’ll recall that counting systems are typically measured in three ‘efficiencies’: betting correlation, playing correlation and insurance correlation. You also need to remember that no one system excels at all three. Even the best system is a compromise; so, what if you had a way to keep track of three different counts? Then, you could use one for sizing your bet, one for the proper play of the hand and one for making insurance decisions. And, for good measure, you could keep track of the number of cards played so that any conversions to the “True Count” would be perfect! Such programs do exist and I am in the process of evaluating one of them. This idea of using your computer is relatively simple; it’s really just a spread-sheet function. But, to hark back to the ‘good old days’ of the computer biz, one truism remains: Garbage In, Garbage Out. I am not a computer programmer, hell, I’m not even a skilled user of Excel but I can show you some good counts to consider. Unlike my previous lessons, there’s not a lot of information available on these counts, so when it comes to indexes (indices?) like we use in ‘regular’ counting systems (you know; “stand with 16 vs. 8 at a true of 7”, etc.), you’re on your own here. But, I’ll give you the basic figures which is a good start.

The Thorp Ultimate Point Count

Optimal System for Variation of Bets

Point Values; A -9; 2 +5; 3 +6; 4 +8; 5 +11; 6 +6; 7 +4; 8 = 0; 9 -3; 10 -7
Betting Efficiency: 100%

Optimal System for Variations of Strategy
Point Values: A +51; 2 +60; 3 +85; 4 +125; 5 +169; 6 +122; 7 +117; 8 +43; 9 -52; 10 -180
Playing Efficiency: 70.3%

The Insurance Count

Point Values: A-9 +4; 10 -9
Insurance Efficiency: 100%
Note: This was covered in the “single-level” lesson.

Although I called the “playing” count an ‘optimal’ system, it’s really only the optimum for a single-parameter count. Don’t confuse ‘parameter’ with ‘level’, however. A single-level count uses point values of 1, 0 or -1 but a single-parameter count just uses a total point value for all your decisions. We’ll cover multi-parameter counts, which use a side-count of the number of remaining cards (like Aces) by type, in the next lesson. It’s certainly possible to achieve a playing efficiency of almost 100% by keeping track of each type of card separately. Now understand that 100% efficiency doesn’t mean you’ll win every hand, because you still don’t know the order in which the cards will appear, but in ‘the long run’ order doesn’t matter; it will eventually work out to be random.

You now have most of the information needed to create a program on your computer which can play very accurate Blackjack. There are two approaches one can take; the first being a program which keeps three different counts and you use the appropriate one as you play. The other is one which doesn’t use any of these counts; it just calculates the bet and proper play based upon the composition of the remaining deck(s). That’s more in the style of a multi-parameter count and I’ll cover those next time. I’ll leave you with a teaser: I have, on my hard drive, copies of programs just like the two I’ve described above.

Multi-Parameter Counting Systems


This isn’t really a counting “system”, but more a way of enhancing some of the counting systems that we’ve covered in previous installments of this series. What “multi-parameter” means is that a separate count is kept of some cards, particularly those which are assigned a ‘point value’ of zero. The best example is the Ace. As you saw in the chapter on single-level counts, some systems assign the Ace a point value of -1 and other systems don’t count it (point value of 0). That’s because the Ace is a weird card in the game of Blackjack; for playing purposes, it’s a ‘small’ card (hit a 12 with an Ace and now you have a 13…whoopee!), but for betting purposes, the Ace is considered a ‘high’ card because it’s the key element in a ‘natural’ which pays 3 to 2. So, if you want a method of counting which is very accurate in terms of betting efficiency, treat the Ace as -1 (or more; it depends on the system), but if you want a method which is highly accurate for playing purposes, treat the Ace as ‘neutral’ (point value of zero). But, you can’t have both…or can you?

What if you treated the Aces as a “0”, but kept track of them separately? Then, you’d have a system that would be pretty accurate for playing purposes and you could make temporary adjustments to the count when you’re figuring the bet to place on the next hand. Here’s a simple example. Let’s say we’re at a single-deck game, and with 26 cards played to this point, the running count is zero. Most systems would dictate a minimum bet, but what if all 4 Aces remained in the undealt cards? Think there’s a decent chance that one or two may come out in the next hand? (Yes, I know the dealer will probably get them all, but that won’t happen every time). In this situation, there are 26 cards left to be played and, since Aces are distributed at a 1 in 13 ratio, we should have seen 2, but didn’t. So, there are 2 ‘extra’ Aces in there and we could add 2 to the running count for betting purposes only, then go back to the ‘original’ running count for playing purposes. Figured on a True Count basis, it’s +4 for betting and 0 for playing; quite a difference.

So, you can see that the ‘side’ count of Aces identified an opportunity that might otherwise have been missed. That’s the power of multi-parameter counting; it’s useful in certain situations. By the way, even though a counting system may assign some value to the Ace doesn’t mean that you can’t also track it from a multi-parameter point of view. For a cool way to track the Aces, see my article “…and I’ll have a side of Aces” in the Gamemaster’s Secrets section of this site.

Are there other cards worth tracking in a multiple-parameter mode? Yes, there are; in fact almost any card can be tracked to some advantage, but it’s not easy and there’s very little information out there on how to use these side counts. For example, knowing that there are ‘extra’ 8s in a deck is very useful if one has a hand of 13 to play against a dealer’s 10, but what would you do differently? If the deck was ‘short’ on 8s, would you stand? Well, that might be the correct play, but I can’t tell you at which point it becomes the correct play. The card-counter is busy enough at the table so adding a side count other than Aces will likely create mistakes that cause the losses to outweigh the potential gains. Maybe, if you’re already using a count like the Hi/Lo where the Ace is a -1, it might be worthwhile to add a ‘side’ of 7s or 9s. Boy, would that be helpful when hitting 12s! And, in a single-deck game, it wouldn’t be all that tough, but in games like that, I recommend using the Hi-Opt 1 count where the Ace is a 0 and you keep a side-count of them. So, we’re back to where we started. But, it probably is possible to keep track of 2 cards and if I was going to do it (I’ve never felt the need), I’d track Aces and 7s. According to Dr. Peter Griffin, in his book “The Theory of Blackjack”, the betting efficiency of the High-Opt 1 count can be raised from 88% to 97% by adding Aces and 7s and the playing efficiency can be raised from 61.5% to 73.6% by doing so.

Going much beyond that virtually requires a computer. Hey…you’re at a computer now! In the previous chapter of this series, I addressed ‘computer-level’ counts which offered extreme accuracy at the game though it’s basically illegal to use a computer in a casino. But, what if you were playing at an Internet casino? Then, you could take advantage of a multi-parameter count and your accuracy might be as high as 90% for playing efficiency and nearly 100% for betting.

I’ll be wrapping this series up with a chapter on unbalanced counts which are probably the easiest to use, yet they can still get you the $$$.

Unbalanced Counting Systems


Almost all the counting systems we’ve examined up to this point are difficult to learn. Not impossible, but certainly not easy, either. If you’ve been discouraged by all the adding and dividing and memorization that it takes to fully utilize these counts in a casino, take heart. An unbalanced count can easily be learned by anyone who can operate a computer and guess what? You’re on a computer right now, so you can certainly learn one of these.

They are called “unbalanced” because, while they still assign ‘point’ values to the cards, when you add all the point values up in a deck or decks, it doesn’t result in zero. By doing this, these counts allow you to play without a ‘true count’ conversion which many people find to be the hardest part of balanced counting systems to learn. Yet, these are still quite effective in 4-, 6- or 8-deck games and the fact is, most ‘casual’ Blackjack players who go to casinos where the games offered are dealt from four or more decks should probably use an unbalanced count. I cannot recommend them for single- or double-deck play because they have their limitations in those games, but otherwise the unbalanced counts are pretty good.

How Effective are Unbalanced Counts?

Of course, we have to first define the word “effective” and throughout this series I’ve quoted a lot of statistics for Playing Efficiency, Betting Correlation and so forth. How the unbalanced systems stack up against all the others will be covered in each individual count’s section, but “effective” as it relates to unbalanced counts has to also be defined as “ease of use”. If you go to a casino only once or twice a month, you probably play for quite a few hours at a time, but I live half-an-hour from 6 casinos, so it’s easy for me to play for an hour at one particular place and move on. Spending more than an hour or two at a game while using a complicated counting system is mentally taxing and, inevitably, mistakes are made. Throw enough mistakes into the equation and the result may be that you’re not gaining any edge over the casino for all your effort. Unbalanced counts are easy to use for long periods of time because they don’t require a lot of memorization or mathematics to be effective. You still have some work to do if you want to make any $$$ using an unbalanced count, but not nearly as much as it takes to master one of the balanced counts. Naturally, you’re giving something up, but in a ‘typical’ 6-deck, the dealer hits soft 17, double after split allowed-type game, it’s not much. In return for just a bit less advantage, you can have the whole family counting! Think of it: grandma, the kids, the significant-other; all can become counters. But seriously, there’s really very little excuse for not at least giving one of these a try. You came to this site, I assume, to learn how to win at the casinos, so if you’re a Blackjack player who’s been losing for years, you can change that now.

The Primary Unbalanced Systems

There’s really just two of these and each compares favorably to the other as well as to other single-level systems (which is what these are), at least in multi-deck games. Good books are available on both of these systems and there’s a lot of additional information available besides that out on the ‘Net. Both of these counts have been analyzed to death, each has its loyal followers and each will get the $$$ if properly used, so I don’t really have a favorite. Your first decision is to stop losing at the casino and the next decision is to pick one of these systems; hell, even the cost of the book is about the same.

The Red 7 Count

Point Values 2-6 = +1; red 7s = +1, black 7s ,8,9 = 0; 10, A = -1

The “standard” comparisons of Betting, Playing and Insurance Efficiencies don’t really apply here because of how these work, but when used in simulations against the Hi/Lo and other single-level systems in 4+ deck games, the win rates are similar.

Most Effective: When used in 6-deck games where at least a 1-12 bet spread can be achieved.

Good Points: Easy to learn, yet can also be enhanced by an “advanced” version.

Bad Points: Not very effective in single- and double-deck games.

The Book to Buy: Blackbelt in Blackjack by Arnold Snyder

The K.O. Count

Point Values 2-7 = +1; 8,9 = 0; 10, A = -1

The “standard” comparisons of Betting, Playing and Insurance Efficiencies don’t really apply here because of how these work, but when used in simulations against the Hi/Lo and other single-level systems in 4+ deck games, the win rates are similar.

Most Effective: When used in 6-deck games where at least a 1-12 bet spread can be achieved.

Good Points: Easy to learn, yet can also be enhanced by an “advanced” version.

Bad Points: Not very effective in single- and double-deck games.

The Book to Buy: Knock-Out Blackjack by Vancura & Fuchs

Well, that about wraps this up. I really hope you find a counting system that suits you, because it feels great to walk into a casino knowing that you have a good chance to win and that feeling comes from knowing how to play the game properly. You can learn it all right on this site but don’t hesitate to contact me if you have any questions.

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