**More Cutting Edge Blackjack**

As I point out in Cutting Edge Blackjack, casinos actually do players a favor by requiring player cards to be placed facedown on the table when standing at single- and double-deck games—if you know how to interpret those cards. The facedown cards visually tip you off to what card mix is on the table that will make your card strategy decisions that much easier—again, if you know what you’re seeing. That’s where my methods come in. They took years to refine, but now they’re available to you.

To confound card counters, casinos changed the game of blackjack to require players to place their first two cards facedown on the table when standing at single- or double-deck game tables. With less information, players couldn’t make precise card moves. That was true for 40 years, from 1962 until 2002, when the first edition of Cutting Edge Blackjack was published, introducing my historic breakthroughs for identifying those cards.

Now, the serious player who wants to win to the max has no excuse not to know, with a great degree of accuracy, what those facedown cards are. However, since my discoveries take up two chapters and 57 pages, there’s no way to cover this in detail in a column. I can give you a few tips, though.

First, understand that I’ve identified a number of different categories of player facedown cards. Each has a different composition, based upon what players tend to stand on in every card situation. My research, in other words, began with a statistical analysis of all the player hands typically stood upon in each situation. Then I had to formulate methods to deal with each reality.

Fortunately, I was able to come up with an ingenious and rather easy system for advantage players that is also highly accurate. Furthermore, I was able to distill these methods in a chapter of general conclusions for all other players. Even if you start by learning a portion of what I have to offer, that will provide you with all the more profits at the end of the day.

Everyone should be able to easily understand the card example shown here. This is one of the more obvious situations you’ll encounter. The dealer has a high up card and the four players ahead of you have stood on their first two cards (I call these First Category facedown hands). You’ve got a horrible hand—the worst, a 16-pointer. If the casino allowed surrender, basic strategists would do so (folding their hand and keeping half their bet). However, that’s not smart here. Why? My studies show that absolutely none of these cards is a 2 through 6.

Why is that helpful? You need a 2 through 5 (or an ace)—most of those cards—to make your hand. (So they have not been over dealt; instead they are overdue.)

Plus, my research shows that 33 percent of First Category hands vs. a high dealer card are pairs of 10s. And more than 70 percent have two high cards (8s through 10s). So at least three of the four hands you see contain two high cards. (Cards that would bust you, cards you don’t want.) Therefore, you should hit your 16-point hand here. The table has a higher-than-normal proportion of high cards. Low cards—which are what you want—are statistically overdue.

Simple example, but my method covers all situations—simple through challenging. Players stand more frequently vs. the dealer’s low up cards, so that’s where it’s more challenging. However, here’s one specific Second Category facedown tip: players’ facedown cards are always two low cards when they’ve stood after taking one or more hit cards vs. low dealer up cards.

We’ve only scratched the surface, but as you can see, the more you know, the more you can win.

**Cutting Edge on Facedown Cards**

You cannot play a precise game, you cannot win to the max, without knowing what cards are on the table. Yet, today, in blackjack’s most winnable games—the single- and double-deck games—the cards are dealt face down, to thwart the advantage players have using cutting-edge methods. That change came in 1962. Before that, Blackjack was almost universally a single-deck game, dealt face up to the very last card. What a great game! Unfortunately, it no longer exists.

So how have today’s gambling writers responded to this very real setback? They simply ignore it.

That’s not acceptable. You cannot make informed card moves if you don’t know what’s on the table. You have to know what those facedown cards are. But how do you figure that out? One writer suggested an overly simplistic solution to this problem, which was so imprecise it’s not worth mentioning. Follow a simplistic solution and you’ll end up with heavy losses. My research shows the composition of facedown card types is too varied for that kind of simpleton’s approach—that is, if you want to win.

I spent 10 years coming up with a way to identify the facedown cards before introducing the world’s first highly accurate way to do so in Cutting Edge Blackjack. Las Vegas’s “librarian to gamblers,” Howard Schwartz, gave my book a rave review, saying it makes players all the more “optimistic” of winning. “It’s an important new tool,” he wrote, “giving players vitally important information necessary to making the best possible card moves.” My methods, which cover players of all levels, are described in two lengthy chapters. Unfortunately, this subject is not conducive to a short column. However, just pulling your coat on this issue is a wake up call from which you can profit. In other words, you now realize you have some work to do. Happy work that you can take to the bank.

In innovating methods to identify the facedown cards, I first did the world’s first (and probably only) thorough statistical analysis of the facedown cards in play versus each dealer up card. I wanted to know what percentage of the facedown pairs of cards were, for example, two high cards, a high card with an ace, a low card with an ace, two low cards, etc. I then categorized the various types of situations that would produce different compositions of each type of facedown card pair. (Howard Schwartz noted that I was the first to do this.)

It soon became apparent that a simplistic approach would not work without a high degree of inaccuracy. In other words, if you have a certain type of facedown hand that’s on the table in the 33–45 percent range in a certain situation, you cannot just ignore it. If you ignore it, you’ll make mistakes in the 33–45 percent range, which makes this type of exercise useless. That was my biggest challenge: I had to create a novel type of blackjack method that covered the percentages really well.

So, for advantage players, I came up with a rotating estimate method to identify what cards are on the table, facedown—and not difficult to pull off, either. That was just one innovation, which computer tests proved highly accurate. For entry-level players, however, I provided a separate chapter full of empowering guidance culled from my research that will prove most profitable.

The point is, you need to learn how to identify the facedown cards. Otherwise you cannot win to the max versus the single- and double-deck games—the most beatable blackjack games you’ll ever play.

More details in my next column.

**Strong Indicators for Blackjack Success**

One of the things I’m most proud about having achieved in my many years of blackjack, card behavior, and shuffling research was my discovery of the “indicators” with which I could gain a far greater edge on the game than basic strategy or card counting had allowed.

By indicators, I mean scientific or mathematical measures that portend what the future would likely be. Since I had been university-trained in scientific research methods and theoretical math, all these skills came in handy as I did my research.

First, though, came the grueling three-year collection of real casino-style card data, with real dealers dealing, collecting, and shuffling the cards in the exacting handling methods used at the nation’s casinos. No computer simulations would do—I didn’t want pretend blackjack in doing my research; I wanted the real thing.

Next came the analysis phase, in which I charted the progress of each player or betting spot. To do this, I intuitively realized that one measure would be to use a unit based upon the betting spot’s wins minus its losses, on a round-by-round basis.

I would later name this unit the Win/Loss Margin Unit, or WLM unit for short. I was pleased to learn that this proved to be an indicator that reveals much.

Here’s how it works:

If the player won the first round, the WLM unit would be +1. With a win, that number would go up one unit. With a push (tie), the number would stay the same. With a loss, the number would go down one unit. Zero would indicate a neutral situation—wins equaling losses. Negative numbers would identify a losing cycle.

Charting the progress of each betting spot resulted in a Wall Street kind of chart, one of which I've shown you, in part, here.

In doing this, I clearly proved that winning and losing cycles are real phenomena. The Old School writers pooh-pooh this idea, but that’s because they did their research the wrong way, using a computer’s random number generator to produce data (which, by definition, produces random results). Real cards, though, do not play out randomly, as these charts and other studies of mine proved.

This led to my analyzing the winning and losing cycles clearly identified in my charts. (Talk about a grueling process!)

In so doing, I discovered something even more earthshaking: the fact that there were repeating patterns, repeating phenomena as I named them, as a result of the standardized shuffling most casinos did.

In other words, many of the same cards were being dealt to the same players from shuffle to shuffle!

Needless to say, all of this produced profitable strategies that I’ve put to good use—and many of which I’ve revealed in my books.

**Blackjack Visual Help: Ink or White? **

When I was a newcomer to blackjack in the mid 1980s, the only way to play seemed to be a one-size-fits-all, inflexible, almost dictatorial strategy called “basic strategy.” I tested this basic strategy with a computer program of my making and found it was a losing strategy. Then I re-read the books available at the time and found even their *authors* begrudgingly admitted it was a losing strategy.

So, if that’s not the way to play, what’s the game all about?

First, many assume that 21 points is a *goal* to shoot for. They don’t understand that sometimes—when the dealer is likely to bust—your best bet is to just *stand pat*. But the faulty Old School recommendation to stand pat on most hands of 12 to 16 points with dealer up cards of 2 to 6 can also cause confusion. They’ll say, “let the dealer bust,” yet this strategy leads to an unacceptably high losing rate. Even with the *most* bust-able up cards (4s through 6s) the dealer scores well roughly 60 percent of the time.

Plus, the dealer’s up card does not give us enough info to make an accurate card move.

My research has shown the dealer’s up cards’ busting rates *vary greatly,* depending on the balance of cards that have been dealt. So you have to learn to be *observant* and *in the moment*.

Solution? Become a good card analyst.

Whether most of the cards have been “low” (which I define as 2s through 7s, plus the aces) or “high” (all other cards) is one thing you should try to determine (not scientifically, but with a good degree of accuracy). This is not terribly difficult to do.

My methods for beginners, for example, include the recognition of this factor by sight: A preponderance of low cards looks like a mass of *white* on the table; high cards—which I call “ink”—create a dark impression.

I also talk about “outs.” This refers to what cards your hand might need to achieve a great score. Beginners should concentrate on cards that would provide a score of 20 or 21 points. If these cards have been *dealt* in greater proportion than other cards, the odds of improving your hand by taking another card are now *low.* So “hitting” your hand (taking another card) might no longer be wise.

Another factor: *How well is the dealer likely to do?*

This is not terribly hard to estimate. Beginners, for example, should find it easy to spot a table full of “ink” (high cards) when the dealer’s up card is low. This is often when you should *not* stand on stiffs (unless most prior rounds featured mostly high cards).

And yet another factor: *odds*. Your odds are *approximations* of your likely success by making any move. It is the *un-dealt* cards that determine your odds of success (and the dealer’s). Their bias affects your likelihood of winning or losing, and the wisdom of making any optional move.

Hint: The un-dealt mix is the *opposite* of what you’ve seen dealt, per each card and category of card. If you’ve seen a lot of low cards, the un-dealt mix is rich in high cards. If a lot of 5s and 6s have been dealt, for example, then the un-dealt mix is *poor* in these cards. Your odds of doing well by “hitting” your 15-point hand are now low. Powerful info.

Your understanding of all of this not only makes the game more fascinating and rewarding but also more *predictable* and *winnable*.

**The Predictability Factor**

One of my readers recently asked if I have developed a system to beat the continuous shuffle machines. My first inclination was to respond asking why they would even want to play these games. But then I realized: Hey, to each their own. We all have our preferences.

Me? I know that in order to increase my chances to win big, I need to play games with a maximum predictability factor. Which is why blackjack is my game—it’s one of the most predictable, and therefore winnable, games in the house. No wonder, then, that some casinos have introduced continuous shuffle machines—they destroy much of the game’s predictability.

Sure, there is still a certain amount of intra-round predictability. For example, in a six-deck game there could never be more than 24 aces dealt per round, and those aces should be fairly well spread out among the decks.

Not so with continuous shuffle games. The nature of the constant shuffling can rearrange things so that strange clumps of cards not often found in hand-shuffled games start to appear. That makes for greater swings of imbalances, which in turn transform blackjack from a game of skill into a game of chance.

I don’t even like the normal shuffle machine tables because I lose the advantage of following the cards through a shuffle, which is so easy to do with the methods I created for dealer-shuffled games. Why would I sacrifice an edge to the house? But continuous shuffle machine tables are even worse because you lose the round-to-round (inter-round) predictability.

If you play without caring whether you win or lose, then fine. But if you’re like me, looking to make some money, and the more the better, then you become more discriminating about the games you play.

While we’re on the subject of player disadvantage, let me mention that I don’t even like playing the multi-deck games anymore because they, too, are far less predictable than the single- and double-pitch games. It’s easy to forget that blackjack was invented centuries ago as a single deck game. And it remained a single-deck game until the 1960s, when casinos began to realize they could limit player gains by adding more decks.

And remember when digital blackjack games were introduced in the late 1990s? They were like video games: you sat down at the table and every player had a screen where a virtual dealer “dealt” them the cards.

Only problem was, players quickly surmised that these were no better than slot machines. Serious blackjack players stayed away in droves. Few sat down at the digital tables and even fewer came back to play them again. It was pretty clear there was no predictability to the games—they were simulated by a computer’s random number generator—and they were programmed to beat the players in the long run.

Of course, the casinos can offer what they want—it’s their prerogative. I have my prerogative, too—I can be choosy about the games I play. And my years of experience tell me that continuous shuffle machines, multiple-deck games, and digital blackjack all put players at a great disadvantage. Hopefully those games will go the way of Digital 21. You won’t find me at those tables. But, hey, to each their own.

**Say No To Solo Blackjack**

There are many reasons why it isn’t smart to play solo against the dealer in blackjack. Let’s examine just one.

Look at the solo and seven-player situations here (graphics 1 and 2). In the solo situation, the card analyst gets just three cards to analyze at first. Not enough information to make an intelligent choice. Plus, graphic 3 (a portion of my Probabilities and Imbalances Calculator analysis), shows that the composition of the un-dealt mix doesn’t change much per round playing solo (the norm for non-10s is 7.69 percent and for 10s, 30.769 percent). You lose a lot in predictability. (By the way, using the most popular card counting system, the Hi-Lo, you get a count of zero. That’s supposed to mean the cards are balanced. Are they? No way!)

Also interesting: Aces are supposed to be good for players according to the Old

School writers. Really? The same cards were dealt to the solo player and the seven players and the solo player got an ace next. Helpful? No. It led to a 13-point hand, a total more likely to bust. Sure enough, the next card, a 9, busted the hand.

The seven-player situation, though, shows you many more cards before your move, so your card analysis can be much more precise. Graphics 4 and 5 from my Calculator show you 54 percent of the un-dealt cards are low cards (which I define as 2s through 7s) and 38 percent are high cards (8s through 10s). (We count the aces separately, yet they act most like low cards because an Ace will never bust the dealer.) So you can see that a seven-player situation gives you much more info, which makes your game choices more accurate.

In the seven-player situation, both players with moves to make know it’s smartest to hit their 15-point hands (as opposed to surrender, an option, if available, the Old Schoolers would recommend) because the imbalance in the un-dealt mix is so rich in low cards and not likely to bust these hands.

This greater predictability means you will win more in multiplayer situations.

**Don’t Buy In to Basic Strategy**

Players in the 1960s were sold a bill of goods. They were convinced that the newly-popularized “basic strategy” method was a winning strategy, and that any other method of play was foolish.

Basic strategy was sold with overblown positive claims. The book that popularized it, Beat the Dealer by Edward Thorp, claimed on its back cover that Thorp had experienced “stunning success” using basic strategy. If you read the book carefully, however, you will discover that this claim is untrue. In fact, the author admitted to sharp declines in fortune on numerous occasions, even with his “Tens System,” which he said was better than basic strategy. Note as well that he attributed any wins to “lucky” streaks, not wisdom. In other words, he was simply dealt good cards.

More important was Thorp’s confession on page 31 of my old copy of that book:

Yet even that cautionary note—that basic strategy was roughly a break-even system at best—was not quite right. He contradicted it with a much less positive prediction on page 18. Here, he admitted basic strategy would lead to likely losses:

Please note that even his rosiest estimation—a negligible .12 percent at best—is not applicable to today’s player. You won’t ever achieve that result because Thorpe was writing about a game that *no longer exists*, one in which one deck was used and it was dealt to the very last card.

His prediction of worse results with “unfavorable” rules is more correct—but even that was based on the single-deck game. He did not make a prediction for players who play against more than one deck (as most of us do today). Yet any honest mathematician will admit that your odds of winning goes down with each deck added to the game (for a variety of reasons). In an online article titled “The Legacy of Beat the Dealer,” Thorp wrote: “. . . as for me, Beat the Dealer has led to a lifetime of wonderful friends, unique adventures, and wealth beyond my expectations.”

I believe this is a bit disingenuous. In truth, Thorpe played a limited amount of blackjack and did not make much at it at all. He certainly did not achieve wealth.

He also depended on OPM—other people’s money, specifically, shady millionaire Manny Kimmel’s stash—to play the game. This was partly to survive the sharp downswings in fortune he admitted his method was prone to. Either he didn’t trust his own system enough to use his own money, or he couldn’t afford the downswings. Either way, his money wasn’t on the line. And that should tell you something.

He quickly gave up his own system, too, the one he’d touted for years, claiming he was more interested in Wall Street.

The truth is, his system was scary and was not what it was promoted to be. You cannot make a good living, much less win consistently, using it. Especially with the games we face today.

The trouble is, since basic strategy players win approximately half of the time, they delude themselves that they actually know how to beat the game. If they kept track of their ups and downs, however, they’d see that this was far from the truth.

**Play Attention to all the Hands on the Table**

A common mistake among blackjack players is that they rarely, if ever, take into account the cards received by the other players on the table, focusing instead only on their own hand and on the dealer’s. That’s because most players grew up with a one-size-fits-all “basic strategy” plan that is blind to what goes on during a round and doesn’t adjust to the realities at hand.

For example, take the player in third base in this single-deck card example. With a 15-point hand versus the dealer’s 7, basic strategy teaches players to hit (take a card), no matter what’s on the table. They’ll often say, “Oh, you took my cards. Oh well.” And then they hit their hand, even though it’s become a ridiculous move.

That would be the worst thing to do in this situation—for a number of reasons. Ask yourself: What are your “outs,” the cards that would give you a decent score if you hit your 15?

Preferably you’d want a 5 or 6, to give you a good chance of winning. But even before the other players at the table make their moves, you observe that one 5 and two 6s were dealt, meaning you have a less-than-normal chance of getting these most-desired cards, or “outs.”

Then four low cards in a row are dealt to the players before you. This is highly unusual in a single-deck game, and should be a warning to you. You now have a higher-than-normal likelihood of getting one of the high cards that will bust you (make you go over 21 and lose).

In addition, look at the second graphic. It shows the remaining high-versus-low cards in the un-dealt mix, where I’ve put the 7s in with the high because they’d bust you, and the aces in with the low because they would not. Even without the warning signals I mentioned above, you have—just on the un-dealt card mix alone—a 3-to-2 likelihood of busting.

Now take a look at the third graphic, showing the “stiff makers,” the cards that would give the dealer a two-card point total most likely to bust with a third card if in the hole. That reveals that the dealer’s likely busting rate is nearly 40 percent—in the range of a dealer’s 4, 5, and 6 under normal conditions. Get it? Good.

So, what should you do?

Everything is telling you to stand here: card flow evidence (the four-card streak of low cards before your turn), the un-dealt mix odds (based upon the cards that would help versus bust you) and the odds of the dealer getting a “stiff maker” leading to a likely busted hand.

This example, by the way, demonstrates how many considerations inform your move from a mathematical and scientific basis. I spent many years studying the little-known card flow and card behavior sciences. These sometimes reveal more telling information than simple percentages can.

**Card Streaks and Peaks**

There are four players at this table. You are the player sitting next to a king-7 in third base. You hit your hand of eight points three times, yet still have an unappealing 14 points—not enough to win unless the dealer busted.

You don’t need to be an expert to know what to do here. Visually, some things should stand out immediately. While you don’t know what the first baseman’s cards are, you do know that those cards are most likely two high cards (which I define as 8s through 10s), although they have a minority likelihood of being instead an ace and a 7, for instance. Since you’ve not yet learned my method for identifying facedown cards (introduced in Cutting Edge Blackjack), we’ll just assume they’re two high cards.

The player to your right most likely has two low cards under his chips (he stood after getting 10 points in hit cards), although he could have a high and low card, as in an 8 and a 2, in a minority situation. But it doesn’t change this picture.

First, notice that there has been a long string of low cards coming into and during your turn. The 4 and 6 the player took before you came right before your hit cards. This sounds obvious, but all too many players don’t notice this kind of thing.

So what does that mean?

Low card streaks—or streaks of either type card—don’t last forever. Far from it. In other words, there is a high likelihood now of an opposite type card being dealt.

Seven-card hands in single-deck blackjack are almost impossible to get. So, you now hold five cards and are up against your limit: take one more, that’s it. If you don’t get what you want with the sixth card, you’re almost certain to bust.

But what are your “outs” here? What card do you need, and will you get it? With a 14, you wouldn’t bust with an ace, 2, 3, 4, 5, 6 or 7 but only a 5 through 7 would give you any hope of beating the dealer who, in this case (due to the preponderance of low cards) likely has a high card in the hole (hence, by the way, the third basemen, with the 17, is a likely loser).

Because of the huge imbalance of low cards on the table, you’re most likely to get a bust card. Even under the best of situations (not the one here) my research shows you have a 79 percent probability of busting when hitting a five-card hand. Disastrous! With the imbalance represented here, that likelihood is far higher.

You’re in a no-win, rock vs. hard place situation here. I would consider standing here, since busting and losing by taking another card is all but a certainty—given the reality that low card streaks don’t last forever.

**One-Size-Fits-All Card Strategies**

One-size-fits-all card strategies such as basic strategy don’t work because everything changes from round to round. Basic strategy only works if the cards are balanced, which is, essentially, never.

You’ll see this graphically demonstrated if you use my Probability & Imbalances Calculator religiously and play out many thousands of blackjack rounds. You’ll hardly, if ever, see the cards on the table or in the un-dealt mix during the course of play represented in the same proportions as they were in a complete 52-card deck, representing a “balanced” situation.

For instance, look at this real-world first-round card example. The Old Schoolers would celebrate this situation as a likely winning scenario. “Let the dealer bust!” they’d shout with glee.

Yet is this really a great situation for the players without the 20-point hands? Should the players with the 8s and aces split in this situation, as the Old Schoolers always advise? What’s the reality?

I’ve provided you a small portion of the analysis of this situation from my Probability & Imbalances Calculator (available exclusively on www.blackjacktoday.com). There’s no debating what I’m about to tell you: neither the player with the 8s or the aces should split in this situation.

Here’s why: With such a preponderance of high cards on the table, what are the odds that the dealer has a low card or ace in the hole? What are the odds the dealer will get another favorable low card or ace to avoid busting when taking any hit cards needed? What are the odds the players with the 8s and aces will get the cards they need to win?

The answers to all the questions above are to be seen in the Calculator graphic. The players and dealer—not taking into consideration any cards the players might take—have nearly 3-to-2 odds of getting a low card or ace. So no matter how you cut it, the players will likely get unhelpful cards and the dealer will have a less-than-normal likelihood of busting (normal for the dealer 4 being 43 percent).

When the dealer’s 4 achieves a score, it on average reaches 19.01 points, which is high for any up card. Here, the likely score will be higher. The players with the 8s and aces will likely wind up with subpar scores and lose both hands to the dealer—hence the wisdom of not splitting those hands here. The 8s are likely losers, split or not, and I’d surrender them if I could. The player with the aces should keep that pair together and hit until a nice high soft total is reached.

You can’t bring my Calculator with you to the table but it makes a great practice tool. And this situation, with so many high cards, doesn’t need a genius to figure out. You don’t need exact numbers to see this at the table and know immediately what to do—and what not to do.

**Here’s a Blackjack Situation for You to Solve ****- PART 2**

Given this first round card situation, I asked you in my last column: 1. how would you bet going into the next round?; and 2. does anything alarm you? I also pointed out that Hi-Lo card counters (like the MIT teams of old) would come up with a zero count here, which is highly inaccurate. The cards are not balanced, as I pointed out. For one thing, there are no aces. And all four 7s were dealt, etc.

Look at graphic #2, which is a small portion of the information provided by my Probability & Imbalances Calculator (available exclusively on www.blackjacktoday.com). There you see that aces now account for more than 11 percent of the deck (the norm is 7.69 percent). By the way, notice that even in this extreme situation, your likelihood of getting an ace is far less than 100 percent, so any system that claims 100 percent accuracy or even close to it in predicting when you might get an ace lies. (Thorp’s Beat The Dealer talked about precision, but his book was written when the game was one deck, dealt to the very bottom—the good old days long gone!)

Hi-Lo players wrongly believe aces overdue situations call for a bet increase (but their counting system wouldn’t tell them that was the case here). Yet my research has proven conclusively that aces overdue situations lower your likelihood of winning and benefit the dealer. For one thing, when the dealer gets an ace—which the old school researchers didn’t take into account—they not only trump most everyone sometimes with a blackjack, but their overall busting rate goes down to a puny 8 percent, taking into account all situations where the dealer gets an ace.

My Precision Betting System (introduced in the Third Edition of Cutting Edge Blackjack) also proved that decks low in 7s, 8s and 9s are bad for the player. When no surrender is allowed, the PI, or Probability Index, is minus-two here, going into the next round. Therefore, taking both of these situations into account, you should lower your bet to the table minimum.

Also cause for alarm? All of the spades have been dealt. This is a symptom of poor shuffling, which almost always spells trouble for most if not all the players at the table. That is, you’re most likely to lose in the long term with this mix of cards.

Also look at graphic #3, another small portion of my Calculator’s number crunching sections, where it shows that low cards (which I define as 2s through 7s) and aces account for 54 percent of the un-dealt mix.

These are the cards that help the dealer avoid busting. Another reason to lower your bet to the minimum allowed. Most players will lose in the next round.

And you can take that to the bank.

**Here’s a Blackjack Situation for You to Solve **

I’ll let you think about it, and I’ll give you the answer, with profitable information you can use, in the next issue of Casino Entertainer.

Take a look at the situation here. Obviously, this round is over. However, smart players make cutting edge betting decisions from the correct analysis of the cards that have been dealt since the last shuffle.

In fact, using my revolutionary Precision Betting Method (introduced in the Third Edition of Cutting Edge Blackjack), you can make a highly accurate assessment of your odds of winning in the next round by analyzing these cards, and, with that information, then make highly precise bets. (Ideally, your bet should accurately reflect your odds of winning in the next round—but the Old School blackjack methods of basic strategy and card counting cannot give you that crucial information.)

So here is what I’d like you to do: look at this mix of cards carefully and decide how you will bet going into the next round. Does anything about the mix alarm you? I especially want the Hi-Lo card counters to think long and hard about this one. For the Hi-Lo count here is zero. (Hi-Lo counters count 2s through 6s as plus-one as they are dealt, and 10s and aces as minus-one as they are dealt.)

A count of zero, to a Hi-Lo counter, is supposed to mean the cards are balanced and therefore the bet should not be raised beyond the lowest level—the lowest bet you’re making. But aces are overdue, are they not? Don’t the Old Schoolers tell you to raise your bet when aces are due?

Aha! There’s a conflict here, for Hi-Lo players. Obviously, that system is not giving you precise information—and it’s giving you conflicting information. For a zero count tells you the cards are balanced. But they’re not, are they? And the fact that no aces were dealt was not revealed by the Hi-Lo system, was it?

Again I ask: How should you bet going into the next round? I’ll reveal the startling answer in the July issue of Casino Entertainer.

**What Do Stones have to do with Blackjack? - May 2014**

To paraphrase John Denver—and with apologies for appropriation—some cards are *diamonds* and some cards are *stones*.

That’s for starters (although we’re not going to get into that in this column), but it is worth mentioning. Because smart players learn what the relative value each of the 10 different cards has to them (in blackjack we just have the ace, 2, 3, 4, 5, 6, 7, 8, 9 and 10s, and the face cards are lumped together as “10s”), especially from the standpoint of *what the availability of each in the un-dealt mix says about their likelihood of winning in the next round*.

I discovered the correct precise value of each of the cards—for the first time in blackjack history—in my 10-plus years of blackjack research, and I revealed the results in *Cutting Edge Blackjack* (as well as my resulting* Precision Betting Method* that came out of it, which is the most precise betting method on the planet).

But today we’re going to look at these stones as a *probability *lesson. This is another important aspect of blackjack—getting into the “odds”—that a serious blackjack player, one that wants to make money that is, needs to understand.

For now, let’s pretend that instead of cards, the game we’re playing features stones. The values we won’t consider for today’s column, just the two basic colors: white (or clear, as in a diamond) and colored.

How does this relate to blackjack? One thing smart players do is analyze the relative proportion of low to high cards—not as old-fashioned card counters did, but from the standpoint of card strategy and the cutting edge tools I’ve invented to predict the likely outcome of events during any given round.

Okay, so let’s say there were just 10 white/clear stones and 10 stones of various dark colors. Your job right now, before you read any further, is to determine:

- How many stones of each group have been “dealt” on the table?
- How many stones each group, therefore, remain in the “un-dealt” mix?

I used stones of two different color groups in this example because it should be obvious to you that you can visually come to a quick answer as to what the general reality is here, that is, dark stones of color vastly outnumber those in the white/clear group. Is that not quickly visually clear? *(Aha!* *But that’s true, too, of the low cards and high cards in blackjack. The high cards are dark, the low, whitish. A quick visual analysis reveals the general proportions.)*

Now you can tell me what the probability—the exact likelihood, the exact odds—of a colored stone being dealt next.

The answer to question #1 was: two white/clear and six colored.

The answer to question #2 therefore was: eight white/clear and four colored.

So the answer to my final question above is: the odds are 2-to-1 the next stone “dealt” will be white. Or, seen in another way, there’s a 66 percent probability or likelihood (8 ÷ 12 = 66 percent). That’s one side of what probability is all about, when it comes to modern blackjack strategies. The more you can predict, the more hands you will win and the more money you will make, because we play according to the odds—we act according to what the *majority* likelihood is. Which of course is rarely close to 100 percent; we’re not talking about *certainty*. That doesn’t exist in blackjack.

More to the point...if you do not want a white stone right now, this is not a great situation for you, is it? See how this pertains to good blackjack?

**Answers to Circle of 13 - April 2014**

In March, I had you play a version of Circle of 13 (see below). The card situation shown here that is based on a game of my invention that I introduce and explain in Cutting Edge Blackjack. The game is played with a suit of cards and is a learning tool to help you understand the concept of probability. I posed a series of questions for you to think about, and, as promised, here are the answers.

Examining what we see here, Old Schoolers would likely tell you the dealer’s 6 is weak and you should expect it to bust. But is that true? I say no, because:

1)Given your answer to question No. 1, what is the exact likelihood the dealer’s hole card is a 10? Zero. All the 10s were dealt already. There are none left. (While I realize this would never occur in a real game, there are dramatic swings in card balances in which equivalent situations occur—where so many 10s were dealt, they’re much less likely to appear.)

2)Is the dealer strong or weak? The dealer is very strong here. The cards that combine singly with the 6 to produce the most bustable totals have been dealt (the 8, 9, and 10s, which would have given the dealer bustable totals of 14, 15, and 16; these cards are also the ones we’d like to be rich in the un-dealt mix, to then bust the dealer). Therefore, the dealer is highly unlikely to bust. (Hint: You could not stand on a 12- through 16-point hand if you had one here.) My research has revealed that all dealer up cards have strong and weak phases, based on the specific mix of un-dealt cards throughout a round. Here, this concept is demonstrated dramatically.

3)What is the relative likelihood the dealer will bust? Very few card combinations would now bust the dealer, so the likelihood is very low. (See the four permutations that would do so—less likely five- and six-card strings, dependent on the 7 coming last, to bust the dealer.)

4)What’s the relative likelihood the player with the 8 and 9, a 17-point hand, will win? Very low. The dealer will tend to draw to at least 17 if not better. When low cards are due, the dealer 6 scores high.

One of the lessons here: You must learn to analyze the cards to determine whether the dealer is strong or weak—no matter what the up card is—so you know how to play your cards.

**The Circle of 13 - March 2014**

I’m not the first researcher and mathematician to announce that blackjack is beatable primarily because it’s predictable. But I have made discoveries and created methods that make the game not only more predictable but also more winnable.

Doing seminars nationwide when time permits, I came up with a beginner’s learning tool that I’ve found beautifully introduces newcomers to cutting-edge blackjack methods and the concept of predictability (at least one aspect of it) and probability (which some people think of as “playing the odds,” although it’s more than that). I call this tool The Circle of 13 and the exercises that arise from it, Circle of 13 Games.

When a mathematician looks to simplify a problem, he looks for the lowest common denominator, that is, the simplest representation that, in a nutshell, explains the greater whole. In blackjack, our lowest common denominator is a suit of cards, which total 13 in all. No matter how many decks are in play, suits are the building blocks that set all the blackjack math in motion, so if you understand what’s going on in a suit of cards and can play a Circle of 13 Game, you are en route to playing a more precise, better game. In every suit there are four 10-point cards: the actual 10s and the three face cards. This proportion—4 out of 13—is the same for every game, whether single or multiple deck. The 10s, therefore, account for a little less than 31 percent of the cards, while the rest count for a little less than 8 percent each. Right away you should understand why the Old School method of “always assume the hole card [the dealer’s hidden card] is a 10” is so ridiculous. On average, that likelihood is just 31 percent, which means playing the Old School way will have you making a mistake 69 percent of the time!

Now, a Circle of 13 Game is where you play with just one suit of cards, dealt to just three players. Deal as they would in a casino, one card to each player (starting with the “first baseman,” the player next to the dealer’s left arm) with the second card to the dealer being the hole card.

The great thing about this is that you can predict events with an exactitude you cannot bring to the real game, and it gets your brain working. It teaches you the concept of probability. This is akin to a beginning pianist starting with scales instead of Beethoven’s Fifth Piano Concerto.

Let’s recreate the example shown here with a suit of cards.

Old Schoolers will tell you the dealer’s 6 is weak and you should expect it to bust. But is that really true? Look at the cards and answer the following questions:

1)What cards remain un-dealt?

2)Based upon your answer to question No. 1, what’s the exact likelihood the dealer’s hole card is a 10?

3)Based upon your answer to question No. 2, is the dealer strong or weak?

4)What is the relative (not exact) likelihood the dealer will bust? (Take the un-dealt cards and pair them with the dealer’s 6 and see how many combinations would bust the dealer.)

5)What’s the relative (not exact) likelihood the player with the 8 and 9, a 17-point hand, will win?

One thing this will teach you is the need to analyze the cards before assuming anything.

Work on this and I’ll give you the full explanation, with all the answers, next month!