The system of counting tens, discussed in the chapter ” Blackjack . Deviations from the standard”, is rather narrowly targeted. It focuses primarily on insurance. Although, as we have seen, the abundance of tens in the game increases the player’s overall chances, and if so, the system allows us to catch situations that are beneficial to us.
Detecting such situations and raising rates in a timely manner is a problem of paramount importance, but the tens counting system does not deal with it effectively enough. The fact is that the most valuable card of a player is not a ten, but an ace , so completely ignoring the count of aces cannot lead to the desired results.
From the player’s point of view, each card that remains in the game is a certain indicator of usefulness or harmfulness. If we arrange the cards of different denominations in decreasing order of value, we get the following sequence:
T, 10, 9, 8, 7, 2, 3, 6, 4, 5.
In the basic strategy chapter, we noted that the ace is the dealer’s strongest card. And now we affirm that this is the most valuable card for the player. Yes, indeed, the ace benefits “ both yours and ours”, but it gives “ ours” much more. Even if you are in a casino where the dealer gets an ace, will not allow you to ” compensation”, the ace is still obviously the strongest deck of cards for us.
We’ll come back to the role that each card plays separately, but for now let’s move on to specific counting systems.
There are two important but, unfortunately, very contradictory requirements for a good counting system:
the system must be effective, it must catch as many moments as possible when it is reasonable to raise rates;
the system should be easy to use, because human abilities for oral counting are limited, and excessive overexertion affects other aspects of the game negatively and inevitably.
Consider a system – perhaps the most popular in the world – in which an attempt was made to combine what at first glance seems inconsistent. In any case, it fully meets the criterion of simplicity.
” PLUS-MINUS” SYSTEM
The system proposed in 1963 Harvey Dabner ( Harvey Dubner). As in the tens counting system, each card leaving the deck is assigned its own numerical value:
2, 3, 4, 5, 6 = +1
7, 8, 9 = 0
10, T = -1
It is easy to verify that the sum of the values in one 52-card deck is equal to zero. The same is the case with the ” big deck”. Systems with this property are sometimes called balanced . Such systems are in the majority, and in the subsequent part of the book it is precisely balanced systems that are considered.
As the cards leave the deck, we monitor the current score. Sevens, eights and nines are ignored, the release of high cards ( ten and aces) leads to a decrease in the score, low ones ( from two to six) – to an increase in the score. The system ” plus-minus”, as any balanced system, has a very simple feature: with a positive score increases the chances of the player, with a negative – are falling. The higher the score, the greater your expected winnings.
But the main question still remains open: to what extent do your odds change depending on the score? When do you start raising rates? It turns out that the current account is not an assistant here, it does not give an answer. To get an idea of your chances, you need to use the so-called real account ( sometimes called the true account).
The real score is obtained by dividing the current score by the number of decks remaining in the game. For example, one deck came out of the game, the current score is +12. We divide it by five (the number of remaining decks) and we get a real score equal to +2.4.
It can be difficult to calculate the number of decks we are interested in. Moreover, this number is generally fractional. As we have already said when analyzing the game with the joker ( chapter Deviation from the Standard), the simplest way to evaluate is to glance at the pile of played cards lying on the table to the right of the dealer. Having estimated the number of decks that have left the game, it is not at all difficult to calculate the number of decks remaining. And if you are sitting not far from the clog, from where the dealer draws the next cards, you can look directly into this box.
All of this, of course, requires serious diligent training. You need to learn to at least roughly estimate the number of decks contained in a pile of cards, you need to get used to the error-free keeping of the current score. Both must be tested at home. And do not regret it on this time: playing with the wrong account can lead to disastrous consequences. If you are not confident in yourself, it is much safer to completely forget about any calculations and always play “an even jackpot”, acting according to the usual basic strategy.
But suppose all difficulties are over – verbal counting has become habitual, you are comfortable with a pile of cards. Let’s go back to standard blackjack and see how your odds change depending on the real account.
-10 = -4.79% +10 = + 7.39%
-9 = -4.49% +9 = + 6.51%
-8 = -4.15% +8 = + 5.65%
—7 = —3.75% +7 = + 4.84%
-6 = -3.30% +6 = + 4.07%
—5 = —2.80% +5 = + 3.32%
—4 = —2.26% +4 = + 2.64%
—3 = —1.71% +3 = + 1.98%
—2 = —1.12% +2 = + 1.36%
—1 = —0.53% +1 = + 0.73%
0 + 0.09%
Obviously, if the score is negative ( -2 or lower), you need to reduce the rates or refrain from playing altogether. On the contrary, if the score is positive ( +2 or higher), it is time to increase the rates. However, it all depends on your temperament.
As we saw in the previous chapter, any deviation of the count from zero, the hypothesis of uniformity collapses, and this leads to the need to adjust the basic strategy. The higher the real score, the more carefully we collect additional cards, the more often we give “ compensation” and use new opportunities when doubling the bet or when splitting cards.
Does the system ” plus-minus” any disadvantages? Of course it does. None of the results obtained by us within the framework of this system claim to be highly reliable. We already know that from the player’s point of view, the ace is stronger than the ten, and the five is ” more harmful” than the two. However, we did not make any distinctions between these cards during the counting process. Meanwhile, the real positive score, obtained as a result of the exit from the game of fives, is much more valuable than the same score obtained as a result of the played twos. The same parallel can be drawn between tens and aces. The moments when the player’s chances really reach the maximum are not always caught. Conversely, it sometimes happens that the system sends false signals to the player.
Whatever the real account in the system of ” Plus-minus” we have to assume that the probability of occurrence of two – is the same as that of the five, and ten will come in four times more likely than an ace . As for the middle cards ( seven, eight, nine), we did not pay attention to them at all. Therefore, we have to proceed from the fact that regardless of the actual score, the probability of each such card appearing remains unchanged – 1/13. All of this echoes slightly with our original uniformity hypothesis.
Trying to neutralize all these shortcomings, the authors of the systems did not skimp on new inventions and constantly went further. The essence of the systems was still based on the real account and remained unchanged. But the cards coming out of the deck began to be assigned different, more ( or less!) Adequate numerical values. The efficiency of the developed systems sometimes increased, with simplicity the situation was much worse. As an example, look at a relatively simple system, which is close enough to the system of ” Plus-minus.”
SYSTEM ” halves”
This system is described in a remarkable book, Stanford Wong ( The Stanford Wong) « Professional Blackjack “. Here are the numerical values that are assigned to cards coming out of the deck:
2 = +0.5 7 = +0.5
3, 4 = +1 8 = 0
5 = + 1.5 9 = -0.5
6 = + 1 10, T = —1
If you don’t like halves, you can multiply all values by two and go to whole numbers. Although you will have to work with a doubled real account.
As in the system ” plus-minus”, the expected return depends on the player’s real account:
-10 = -4.63% +10 = + 7.24%
-9 = -4.33% +9 = + 6.39%
-8 = -4.01% +8 = + 5.56%
-7 = -3.64% +7 = + 4.78%
-6 = -3.20% +6 = + 4.01%
—5 = —2.73% +5 = + 3.28%
—4 = —2.20% +4 = + 2.61%
—3 = —1.67% +3 = + 1.96%
—2 = —1.10% +2 = + 1.34%
—1 = —0.52% +1 = + 0.72%
0 + 0.09%
This is practically the same as what we saw in the previous section. However, this is not the point.
The numerical values assigned to the cards are in this case more accurate, so the system becomes more efficient and, most importantly, more reliable. The signals that she sends to the player are, in the overwhelming majority of cases, correct, and they can be treated with a greater degree of trust. The percentages quoted are more reliable than before. And although deviations from these averaged indicators are found quite often, in comparison with the ” Plus-minus” system, they are small.
On the other hand, verbal counting with halves becomes noticeably more difficult, and mistakes are usually very costly. We do not recommend starting your career as a counter with this system.
Both systems – ” Plus-minus” and ” Halves” – are aimed at detecting situations where the player’s chances are especially high. You might want to combine all of this with a smart approach to insurance. In principle, you can double-count by keeping track of the real account using one of these systems and counting tens at the same time. But working with double counting is very, very difficult. Even if this succeeds, you will quickly get tired and, at best, leave the casino with a headache. And at worst, you will start making mistakes without noticing it yourself, and you will have to leave the casino because there will be nothing to play with. Only an experienced player, acting at the table at the professional level, can dare to double count.
Nevertheless, we will give one recommendation. Working with the system ” plus-minus” you can go to the insurance, if the actual expense exceeds 3.33. In the ” Halves” system , this threshold value is slightly higher – 3.67. Of course, in terms of their accuracy, these criteria are inferior to what we would have, counting only tens.
Back in 1962 an American professor Edward Thorp ( of Edward O. The Thorp) has published the exact numerical values that should be assigned to cards to conduct the most effective account. Subsequently, he proposed the Thorp Ultimate system, but it is hardly applicable in practice:
2 = +5 7 = +4
3 = +6 8 = 0
4 = +8 9 = —3
5 = +11 10 = —7
6 = +6 T = —9
Numerical values are too large, and you can work with them at the table only with a calculator in your head. However, they give a very good idea of what a particular card is worth.
We would venture to offer our own scoring system focused on standard blackjack and allowing you to judge the value of different cards with even greater accuracy:
2 = +8 7 = +5
3 = +9 8 = —1
4 = +12 9 = —5
5 = +15 10 = —10
6 = +9 T = —12
Both systems are of academic interest only. It is very difficult to recommend them for practical application.
In 1980, Lance Humble ( in Lance Humble) and Carl Cooper ( a Carl to Cooper Cooper) wrote a book with a funny name « of The World’s Greatest’s the Blackjack Book» – the greatest book in the world of blackjack. There was proposed a fundamentally new system called Hi-Opt I:
2 = 0
3, 4, 5, 6 = +1
7, 8, 9 = 0
10 = -1
T = 0
The Hi-Opt II system was recommended as a more accurate ( but more complex) system:
2, 3 = +1
4, 5 = +2
6, 7 = +1
8, 9 = 0
10 = —2
T = 0
What is fundamentally new here? As we know, the most valuable card for a player is an ace , but in these systems it is assigned a zero value. In other words, aces are ignored when keeping score. What’s the matter?
Each card that remains in the game has one or another value, which manifests itself in two aspects:
influence on the expected winnings and, as a result, on the increase or decrease in rates;
influence on the changes that need to be made to the baseline strategy.
Both of these influences coexist very closely. If the card is “ good” and helps to increase your chances, your strategy should become more restrained when drawing additional cards, but doubling and splitting should be done more freely. If the card is ” bad”, the strategy is directed in the opposite direction. But it turns out that all this is true for all cards, except for aces. From the point of view of changing the line of play, it is better to ignore the aces.
It is in this purely mathematical fact that the main essence of both Hi-Opt systems is expressed. They are focused not on detecting situations when it is profitable to raise rates, but on more flexible and productive changes in the basic strategy.
Let’s say you prefer to play with an “ even jackpot”, and if you raise your stakes, then insignificantly. In this case, Hi-Opt systems are your best assistant. But if you are inclined to play aggressiveness, these systems are not enough, you need some additional tool. And there is such a means – it is recommended to carry out a parallel calculation of the aces coming out of the deck. In theory, this really turns out efficiently, but in practice it is associated with the recently mentioned double counting. We have already spoken about the attendant difficulties. Until you become a professional, it is better to refuse double counting.
If you like to vary the rates in a wide range and are inclined to play offensively, systems where aces are assigned a more ” natural” number value are more suitable for you .
HOW TO DEAL WITH THE NUMBER 13
We can talk endlessly about how to play blackjack , but at the end of this chapter we will change the topic a little.
You may have seen tables with two small circles ( or squares) with the words ” over” and ” under” located next to the boxes . Here you can place side bets on ” over-under” before the start of each hand . By betting on over, you win if you receive two original cards with a total of more than 13. A bet on under wins if this amount is less than 13. Ace s are always valued at one point when calculating the amount. If the total is 13, any side bet loses.
If you win, the side bet is paid 1: 1, if you lose, of course, it is lost. As a rule, it cannot exceed the main bet you placed on blackjack.
This innovation appeared in the United States in 1988, and in recent years, the game for the amount of points has been found in Russia. Tables, suitable for betting on ” more-less “, you will find not all casinos, but they are in many establishments.
Let’s try to find a basic strategy based on the uniformity hypothesis. This hypothesis assumes playing on an infinite deck, and for such a deck the problem is solved literally on the fingers.
Let’s draw a 13 × 13 square plate:
T 2 3 four five 6 7 8 9 ten ten ten ten
T – – – – – – – – – – – – –
2 – – – – – – – – – – – – –
3 – – – – – – – – – = = = =
four – – – – – – – – = + + + +
five – – – – – – – = + + + + +
6 – – – – – – = + + + + + +
7 – – – – – = + + + + + + +
8 – – – – = + + + + + + + +
9 – – – = + + + + + + + + +
ten – – = + + + + + + + + + +
ten – – = + + + + + + + + + +
ten – – = + + + + + + + + + +
ten – – = + + + + + + + + + +
The rows correspond to the first original card, the columns to the second card ( ten are many and they are mentioned four times). The cells of the table correspond to all possible combinations of two cards. All these combinations are equally probable. In each of the 169 cells there is a ” +”, ” -” or ” =” icon , which characterizes the sum of points on two cards ( more than 13, less than 13, equal to 13). It is easy to calculate that there are 79 ” +” signs and 76 ” -” signs in the table . Therefore, an over bet will win 79 times out of 169, an under bet in 76 cases. Obviously, losses happen more often than wins.
The basic strategy consists of three words: side bets are not profitable .
What can you count on? The only hope remains – let’s try to keep track of the cards leaving the game.
When the next shuffle begins, side bets are categorically contraindicated. The player’s chances on a deck of 312 cards are even worse than on an infinite one. Our time has not come yet.
We must, obviously, wait for the right moment. A lot of low cards ( such as an ace or two) or, conversely, a lot of high cards ( ten, nines) should come out of the deck . The release of low cards will allow you to make a profitable bet on over, high cards – on under. It is these cards that you must first of all pay attention to when counting.
According to the already known samples, the cards that are important for us receive certain numerical values, after which it comes down to tracking these cards and finding a real account. One of the most effective systems was proposed by Stanford Wong in the already mentioned book ” Professional Blackjack “. The system is called Crush Count for a reason . Let’s take a look at the numerical values that are assigned to various cards:
T, 2 = +2
3 = +1
4, 5, 6, 7, 8 = 0
9, 10 = -1
We monitor the exit of the cards of interest to us and, as usual, calculate the real score. And patiently waiting in the wings. When the real score reaches +3 or higher, over bets become mathematically justified. The larger the score, the more attractive these rates. Profitable bets on under happen a little less often: the real account should fall to -5 or lower. That, in fact, is all science.
Over-and-under side bets are one of the greatest perks of blackjack . Situations in which the player has a mathematical advantage over the casino do not arise so rarely. If you use a crushing counting, the number 13 may well be lucky!
WHY DO WE STILL LOSE?
In terms of mathematics, blackjack is the most profitable game the casino has to offer. In fact, this is the only game where the casino has no mathematical edge, and strong players can gain an advantage by using card counts. The scientific theory of the game appeared in the United States in the early 1960s and has been constantly evolving since then, opening up new and new possibilities for players. American universities hold conferences on blackjack, periodicals are published, and numerous new books appear regularly, both for ordinary players and professionals. But, despite all this, gambling establishments have a constant and tangible profit on blackjack. And the majority of players, accordingly, suffer losses. This is the case both with us and in the West. Why is this happening?
As with all people, players have disadvantages. Each player has their own, but there are many in common.
There are players who literally can’t stand big wins. They start to scatter money shamelessly, and then leave the casino with empty pockets. Victory tastes bitter for them. Psychologists say that a feeling of pity, compassion for the enemy is triggered here – it’s somehow awkward to play around. Even if you beat the casino, where, it happens, almost the entire salary goes. And sometimes the gain disappears under the prosaic influence of alcohol, which, in joy, is consumed beyond measure.
Others just get tired after a long painstaking game and start throwing money towards the curtain – pan or miss. And if they win, they are surprised – they say, how simple everything is – and continue to play for high stakes, although they just promised themselves to make the last bet.
But more often than not, the player begins to collapse after a long series of failures. A major loss is a serious psychological blow, after which it is difficult even for a professional to resist. As a rule, there is a desire to turn fate and immediately recoup. More often than not, it ends badly: the gambler takes possession of the excitement, the rates go up sharply, and with them the loss increases. Few people manage to pull themselves together and complete a losing streak by simply stopping the game or at least lowering the stakes.
Inability to manage money, inability to manage ourselves, lack of self-discipline – all this incredibly hinders us, no matter what we play. But the most insidious game is by far blackjack . The authors have often heard from casino managers that among all games roulette brings the smallest profit for the casino. The same roulette in which the casino has a 2.7% advantage due to zero. But in ” equal” blackjack people lose more.
Many are still not familiar with the basic strategy , and if they know about it, then by hearsay. Oddly enough, there are many such players not only in our country, but also in the USA, where it costs nothing to find a good book on blackjack. Ignorance of the basic strategy is very expensive: it is better to give up splits, doubles and “ payoffs” altogether than to use them at random.
Remembering the basic strategy is easy. But the player who has undertaken this work rarely stops at what has been achieved and tries to go further. He introduces certain elements of the score into the game. And here new troubles begin.
According to Western experts, after the scoring systems gained popularity, the income of blackjack casinos increased. And they grew up a lot. This shows that systems do more harm than good to the average player. Systems are delicate and require very careful handling.
Firstly, most systems are quite unstable in relation to the errors that the player makes when calculating the real score. You go astray and, having waited for the moment that seems profitable to you, you sharply increase the rate. You lose, you notice that the score has practically not changed, and again you play for high stakes. You may be lucky, but most likely your mistake will lead to a crash.
Secondly, players tend to overestimate their own abilities. You believe that you have completely mastered the system, the counting is carried out without any effort, you have learned how to adjust the basic strategy. If you came to this conclusion a month after you got to know the system, you are wrong. See if you have lost a lot during this period.
And finally, most importantly, players place too high hopes on systems. Any counting systems are imperfect – we talked about this quite clearly. And besides, the systems only promise you average winnings. This does not mean at all that you will start winning often. Sometimes you will still have long streaks of failure. This is inevitable, the systems do not cure it.
It is known that it is the counters that react particularly painfully to large lesions. In their opinion, the loss is extremely unfair, because ” this is not according to science.” And if so, we must immediately rush into battle: ” We will recoup, the system is with us.” That’s how disasters happen.
If losses hit you, try to wait out the failures. When you’re unlucky, no system will help you. Try to be patient. Survive the blow of fate and do not turn the other cheek. We understand that this is not easy, but still – try it!