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The Basics Of Card Counting

Perhaps, many gamblers know that a knowledgeable gambler can beat the casino. In such stories the game blackjack and the notion “card counting” were most often mentioned. Possibility of use of card accounts in an online casino has its limit, as the Internet-casinos usually mix the card batch after each deal, however, there are some online casinos, which offer to play up to one-third of the batch (or rather, not one of the batch, but a pack of 6 or 8 batches), and also there is a video of the casino hall, where blackjack is played just like in real casinos, so there is quite possible to try to use some system of accounts (although in online casinos you needn’t count yourself, you can entrust it to your computer).

Film lovers, probably, remember the scene from the “Man of the rain”, where the hero Hoffman after a short training masterfully counted the cards, thanks to which the brothers won a considerable amount of money. Hero Cruz advised him to remember the outcome of small and big cards and show by his bets rates show which cards were more. Why was all this done? How can it increase our chances to win? Quite simply – the release of part of the cards changes the probability of appearing of various cards in future handouts. If at the start of the game the probability of the arrival of any card (excluding suit) is 1/13, then during the game with an uneven output of various cards this probability can increase or decrease. So, the gambler can play the part of the batch, where there is the big amount of small cards and aces, but a few tens or vice versa. The basic strategy and the advantage of the casino is calculated when the probability of falling out of cards is the same, together with the changes in the probability of the arrival of various cards both optimal strategy and mathematic expectation are changed. What position of batch is more advantageous for the gambler? That is the one where are more aces and tens. The logic here consists in this – first of all, the gambler gains an advantage due to increased payments for blackjack. That is, the more there are blackjacks, the more advantage there is for the gambler, because in case of a blackjack for the dealer he loses 1 bet, and with his own blackjack he wins 1,5. Secondly, the dealer need to take at least 17 if there are many tens in the batch, the probability that the dealer will burn, getting more cards, while the gambler can change the strategy and not take with 12-16 scores, is higher. Thirdly, in case of doubling the possibility that the gambler will get 19-21, winning the double bet, is higher.

So, we have disclosed what is beneficial for the gambler and when he gains an advantage. We shall try to understand, in what way it works in practice. But in practice several systems of the account (more detailed next time) were developed, but the principle of the work in them is the same. Card counting was actually “opened” by Edward Thorpe, who already in 1962 determined the optimal values, which cards should have. Each card has its value which differs from -9 to +11 and only a man-calculator can count using this this system. However take a look at Thorpe’s surveys to understand what cards in the batch are the most useful and what are harmful and what are neutral: 2 is estimated as +5, 3 +6, 4 +8, 5 +11, 6 +6, 7 +4, 8 0, 9 -3, 10 (to the tens refer all ten-pip cards from 10 to a king) -7, an ace, a -9.

In the next 1963 year a new system of “Plus-minus”, which was more convenient for use and became the basis for subsequent development, appeared. In this system, each card is assigned numeric values, but there are only three of them: +1 (for cards from 2 to 6), 0 (for 7-9) and +1 (for tens and aces). It is not difficult to guess that the sum of values in a single 52-card batch is equal to zero. So it is with the “big batch”. Systems with such a peculiarity are named balanced.

As the cards are released from the batch we are watching the current account. Sevens, eights and nines are ignored, and the output of the elder cards (tens and aces) leads to a decrease in accounts, Junior (from two to six) – to an increase in accounts. The system “Plus-minus”, as well as any balanced system, has a very simple peculiarity: in case of a positive account the chances of the gambler increase, in case of a negative – fall. The more the account is, the more your expected winnings are.

But the main question remains open: the extent to which your chances change depending on the account? At what point of time should the gambler begin to raise interest rates? The current account here does not help and gives no answer. To estimate our chances, we should use the so-called real account (it is called the true account). The real account is obtained when we divide the current account into the number of the batches remaining in the game. So, after one batch has gone out of the game, the current account is estimated as +12. Divide it by five (the remaining number of decks) and obtain a true account, equal to +2,4.

Counting the number of batches of cards can be difficult taking into consideration that this number is generally fractional. The simplest estimation method is to look at the stack of the played cards that are lying on the table to the right of the dealer. By estimating the number of card batches, having come out of the game, it is easy to count the number of card batches, remaining in the game. And if you sit close to the sabot, where the dealer takes another card, you can have a look directly into the box. It, for sure, requires serious diligent practice. You have to learn at least to estimate roughly the number of card batches in a stack of cards, you must get accustomed to the inerrant conducting of current accounts. You should try both things at home. And do not think about the loss of time for it: a game with the wrong account can result in catastrophic consequences. If you lack self-confidence, it is much calmer to completely forget about any calculations and always play “a flat jackpot”, acting according to the usual main strategy.

If you used the “Plus-minus”, then you will get such a “makeweight” to the standard mathematic expectation of the game for various real accounts.
–10 –4,79% +10 +7,39%


–3 –1,71% +3 +1,98%

–2 –1,12% +2 +1,36%

–1 –0,53% +1 +0,73%

0 +0,09%

In case of a negative account (-2 or below) you should reduce the bets or stop playing. On the contrary, if the result is positive (+2 or higher), it’s time to increase the bets. But the decision depends on your personality. As it was mentioned earlier any rejection of the account from zero happens, the hypothesis about the uniformity is crumbling, and this leads to the necessity to adjust the basic strategy. The higher the real account is, the more careful we recruit additional cards, the more often we take the “co-lease” and use new opportunities in a doubling of the rates or in the division of cards. You can search in the internet modified table of the basic strategy or calculate those using programs. A small example is given in the book mentioned above.

Does the system “Plus-minus” have any shortcomings? For sure, it has. The results we got in the framework of this system do not pretend to high accuracy. We are aware of the fact that from the gambler’s point of view an ace is stronger than a ten, and a five “meaner” than a deuce. However, in operating the account we didn’t differentiate between these cards. Meanwhile, the real positive account, received as a result of an exit of fives from game lines, has more value than the same account, resulting from the played deuces. The tens and aces have the same in common. The moments when the chances of the gambler really reach their peak, is caught not always. And on the contrary, sometimes it happens so that the system sends the player false signals. Whatever the real account is, in the system we are forced to believe that the probability of falling out of a deuce is the same, as of a five, and a ten will come four times more often than an ace. We don’t pay close attention to such medium-sized cards, such as a seven, an eight or a nine.

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