Cards counting basics 

Probably many of you have heard that a competent casino player can defeat a casino. In majority of cases the game is Blackjack and the method is “cards counting”. A possibility to apply the “cards counting” method at the online casinos is rather limited as the casinos usually shuffle the cards after each deal, but there are some casinos offering to gamble until the third pack (or rather not one pack but a set of 6-8 packs).

There are also live dealer online casinos where the blackjack is played as at brick and mortar casinos, so you can really try to use any cards counting system (though on-line you shouldn’t count, you can intrust it to your computer).Probably most of you can remember the scene from the “Rain man” where a Hoffman’s hero after some training counted the cards in an expert manner thereby the brothers won a lump sum.

Cruse’s hero told him to remember low and high cards coming out and to show with his stakes what cards mostly came out. Why do they do that? How can it help to win?That’s rather simple, with a part of cards coming out a probability for various cards to come changes. If in the beginning of the game a probability of any card to come (without taking into account the suit) is 1/13, then as far as the game goes with irregular coming out of various cards such probability can increase or decrease. As a result a casino player can play with a part of the pack with low cards and aces mostly but with a few tens or vice versa.A basic strategy and the advantage of the casino are counted for the case where a probability of card coming is the same, together with the change of the probability of various card coming an optimal strategy and a relevant mathematical expectation. What situation of the pack is more advantageous to the player? That where aces and tens prevail. 

The logic is the following: First, a player has an advantage because any blackjack will pay off at odds of 3:2 on the original bet. So the more blackjacks, the more advantageous is the situation of the player. In case of the dealer got blackjack the player loses one stake and while the payoff for a player blackjack is 3:2.Second, if the dealer has less than 17, he must hit, if there are many tens in the pack, then a probability increases that the dealer would bust taking the cards while the player can change the strategy and not take at 12-16 points.Third, in case of doubling, there is more probability that a gambler will get 19-21 having won a double stake at that.

So we have found what advantage has a player and now we should understand how it’s used in practice.In practice there is a range of cards counting systems developed but their principle of work is the same. The cards counting in fact was discovered by Edward Thorp who in 1962 had already determined optimal values the cards should have.

Unfortunately, each card has its own value ranging from – 9 to +11. The system was rather complicated to use and only players with a sophisticated memory count following this system. But have a look at Thorp’s discoveries to understand which cards are the most useful in the pack, which ones are harmful and which ones are neutral: 2 shall be estimated as +5, 3 +6, 4 +8, 5 +11, 6 +6, 7 +4, 8 0, 9 -3, 10 (ten shall mean all ten-point cards from 10 to a king) -7, ace -9.Next year in 1963 a system “high low” appeared which was more applicable and mostly became the basis for further developments. In this system each card is attributed a numerical value but they are only three: +1 (for the cards from 2 to 6), 0 (for 7-9) and +1 (for tens and aces). It’s easy to make sure that the sum of values in a 52-card pack is equal to zero.

The same is the case of “a big pack”. The systems with such feature are sometimes called balanced. As far as the cards come out of the pack we follow the current score. Sevens, eights and nines are ignored, coming out of senior cards (tens and aces) leads to the score decreasing, that of junior cards (from two to six) – to the score increasing.

The system “high low” as every balanced system has a very simple feature: when the score is positive a gambler’s chances rise, when it’s negative they fall. The higher is the score the larger is your expected gain.

But the main question is still open: how do your chances change depending on the score? When it’s better to rise the stakes? As it happens the current score can’t help here. To have an idea of your chances make use of a so called real score (sometimes it is called true score). A real score is a result of dividing of the current score into the number of packs being in the game. For instance, one pack left the game, the score is equal to +12. Let’s divide it in five (the number of the pack left) and we get a real score which is equal to +2,4.You can have some difficulties to count the number of the packs. As this number is generally fractional.

The simplest way to estimate is to have a look at the set of cards out of game lying on the table on the left hand of the dealer. Having figured out the number of the packs which came out of the game, it’s not difficult to count the number of the packs left. If you are sitting at the shoe the dealer takes next cards from, you can look into this box. Sure, all that requires hard trainings. You should learn at least roughly to estimate the number of packs of the cards being in a stack, you should get used to unmistakably maintain of the current score. Both of them should be tested at home conditions. And don’t grudge the time for that: a game with mistakable score can result in disastrous effects. If you don’t feel sure, it’s better to forget of any calculations and always gamble at equal stake following a usual basic strategy.

If you use the “high low” system, then you will get the following “makeweight” to a standard mathematical expectation for different real scores.