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 1/36 or 1.0, then as far as the game goes with irregular coming out of various cards such probability can increase or decrease. As a result a dewapoker 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 increases. In the case of the game there are only four cards of one rank, the probability of card coming is 1/3 or 0.8 and in the case of two aces it’s 1/2 or 0.6. As far as the game is concerned there are only three such probabilities. So the probability of card coming increases by one sic in the case of two aces it’s 0.6 and 1/3 in the case of three kings. The rest of the cards have the same probability of coming.

Let’s understanding these probabilities of card coming for the case of the game without going deep into the technicalities of probability theory. First, a probability of card coming = 1/3 in the first pack of cards and 0.8 in the second pack. Probability of an unknown card coming = ½(1/3) in the first pack and ¼(1/3) in the second pack. And probability of an unknown card coming = ½(1/2) in the first pack and ¼(1/2) in the second pack.

You will hardly come across situations when the probability of coming is zero especially in a shoe with 6-8 cards. So, when the probability of coming is non-zero, we will know that the probability of an unknown card coming is also non-zero. This means that the probability of an unknown card coming in the next deal is also non-zero.

Well, the principle is the same when an opponent plays his first cards. The probability of an opponent holding aces in his hand is 5 % ( chap. 13.1) exactly as the probability of an opponent holding aces in his hand. The one case when the opponent does not enter in the play, the probability of an opponent holding aces in his hand is only 8 % or rarely. This probability is also called dispersion.

The dispersion is the probability that a horse will not win the race (20 – 40%) depending on the number of opponents in the race (OND/COM). For example, if there are 6 opponents in the race, the probability that the horse will not win is 5/6 or 0.80. The same principle applies to a football team. If there are more than 3 opponents, the probability that the team will not win is 20 – 30 % and this is also dispersion.