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Counting cards at Blackjack

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Blackjack card counting

We already saw on the other pages that a player who uses the base strategy has a disadvantage of 0.5% at respects of the bank. This is a minor disadvantage if you compare it with other casino games like roulette(2.7% or 1.35%) and Punto Banco(clear 1%).
It is even more remarkable that there is a legal technique which enables the user to gain an advantage on the bank. This technique is called card counting. The idea can be explained using a imaginable casino game. The most easy game Red Cat is played with a pack of cards. First the dealer shuffles the cards. Players can make there bets, whereupon the dealer turns one card around. If the card is red the players win and get 195% of there bet. If the card is black they lose. You don’t have to make any decisions so there is no base strategy for this game. There are 26 red and 26 black cards and the base-disadvantage equals 2.5%. So it’s a kind of roulette? Only for those who don’t pay attention! It’s obvious that when the black cards are drawn more often then the reds the player has an advantage. Imagine that there are 22 cards drawn. 16 are black and 6 are red, instead of the 2.5% disadvantage the player has a 30% advantage!

In the mean time the dealer has raised the has raised the bets from /0,50(table minimum) to / 1000. Imagine that the 49th card of the pack is the last(26th) black one. The remaining three cards must be red and the player who pays attention wins without any risk the last three games with maximum bets. To make it easier to separate favourable from unfavourable situations we introduce the following counting-system: after shuffling we set the counter to 0, if a black card is drawn we raise the counter with one, and if a red card is drawn we decrease the counter with one. To find the players-advantage we use the following expression: advantage(%) = -2,5 + 97,5 x (count/N). N = the number of remaining cards. If the count is 0 there are just as many red as black cards; the player has a 2,5% disadvantage. Of there are only N red cards remaining then the counting is N and the player wins for sure( advantage = 95%) On the other side he will surely lose( advantage = -100%) when there are only black cards remaining, that means count = -N. Because the card counter can use this expression to determine his exact advantage and adjust his bet, he plays with an advantage instead of a 2,5% disadvantage.
This analyse of Red Cat teaches that:
– The advantage can change if you play a card game, because the composition of the cards in play also changes.
– The more cards there are being dealt the more the advantage will change for the card counter
– A counting system is a useful tool to separate favourable from unfavourable situations.
It’s very easy to come up with a counting system for Red Cat. That’s because there’re only two kinds of cards and it’s immediately clear that the red cards are good for the player and the black cards for the bank. Remember not all card games are countable. Imagine the next imaginary card game: Yellow Fever is played with a pack of well shuffled cards. The players can make there bets. Whereupon the dealer puts a card in the players-box and a card in the box of the bank. The highest card wins. If the cards are equal it’s a stand off(drawn). The bank doesn’t has a starting advantage with Yellow Fever. Changes in the composition of the pack of cards don’t have any influence on the advantage. The player would like to get an ace, but this card could just as easily end up at the bank. A two is bad for the bank, but also for the player. The rules of Yellow Fever are so symmetric that it’s impossible to count cards. The big question now is if it’s possible and useful to count cards with Black Jack. Does BlackJack look more like Red Cat or more like Yellow Fever. If you only look at the base strategy this last one is more likely. From calculations can be learned that it’s both for the player as for the bank unfavourable to start with low cards while it’s favourable for them to start with a ten. Only aces are much more favourable for the player then they’re for the bank.
Around 1960 showed the American mathematical Edward O. Thorp that it isn’t that easy.
The player and bank hands are formed by multiple cards. Thorp discovered that when there still lots of aces, tens and nines in the pack, that that’s favourable for the player. On the other hand the small cards(2 to 7) are favourable for the bank. There are three important reasons why situations with many large and a few little cards are favourable for the player.
– The most important reason is a consequence of the rules. The bank has to keep buying cards with bad hands(12 to 16), while the player can stop. This difference is the most important when the first card of the bank is a small one(2 to 6). If there’re are many tens and nines remaining in the pack, the change to bust increases for the bank. While the player often splits and doubles with small cards.
– Another reason is an immediate consequence of the Black Jack bonus. When there’re many tens and especially many aces in the pack, the change for a BlackJack increases, both for the player as for the bank. However because of the bonus this is favourable for the player.
– The last reason is a consequence of the rule that a player is free to take his decisions. Therefore the player is able to stop using the base-strategy whenever he thinks that it’s more favourable. The most important decision is the insurance. When more then a third of the cards in the pack is are tens, it becomes favourable to insurance. Therefore tens are the most important cards when it comes down to making decisions.
Thorp realised that favourable situations can be recognized by using a counting system that keeps up big cards versus small cards. To make profit in the casino, the only thing you have to do is: Bet low in the unfavourable situations and bet high in the favourable situations!
Thorp was the first to publish a book that’s about this winning strategy. There have been sold more than half a million copies of this book(Beat the dealer, a winning strategy for the game of twenty one.). However the book’s being labelled as obsolete it’s still a golden oldie. Afterwards there has been published more powerful and simple systems, mostly because of players like Ken Uston and Stanford Wong. The idea of Thorp, keeping up the proportion of big versus small cards, stays the most important thing. The High-Low-system in the book is recommended by different authors(like Dubner, Braun, Revere and Wong) as a good and relative easy method to count cards and obtain a advantage on the bank. The High-Low-system in this book is completely adjusted to the Dutch rules and conditions.
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High Low

The base idea of counting cards is that the composition of the cards in the pack have influence on the advantage of the bank. Because there’re cards being dealt while the game goes on the composition is constantly chancing and because of that there’re frequently favourable situations for the player. You can take profit from this by raising your bets. It’s now important to know the optimal system, that means a system where the profit is maximal by using bet raises and game-adjustments. By using calculations the optimal card-values have been determined. The optimal card-values for the Dutch rules and conditions are showed in the following table. The optimal card-value of the 10 has been determined to -100. Aces and tens are just about the only favourable cards for the player, nines are useful but less. Small cards are useful for the bank, especially the five followed by the four. This cards are helping the bank the most with turning a bad hand(12 to 16) to a good hand. In the High-Low-system the card-values have been determined to three values: -1, 0 and +1. +1 is good for the bank and bad for the player. 0 is neutral. -1 is bad for the bank and good for the player.



Optimal and high-low-countvalues


2      3       4       5       6

7       8       9

T    A



62    77    104   135     71


55       8   -23       0       0       0

-100 -89     -1    -1

There’re four times as much tens as there are other cards( as usual the T stands for 10, jack, lady and lord.) to make sure that there’re as many -1 as +1 cards. The sum of the card-values for all 312 cards is therefore equal to 0. The seven and the nine are cards with relative little influence. Therefore it’s better to set there card-value to 0 than to +1 or -1. With the years passing by there’ve been lots of different, more difficult counting-systems invented and recommended by BlackJack-experts.
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