Counting cards in Blackjack: The High-Low system

There are many card counting systems that have been devised for beating Blackjack over the years. One of the best in terms of simplicity and effectiveness, is the High-Low system, a Blackjack system designed by Harvey Dubner in 1963. It was called the Point Count system by Edward Thorp in his second edition of Beat The Dealer (1966), but it is more generally referred to as the High-Low system, f.e. in Stanford Wong's Professional Blackjack (1975).

How do you count cards using the High-Low system?

Counting cards using the High-Low system is surprisingly easy. All you have to do is track one number during a game of Blackjack, the running count. Suppose the cards are shuffled, and a game of Blackjack begins. Your running count is then zero. After the first hand is dealt, you start counting the high and the low cards that are dealt on each round. In particular, you add or subtract one point to or from your running count, depending on the cards that are dealt, and according to the following table:

 Ace,King,Queen,Jack,Ten (high cards) -1 7,8,9 0 2,3,4,5,6 (low cards) +1

If you correctly add and subtract these numbers to, and from, your running count during a game, your running count gives you an estimate of the number of high cards that are *not* dealt yet. A positive running count indicates there are more high cards left in the deck than dealt already. A negative running count indicates there are more low cards left in the deck than dealt already.

Keeping a running count is easy to do, as we demonstrated in the previous paragraph. However, it wouldn't do you any good if you didn't vary your bet size according to your running count. Computer simulations, originally done by Edward Thorp, have shown that a deck with a large percentage of high cards (10-A) left, is favorable to the player. For example, with many high cards left the chances of getting a Blackjack are higher. A positive running count indicates that the deck contains more high cards than low ones. You should therefore raise your bet size, when your running count gets higher.

Edward Thorp's simple point count system can be summarized as follows:

 Always play basic strategy (more information on basic strategy can be found here). If your running count is zero, or negative, only bet one unit. If your running count is positive, bet as many units as your running count total.

Refinement of the simple point count system: calculating the true count

There are many Blackjack variants available today. One important feature that distinguishes one Blackjack game from another, is the number of decks from which the cards are dealt. Single-deck Blackjack is increasingly hard to find, and Blackjack with four or more decks is much more common.

The simple point count system described above, doesn't take into account how many cards there are left in the shoe. As you can imagine, if your running count is +4, it makes a whole lot of difference whether there are 26 cards left in the shoe, or for example 208. Generally speaking, a positive running count is worth less to you, the more cards there are left in the shoe. If you would use the simple point count system in a Blackjack game with four decks or more, *without* adjusting your running count for the number of cards left in the shoe, you're headed for disaster.

Fortunately, this problem is solved easily by calculating the true count. The true count is based on your running count *and* the number of cards that are left in the shoe. To be more precise, the true count is your running count divided by the number of decks that haven't been dealt yet. An example will illustrate what consequences this should have for your bet size: if we compare single-deck Blackjack with two-deck Blackjack, and assume the game has just begun, and the running count is +4, you would bet 4 units in the single-deck game, but only 4/2=2 in the two-deck game. The running count in both games is +4, but the true count in the two-deck game is +4 divided by 2, because there are approximately two decks left to be dealt.

Refinement of the simple point count system: deviations from basic strategy

In all calculations and examples above, we've assumed you are playing basic strategy. However, you can gain an additional (small) advantage if you deviate from basic strategy in special cases, depending on your running count (or better your true count). When the true count becomes high, you should stand more, double down more and split more, than prescribed by basic strategy (the opposite is true when your true count becomes negative). In fact we could give you a table for each true count, that described the correct deviations from basic strategy. This is however beyond the scope of this article. Also keep in mind that deviating from basic strategy in general only marginally improves your advantage. If you're really interested in this subject, we advise you to consult Professional Blackjack, a good book on this subject, written by Stanford Wong.

Remember Blackjack card counting only works in land-based casinos and *not* in online casinos, because in an online casino the deck is reshuffled after each round.

Tip: Both Cryptologic and Boss Media offer a single deck Blackjack game. The house edge on the former approaches zero, and on the latter it's actually slightly in favor of the player. Microgaming offers a variety of Blackjack variants, ranging from two to eight decks.

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