Card Counting Systems

In order to be completely accurate, a system must be based on the effect that removing a card of any value will have on the player’s advantage in the remaining deck. Mathematically, the effect of removing the first card from a deck is shown in the table below.

2 +0.37%
3 +0.44%
4 +0.52%
5 +0.64%
6 +0.45%
7 +0.30%
8 0.00
9 -0.13%
10 -0.53%
Ace -0.49%

For the next card, the same values would be applied, but would need to be multiplied by 1.02 to be accurate, the third by 1.04, and so on, in order to remain accurate to the proportional values that are available in the remainder of the deck.

Without the assistance of a computer or other calculating device (which are patently disallowed in virtually all casinos), it would be impossible to perform all the calculations necessary to provide a perfect reflection of the player’s advantage while a game is in progress.

Card Counting Systems Compared

Instead, there are a number of card counting systems that use whole numbers that remain constant throughout the counting process to provide an estimation of the advantage. The accuracy of their estimation often comes at the cost of increased complexity, hence difficulty to learn and implement. Here are some of the more popular card counting systems.

High Low Card Counting System

2 3 4 5 6 7 8 9 10 A
1 1 1 1 1 0 0 0 -1 -1

The high-low system, used in the tutorial, values low cards (2-6) at +1 andhigh cards (tens and aces) at -1. To give credit where credit is due, this system was developed by Stanford Wong, a prolific author who has authored volumes on almost every casino game.

Red Sevens Card Counting

2 3 4 5 6 7 8 9 10 A
1 1 1 1 1 * 0 0 -1 -1

Arnold Snyder’s “Red Sevens” system also seems to be derivative of the High-Low system. It is, in all ways, identical High-Low, except that red sevens count as +1 (black ones count as zero). In effect, this gives all sevens the value of +0.5, which is fairly accurate when considering the effect of a seven on the player’s advantage.

Green Fountain Card Counting

2 3 4 5 6 7 8 9 10 A
1 1 1 1 1 1 0 -1 -1 -1

Koko Ita’s “Green Fountain” systems is similar to High-Low—the difference being that sevens and nines are not treated as “neutral” cards. Arguably, this is closer to the actual mathematical weight of the cards, as the seven and nine are not completely neutral—but at the same time, the effect of either is less than a third of a percent.

Uston Advanced Plus Minus

2 3 4 5 6 7 8 9 10 A
0 1 1 1 1 1 0 0 -1 -1

Legendary blackjack professional Ken Uston pioneered this system, which is largely identical to the high-low count, except that deuces are treated as neutral and sevens as dealer-favourable. Weighed against the mathematical impact of the cards, both assumptions are mistakes, but they more or less cancel each other.

Griffin Card Counting

2 3 4 5 6 7 8 9 10 A
0 0 1 1 1 1 0 0 -1 0

Peter Griffin’s card counting system deviates from high-low by treating twos, threes, and aces as neutral and sevens as dealer-favorable. Although this system meets the criterion of being at least 90% accurate, it’s one of the least reliable discussed here.

Unbalanced Tens Card Counting

2 3 4 5 6 7 8 9 10 A
1 1 1 1 1 1 1 1 -2 1

This system counts all cards except tens as having a value of 1, and the tens as a -2,In effect, it system leads the player to count only the tens, which is worse even than Griffin’s system. Arguably, it’s effective only in estimating the soundness of the “insurance” and “even money” side bets.

High Opt 1 Card Counting

2 3 4 5 6 7 8 9 10 A
0 1 1 1 1 0 0 0 -1 0

This system is the first of two deviations on the high-low system popularized by Lance Humble and Carl Cooper. The primary difference between this strategy and the original is that aces and deuces are treated as “neutral” cards. Though this would seem to defy common sense, it works out to be a reliable system in computer simulations.

High Opt 2 Card Counting

2 3 4 5 6 7 8 9 10 A
1 1 2 2 1 1 0 0 -2 0

Another of Humble and Cooper’s adjustments on the high-low system is shown to the right.This system introduces varying “weights” for cards. When compared with the absolute effects of removing a card, the four, five, and ten each change the casino odds more than 0.50%, and are valued at twice the normal weight.

Zen Card Counting

2 3 4 5 6 7 8 9 10 A
1 1 2 2 2 1 0 0 -2 -1

Arnold Snyder’s “Zen” system places extra value on the four, five, six, and ten. This is essentially correct, although the ace also falls within the same range and is given only a -1 weight.

Wong Halves Card Counting

2 3 4 5 6 7 8 9 10 A
1 2 2 3 2 1 0 -1 -2 -2

Among the most accurate counting systems is Stanford Wong’s “halves”, which uses a variety of values to better reflect the actual mathematical impact of cards of varying values. This is arguably the most reliable system available, and produces an accurate estimation in almost 99% of all situations.

Uston APC Card Counting

2 3 4 5 6 7 8 9 10 A
1 2 2 3 2 2 1 -1 -3 0

Ken Uston’s APC system also uses an array of values to assign different weights to each card. As with many systems, the impact of aces and deuces seems to be underestimated—and curiously, a value of +1 is assigned to the eights, which are the only card that is completely neutral. At yet, this system meets the criterion of being at least 90% accurate.

Best Card Counting System

Deciding which system is the “best” is generally a matter of personal preference—balancing the reliability of a system against the feasibility of learning and using it.

All of the systems discussed above produce reliable results. They lead a player to correctly estimate his advantage in at least 90% of all situations. While none are perfect, the High Opt 2, Red Sevens, Uston APC, Wong Halves, and Zen systems all yield results that are closest to perfection (more than 95% accurate).

Ease of learning and implementation, however, is entirely subjective and depends on the mental dexterity of the individual player. Arguably, the “easier” systems are those that do not require you to memorize different values for different cards (i.e., some are plus or minus one, others two, others three). In that case, the Unbalanced Ten, High-Low, High-Opt 1, and Uston plus/minus systems would be considered the easiest.

If you’re looking to learn card counting for the first time, it would be worthwhile to attempt to learn one of the more accurate systems like Blackjack Apprenticeship and if you find it too difficult, downgrade to one of the easier ones. If you already count cards and are looking to switch systems, the best advice is to stick with what you’re using (unless it’s wildly inaccurate). Chances are the mistakes you’ll make in the process of learning a new system will be costly—and the difference between one system and another tends to be a few percent, or a few tenths of a percent.