A Guide to Card Counting Systems

How is card counting done?

The card counting system described below is an unbalanced 10 count that is 100% accurate for determining when to take insurance. As a general purpose card counting system, it is relatively weak and not particularly recommended, but it illustrates many of the principles behind card counting. This is intended only to give a feel for how card counting is done, and is not recommended for actual practice, although I’ve used it because of its simplicity. This counting strategy is listed as ‘Unbalanced 10 Count’ in other parts of the FAQ list.

For single deck games:

Start the count at -4 when the deck is shuffled.
Count -2 for 10, J, Q, K
Count +1 for everything else (including aces)
Bet low when the count is negative, high when the count is positive (actually, simulations show that you can bet high for a count of -2 or above).
Take insurance when the count is positive.
Play basic strategy at all times.

For N deck games:

Start the count at (-4 * N).
All other rules are the same.

Notes:

The unique feature of this counting method is that it is perfectly accurate for dealing with insurance. When the count is positive, the player has the advantage when taking the insurance bet. When the count is negative, the house has the advantage, so insurance should not be taken.

Counting is best done by counting several cards at once. It is easy to practice this counting method in the following way:

Count through a deck of cards, counting one card at a time. Start at -4, and count through the entire deck. After all of the cards have been seen, the count should be ZERO. If it is not zero, a mistake has been made somewhere. Repeat counting through the deck one card at a time, until you can do it quickly without making mistakes.
Count through the deck, counting two cards at a time. Look for thefollowing patterns, adding the correct amount for each pattern
(X = 10, N = non-ten)
NN: +2
XN: -1
XX: -4
Again, the count should be zero after all cards have been seen. Repeat until you can do it efficiently.
Count through the deck, counting three cards at a time. Look for the following patterns, adding the correct amount for each pattern.
(X = 10, N = non-ten)
NNN +3
XNN 0 (this pattern is common)
XXN -3
Practice against a computer blackjack game. When I play, I usually count the cards by counting an entire hand (player’s or dealers) at once. If there are more than three cards in the hand, I mentally break it up into groups of 1, 2, or 3 cards (I usually look for ‘XNN’ patterns and ignore those cards, since they add up to zero). I usually count the cards just before the dealer picks up the hand (exception: for insurance, you should count your cards and the dealer’s up card immediately).

Which card counting system is ‘best’?

The first approach is to evaluate different systems by simulation. This approach obscures the particular advantages of each system, but it’s easy to see how a system will perform in one particular realistic casino playing situation, and not hard to judge the tradeoff between performance and ease of use (see Q/A B18 for more details).

The second approach estimates several performance parameters of each system that collectively approximate the system’s inherent potential. This allows the strengths of different BJ systems to be studied in detail, which should allow better, more precise comparison of different systems and aid efforts to improve a particular system. This approach gives results which may be used to determine which counting system is theoretically most profitable but does not address the issue of how easy it is to use the counting system under actual playing conditions (see Q/A B19 for more details).

It’s not yet clear how these two studies relate, and no rec.gambling.blackjack consensus has emerged as to how the more sophisticated performance parameters actually translate to advantage at the tables as in the simulations.

What counting system is easiest to use?

Background: Lots of systems are available. There is an important tradeoff between complexity and theoretical power, as more complex systems are harder to use and more error-prone.

Answer: You pick ’em. A rec.gambling.blackjack study was accomplished that compared different systems, and here a summary of what came out:

Complexity is a subjective measure with guidelines described in the results paper.

Complexity is a subjective measure with guidelines described in the results paper. Power is the integer closest to p/0.05%, where p is the % advantage of the strategy one-on-one in a single deck, dealer hits on soft 17, no DDAS, resplitting-allowed game that’s dealt down to 20 cards and using a 1-4 betting spread. 15,000,000 hands guarantee correctness to within 1 point 99% of the time.

name complex power card weights reference
A 2 3 4 5 6 7 8 9 X
————————————
BASIC 0 -5 Steve Jacobs
UNBALANCED 10 2 13 1 1 1 1 1 1 1 1 1 -2 Steve Jacobs
SUPER-SIMPLE OPT-I 2.5 16 1 1 1 1 -1 WGBJB (1)
REVERE PM 3.5 16 -1 1 1 1 1 1 -1 PBaaB
RED SEVEN 3.5 19 -1 1 1 1 1 1 R:1 -1 BiB
OPT1-6+6 5 18 1 1 1 1 -1 WGBJB
WONG HIGH-LOW 5 19 -1 1 1 1 1 1 -1 PB
ZEN 5 19 -1 1 1 2 2 2 1 -2 BiB
HORSESHOE 6 14 1 2 2 3 2 2 1 -1 -3 MDB (2)
REVERE POINT COUNT 6 17 -2 1 2 2 2 2 1 -2 PBaaB
OPT1-6+6 W/ ACE 7 23 1 1 1 1 -1 WGBJB
ANDERSEN 9.5 16 -2 1 1 1 2 1 1 -1 -1 TtToLV
USTON APC 10 22 1 2 2 3 2 2 1 -1 -3 MDB

WGBJB: ‘World’s Greatest BlackJack Book’ by Humble and Cooper
PBaaB: ‘Playing Blackjack as a Business’ by Lawrence Revere
BiB: ‘Blackbelt in Blackjack’ by Arnold Snyder
PB: ‘Professional Blackjack’ by Stanford Wong
TtToLV: ‘Turning the Tables on Las Vegas’ by Ian Andersen
MDB: ‘Million Dollar Blackjack’ by Ken Uston
(1) with modifications by Matthew Wilding
(2) with modifications by Paul C. Kim

Which Blackjack card counting system is most effective?

The playing efficiency, betting correlation, and insurance correlation is listed below for several counting systems. These numbers give an indication of the effectiveness of the counting system. When two numbers are listed, the second number results from adding an ace side count in addition to the ‘main’ count.

See answer B3 for definitions of ‘betting correlation’, ‘playing efficiency’, and ‘insurance correlation’.

EXPLANATION OF COUNTING SYSTEMS
===========================================
COUNTING COUNTING VALUES ‘BEST’ EFFICIENCY CORRELATION
SYSTEMS 2 3 4 5 6 7 8 9 X A SOURCE PLAY+ace BET+ace INSURE
——– —————————- —— ——– ——– ——
Griffin 0 0 1 1 1 1 0 0 -1 0 Griffin 64-64+ .85-.95 .85
Hi-Opt I 0 1 1 1 1 0 0 0 -1 0 Humble 61-63 .88-.97 .85
Hi-Opt II 1 1 2 2 1 1 0 0 -2 0 Humble 67-67+ .91-.99 .91
High-Low 1 1 1 1 1 0 0 0 -1 -1 Wong 51-63 .97 .76-.85
Ita 1 1 1 1 1 1 0 -1 -1 -1 Sys.Res. 53-63+ .96 .69-.76
Red 7’s 1 1 1 1 1 ** 0 0 -1 -1 Snyder 54-64+ .98 .78-.87
Unbal 10’s 1 1 1 1 1 1 1 1 -2 1 Roberts 61-61+ .73-.94 1.00
Uston +- 0 1 1 1 1 1 0 0 -1 -1 Uston 55-64+ .95 .76-.85
Uston APC 1 2 2 3 2 2 1 -1 -3 0 Uston 69-69+ .91-.99 .90
Wong Halves 1 2 2 3 2 1 0 -1 -2 -2 Wong 57-67+ .99 .72-.85
Zen 1 1 2 2 2 1 0 0 -2 -1 Snyder 63-67+ .97 .85-.91
** red 7’s +1, black 7’s 0