Strategies for Counting Cards - How Tos
How to Count Cards
How to Create a Blackjack Strategy - Card Counting
Techniques
Card counting strategies range from fairly simple to absurdly complex.
This page provides instructions on creating a card counting strategy and
in doing so describes the various characteristics of counting systems.
It may be of interest even if you don't wish to create a strategy but
want to learn about the make-up of such systems.
Creating a new strategy is not difficult if you start with an existing
strategy. If you wish to start from scratch there is a bit more work.
There are plenty of strategies in the books. (See Card
Counting Strategy Comparison for a list of popular strategies and
Blackjack Strategy
Advisor for advice on selecting a strategy.) But, many people
do like to at least modify a current strategy to better fit their needs.
Card Counting Tools
The following tools are needed:
- Efficiency Calculator - Tells you how efficient a particular count
is
- Index Generator - To create new playing indexes
- Simulator - To fine-tune and measure the effectiveness of the new
strategy
All three of the above exist in CVData.
If you wish to create optimal betting ramps and make very quick comparisons
with existing strategies, you can also use CVCX.
Tag Values for Counting Cards
First you need to settle on the card point values. If you have already
done this, you can skip to the Index Generation section. Although reading
this section may add to your understanding. Each card has a point value
like +1 or -1. There are several characteristics of counts as follows:
- True Count vs. Running Count - As cards
are seen, you keep a running sum of the card tag values. Running Count
systems use this count for both betting and playing decisions. True
Count systems require that you divide the RC by a number representing
the number of cards that have been seen. There are various methods of
converting RC to TC (e.g. division, multiplication, tables.) TC systems
generally use this TC for all playing decisions. Most also use it for
betting decisions. There are exceptions to both of these rules. RC strategies
are generally easier to use and TC strategies are generally more accurate.
- Balanced vs. Unbalanced - In a balanced
strategy, all of the point values sum to zero. In an unbalanced strategy,
the sum of all the cards is positive. Unbalanced strategies have an
advantage because they can be used in the easier running count systems.
Although they can also be used in TC systems. Balanced strategies have
an advantage in that they are generally a bit more accurate (there are
exceptions) and the count hovers around zero making counting easier
and betting strategies easier.
- Ace-Reckoned vs. Ace-Neutral - Generally
the Ace is counted as a negative number (Ace-reckoned) or zero (Ace-neutral.)
Ace-Reckoned strategies are generally better for shoe games and Ace-Neutral
strategies are generally better for single and double deck. (Not always
true.) There are compromise strategies (e.g. Zen, UBZ II) where the
Ace is counted at half of the normal value. This is particularly good
for double-deck and not bad for single deck or shoes. These days, Ace-reckoned
strategies are more popular.
- Level - The level of a strategy refers
to the highest value assigned to cards. Level 2 and 3 card counting
methods are more efficient, but quite a bit more difficult for most
people. Level 3, 4 & 5 strategies also exist. But this is overkill.
The most popular strategies these days are level 1. In a level 1 strategy,
tens are counted as -1 and some or all low cards are counted as +1.
- Side Counts - Some strategies use one
or more side counts. The most common is counting the Aces in a separate
count to make betting more accurate in Ace-neutral systems. This is
because Aces are large cards for the purposes of betting but small cards
for the purposes of playing when you don't have a Blackjack. There are
several methods of side counts described at Side
Card Counting Techniques.
- Suit/Color Aware Counts - Some count
will have different tag values for red and black cards. Examples are
Red7 & KISS. The attempt here is to gain most of the advantage of
a higher level strategy without the higher range of counts. I would
expect the error rate would increase somewhat but have no figures for
this.
- Other ease of use considerations - The
fewer the number of cards counted the easier it is to count cards. Also,
the more card pairs that add to zero the better. This is because most
counters count pairs of cards when possible. If you see a +1 and a -1
card at the same time, you automatically ignore them since they sum
to zero.
Now, how do we decide on the card tag values? First you need to decide
on the above characteristics. Second, it is good to take a look at the
popular strategies that exist. See Card Counting
Systems Comparison for a list along with their tag values. Next, you
need to understand Betting Correlation, Playing Efficiency and Insurance
Correlation. These are terms created by Peter Griffin in Theory of
Blackjack. Reading this book will help you a great deal. These terms
are defined as:
- Playing Efficiency - PE indicates how
well a card counting system handles changes in playing strategy. Playing
efficiency is particularly important in hand-held games (one or two
decks.)
- Betting Correlation - BC is defined as
the correlation between card point values and the effect of removal
of cards. It is used to predict how well a card counting system predicts
good betting situations and can approach 1.00 (100% correlation.) BC
is particularly important in shoe games (six or eight decks.)
- Insurance Correlation - IC is defined
as the correlation between card point values and the value of cards
in Insurance situation. A point value of -9 for tens and +4 for all
other cards would be perfect for predicting if an Insurance bet should
be placed.
The next question is how to calculate PE, BC and IC. In CVData you can
use the Efficiency Calculator. On the main screen, select Tools then Efficiency
Calculator from the menu. The calculator will appear with space for the
ten card tag values. Click on the ? for instructions and an explanation
of BC, PE and IC. You can experiment to your heart's desire. PE's max
out a .7 for non-side counted systems. BC's max at 1.0.
Index Generation for Counting Cards
Once you have your card values, you need to generate indexes. First,
you need to make a few general decisions:
- Initial Running Count - The IRC is the
count you start with after a shuffle. Balanced strategies nearly always
have an IRC of zero. This causes the count to hover around zero. A few
people start with a higher number because they don't like to count negative
numbers. This has no effect on the efficiency of a strategy. Unbalanced
strategies usually have negative IRC's. This is because the count rises
as the shoe is played. The IRC is often set so that there is an advantage
after the count becomes positive. Also, different IRC's are generally
used for different numbers of decks. This is not necessary; but makes
it easier to remember playing and betting decisions since the count
has to rise significantly farther for shoes than for single-deck. Some
people use zero for unbalanced IRC's to avoid large negative numbers.
- True Count Calculation - You need to
decide how to convert the running count to the true count if your strategy
uses True Count decisions. The most common methods are to divide by
the number of full decks or half decks remaining. There is little difference
in overall effectiveness. Full-deck is slightly better for betting and
half-deck is slightly better for playing. HiLo Lite and the 1998 version
of Zen divide by quarter-decks remaining. This makes betting a bit easier;
but a bit less accurate. (You can see this explained in Blackbelt
in Blackjack by Arnold Snyder when the next version is printed.
It is currently out of print.) Some people use multiplication instead
of division. Another method is to use a table of True Counts by shoe
depth and running count. This is described in Blackjack Bluebook
II by Fred Renzey. All of these methods are supported by CVData
and CVCX.
- Rounding/Truncating/Flooring - Nearly
everyone uses integer index values for playing decisions. So, how do
you round the true count after division? It doesn't matter greatly as
long as you use the same method for play and index generation. But,
Flooring is currently preferred. That is, if there is a fraction, round
down to the next lower value.
- Which indexes - In older strategies huge
numbers of indexes were used. But, most indexes have very little value.
You can find a discussion on this subject in Blackjack Attack
by Don Schlesinger. (If you wish to count cards, you should read this
book for many other reasons.) See the discussion on Illustrious 18 and
Catch-22. Theory of Blackjack also has a discussion on the value
of indexes. But, it is concerned primarily with single-deck and doesn't
take into account the frequency of decisions.
- Risk-Averse vs. Expectation Maximizing Indexes
- Older strategies generally used expectation maximizing indexes. (There
are exceptions.) Such indexes result in decisions that give the greatest
average gain for each bet. But, this is not always the best bet as the
gain is so small in some cases it may not be worth the extra risk as
in close doubling down decisions. Risk-Averse indexes reduce the risk
which reduces the variance which allows you to slightly increase your
betting levels. This provides a slight overall improvement in results.
RA Indexes are now preferred since they perform a bit better with no
extra effort. Blackjack Attack contains a discussion on RA indexes.
- Index Compromises - Older strategies
used the best possible indexes they could calculate at the time. Some
newer strategies make compromises for ease of use. For example, the
double down indexes for 9 vs. 2 and 9 vs. 7 may not be the same; but
they are so close you can compromise and make them the same. This makes
them easier to remember and use. If you wish to use compromise indexes;
you will need to first generate the correct indexes using an index generator
and then use trial and error with simulations to test various compromises.
Red7, HiLo Lite, Basic Omega II and 1998 Zen use compromise indexes.
- Rules Compromises - Stand on 17 vs. Hit
on 17, Multi-deck vs. Single-deck, Double after Split vs. no DAS. These
all affect indexes. You need to decide if you want to go through the
effort of using different indexes or determining what games you will
most often play and just use those indexes. Or, compromise by using
indexes that are in-between.
- Composition Dependent indexes - These
are indexes that look at the exact composition of your hand (8, 6, 2
vs. 10) instead of the total of the hand (16 vs. 10.) They add slightly
to system effectiveness. But, few people use them.
- Multi-Parameter Indexes - These are used
along with side-counts to improve playing decisions. MP Index Tables
are rarely used today.
The CVData manual includes detailed instructions on creating card counting
indexes in the section titled "Tours - Create a Blackjack Strategy."
Once you have created the indexes, you will want to run sims with different
rules and penetrations to test your system. CVData can do this automatically
after the indexes are generated. But, CVCX is much easier for making quick
comparisons. With CVCX you can run many different penetrations, rules,
spreads and decks at once. You can also ask it to compare the strategy
with all of the strategies in the CVCX archives. There are over 150,000
sims in the archives. The best method of evaluating the overall strength
of a strategy is by the SCORE as described in Blackjack Attack.
Hints and Tips
- Read The Theory of Blackjack by Peter Griffin. Particularly
chapters 3 and 4 as they will explain the value of card tags and indexes.
- Some strategies use compromise indexes. Hi-Lo Lite and Red 7 are examples.
These are indexes that are changed so that many decisions use the same
index. To create these, generate the accurate indexes first and then
run sims with different indexes to see which ones can be changed without
impacting overall SCORE. These sims must be over two billion rounds.
- Indexes do not make a huge difference in shoe games. The more decks,
the less value you get out of accurate indexes.
- The gain from using risk-averse indexes is really quite small. But,
there is no downside.
- To accurately calculate the SCORE, you must use an optimal betting
ramp. CVCX can do this for you. If you don't have CVCX, you can estimate
a betting ramp from looking at the Chapter Ten tables in Blackjack
Attack.
- Some Split indexes are very strange. Splitting or not splitting goes
back and forth as the count changes. This is because they are both offensive
and defensive. That is, sometimes you split to make more money and sometimes
you split to lose less money. 2, 2 v 3 or 3, 3, v 7 for example. It
really doesn't matter much what you do with these hands.
- Indexes can change as the penetration changes. This is particularly
true with unbalanced card counting strategies, but also true with balanced
strategies.
- To learn how to count cards, try the blackjack tutorial, game, practice
and drills at CV Blackjack Card Counting
Software.
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