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Counting Cards

If you have the read Card Counting Theory article of this website you will have some knowledge of what goes into creating a blackjack card counting system. If you have not read this article and just simply want to know how to count cards, there are some things that you need to accept as true:

• Some cards when removed from a full shoe tend to be favorable to player
• Some cards when removed from a full shoe tend to be unfavorable to player
• Card counting separates the 10 possible ranks into 2 or more groups
• The only card counting system that is not an approximation is to separate cards into 10 groups, 1 for each rank, and be able to use this information with 100% accuracy for both betting and determining best playing strategy
• Practical card counting systems are all an approximations
• The counting system you have chosen is a reasonable choice with respect to the above points

The purpose of this article is to show by example how to count cards in blackjack. It has nothing to do with the effectiveness of a given system or even card counting in general. Its only purpose is to show how to implement a counting system starting with counting in its most basic form.

Best Card Counting

Counting Basics - Any counting system is comprised of 2 or more rank groups. Below are examples of 3 simple counting systems and how ranks are grouped in each one:

1. Sample count 1 (2 groups)
   • Non-tens (All non-ten value ranks)
   • Tens and picture cards (All ten value ranks)
2. Sample count 2 (3 groups)
   • Ranks 2, 3, 4, 5, 6
   • Ranks 7, 8, 9
   • Ranks T, A (All ten value ranks and aces)
3. Sample count 3 (3 groups)
   • Ranks 2, 3, 4, 5, 6, 7
   • Ranks 8, 9
   • Ranks T, A (All ten value ranks and aces)

One method of counting would be to simply count how many of each rank group remains to be dealt in the shoe. If each of the sample counts were dealt from a single deck then at the start of the shoe the number of cards in each count's rank groups woud be as follows:

• Count 1
  • (Non-tens): 36
  • (Tens and picture cards): 16
• Count 2
  • (2, 3, 4, 5, 6): 20
  • (7, 8, 9): 12
  • (T, A): 20
• Count 3
  • (2, 3, 4, 5, 6, 7): 24
  • (8, 9): 8
  • (T, A): 20

After that as each card is dealt the number of each rank group present would be updated and the portion of the shoe that each rank group accounts for would change.

Example: after a 5 is dealt from a full single deck:

• Count 1
  • (Non-tens): 35/51
  • (Tens and picture cards): 16/51
• Count 2
  • (2, 3, 4, 5, 6): 19/51
  • (7, 8, 9): 12/51
  • (T, A): 20/51
• Count 3
  • (2, 3, 4, 5, 6, 7): 23/51
  • (8, 9): 8/51
  • (T, A): 20/51

As more cards are dealt each new set of data would need to be interpreted and applied.

The above is the best way to count cards. However it is still too difficult to implement. Although it's better than trying to count every single card, it could use some simplification.

Simplified Card Counting

Tags - The key to simplifying a counting system is rank group tags. A tag is a simple +/- number associated with all of the ranks within a given rank group. The sign of the tag is determined by the group's general effect on player's overall probabilities. There are 2 ways to determine the sign of a tag. Each is opposite to the other but it doesn't matter how it is done as long as it is applied consistently. It's just a matter of definition.

1. Sign of tag is referenced to what has been removed from shoe
2. Sign of tag is referenced to what remains to be dealt in shoe

Example: Assume a rank group consists of (2, 3, 4, 5, 6, 7). The removal of one or more cards of this group from a shoe tends to increase player's advantage and if a shoe has relatively large number of cards of this group then this tends to decrease player's advantage. The tag's sign would be defined as positive using method #1 but negative using method #2. This website prefers method #2 and that is what will be used.

Simplifying best card counting method from above - Any tag may be assigned to any rank group. However the numerical value should somewhat approximate the relative worth of each group. (See Card Counting Theory article of this website for some idea of what's involved.)

Assigning tags to the 3 sample counting systems from above and computing each system's full shoe count value (called running count or RC for short) from the tags and number of rank group present, each count can be evaluated as a single number.

• Count 1
  • (Non-tens): -1
  • (Tens and picture cards): +2
• Count 2
  • (2, 3, 4, 5, 6): -1
  • (7, 8, 9): 0
  • (T, A): +1
• Count 3
  • (2, 3, 4, 5, 6, 7): -1
  • (8, 9): 0
  • (T, A): +1

As cards are dealt RC is recomputed. If a negative card is dealt then that makes RC less negative so 1 is added to existing RC. If a positive card is dealt then that makes RC less positive so 1 is subtracted from existing RC in Counts 2 and 3 and 2 is subtracted in Count 1 since that count's tag for a positive card is +2. RC is simply updated as cards continue to be dealt until cards are shuffled. At that point RC is reset to its full shoe initial value and the process is repeated.

At this point we've managed to crudely represent the evaluation of 2 or more groups of cards in a single number but we're not quite done. What if you were asked to evaluate how successful a baseball player is but are only given how many hits he has. Let's say he has 100 hits. If accomplished in 1000 at bats that's not good. If accomplished in 200 at bats that is really, really good. If accomplished in 100 at bats that could be the most amazing feat ever by a ballplayer.

The same type of analysis applies to running count. If RC is +4 and 4 decks or 208 cards remain to be dealt then another parameter is needed that evaluates to +1 per deck. If RC is +4 and 1/2 deck remains to be dealt then this new parameter should evaluate to +8 per deck. This new parameter is called true count or TC for short.

The general formula to compute TC form RC is:
TC = 52 * RC / (number of cards remaining to be dealt)
where number of cards remaining to be dealt is an estimate

Another way of expressing the same thing is:
TC = RC / (number of decks remaining to be dealt)
where number of decks remaining to be dealt is either an estimate or
exactly - number of decks decks = (exact number of cards remaining to be dealt) / 52

TC is the final measure in a counting system's evaluation of a shoe's composition. It is not necessary to be extremely accurate computing TC because a counting system is only a very rough approxiamtion of a shoe's composition anyway. Reducing a counting system to a single TC value makes its implementation far simpler than the Best Card Counting method from above and the compromise made is to give up some potential accuracy in favor of simplification.

Balanced and Unbalanced Counts

There is one more step that can be taken in the quest for simplification. Some counting systems forget about TC altogether and just use RC. Commonly this is done in so called unbalanced counting systems.

• A counting system is said to be balanced when initial running count at the beginning of a shoe is such that at the end of the shoe, when every card is dealt, running count is exactly zero.
• A counting system is said to be unbalanced when initial running count at the beginning of a shoe is such that at the end of the shoe, when every card is dealt, running count is a value other than zero. The non-zero value when all cards are dealt is a measure of how far the unbalanced system is offset from balanced.

So far all of the sample counting systems presented have been balanced. They are designed to be balanced since each one's initial RC value is computed by summing rank group tags times number of cards in each rank group relative to a full shoe.

By the same token any of the sample counting systems could be changed to unbalanced systems simply by setting the initial RC to something other than this computed value. This offset is at the count user's discretion and could be used, for example, to eliminate negative numbers. However, once a count is offset to unbalanced it can no longer be true counted.

Counting systems that are used as unbalanced systems generally have these properties

• Their natural balanced initial RC is less than zero
• When their natural balanced RC equals zero (known as the count's pivot point) there is a positive player expectation

Counting systems with the above properties are generally offset by an amount equal to the difference between 0 and its natural initial RC for a single deck. That same offet is then applied to any number of decks.

This may sound difficult but it's not. For example sample Count #3 has a natural initial RC of -4 for single deck. The difference between 0 and -4 is +4. Therefore +4 is used as the offset from balanced for all number of decks. For your information sample Count #3 when converted to unbalanced in this way is the Unbalanced KO System.

Conclusion

Card counting is not an exact science but it can be a practical way to improve player's expectation in the game of blackjack.