Card Counting Basic Strategy
Card Counters' Basic Strategy: Is It For You?By Hal Marcus
(From Blackjack Forum Vol. XXIII, #4, Winter 2003/04
© 2003 Blackjack Forum
[Note from Arnold Snyder: The purpose of this article is to help players who are already counting cards to decide if they should use a fixed, altered version of blackjack basic strategy for their playing decisions, rather than varying their playing strategy by the count.
If you are new to card counting and other professional gambling methods for winning at blackjack, and want to learn how to get started with an easy system and strategy, see our Intro to Winning Blackjack page.]
Card Counting Basic Strategy, Introduction
One day in 1999 I started thinking about the different ways a player can gain an advantage over the casino through card counting:
Number 3 produces the greatest gain while requiring the greatest amount of effort. When using number 3, one can mitigate the effort required to a large extent by memorizing just the Top 16 indexes compared to a full table of 160+ indexes.
[Note from Arnold Snyder: The "Top 16" indexes referred to in this article are the 16 most important basic strategy deviations in a shoe game to a card counter's win rate. They are: Insurance, 16 v. 10, 16 v. 9, 15 v. 10, 13 v. 2, 13 v. 3, 12 v. 2, 12 v. 3, 12 v. 4, 12 v. 5, 12 v. 6, 11 v. A, 10 v. 10, 10 v. A, 9 v. 2, and 9 v. 7. For the count at which you deviate from basic strategy for the playing of these hands, see your card counting system.]
Standard blackjack Basic Strategy ignores the bet spread that card counters use when the count indicates the deck has switched to a player advantage. The development of a Count Index Playing Strategy considers the count to determine when to deviate from Basic Strategy, but also ignores the bet spread. What kind of strategy could be developed if the bet spread were taken into account?
Let's consider a six-deck game, 16 v. 10, where Surrender is not allowed. The Basic Strategy decision is hit. When using the Hi-Lo set of point count values, the index in the Count Index Playing Strategy is 0, meaning you should deviate from Basic Strategy and stand when the True Count >=0.
My thought was what is the best way to play 16 v. 10 all the time when factoring in the increase in your bet when the True Count >=0? If you are not going to deviate from Basic Strategy based on the count, does there exist a modified Basic Strategy that would improve your win rate?
Let's call the modified Basic Strategy, to be modified to take into account a card counter's bet-size variation, Card Counting Basic Strategy (CCBS).
In designing such a strategy, one thing I had to research was how sensitive the resulting set of modifications would be to variations in the bet spread and deck penetration? Things could get unwieldy quickly if there were substantial differences among Card Counting Basic Strategies as you used different bet spreads and factored in different levels of penetration.
For instance, if you use three different bet spreads, depending on the casinos you play, and experience four different levels of penetration at those casinos, you could be facing 12 different combinations and thus 12 possible sets of Card Counting Basic Stategies.
Developing a Card Counting Basic Strategy: Methodology
The Blackjack 6-7-8 Software, from within the program's "Develop A Playing Strategy" module, provides for the development of a Card Counting Basic Strategy. First, let's discuss how the program develops Basic Strategy, which is done by simulation instead of by using combinatorial analysis. The parameters to choose are:
To replicate the results from using combinatorial analysis, one would choose the penetration to be a shuffle after each round. I preferred to choose a level of penetration that represents what you will experience at thetables, such as 75% for a 6-deck game.
Then the Blackjack 6-7-8 software takes each 2-card combination (for 16, for example, the 2-card combinations are 10-6, 9-7, and 8-8) and plays blackjack against the various dealer upcards. For one cycle, the program will stand each time. On the next cycle the program will hit each time, etc. until all the decisions have been played.
The results for the different two-card combinations are then combined by weighting the outcome for each two-card combination by a factor that reflects how often the two-card combination appears (for 16, 10-6 appears more often because there are four times as many 10s in the shoe as other types of cards). Once the results are compiled for the two-card combination for each decision, the result with the largest win determines the correct playing decision.
To derive CCBS, the parameters chosen consist of the three parameters stated above for Basic Strategy plus two more:
The process for developing CCBS begins with the process used for Basic Strategy, modified to use the count for each hand to determine the bet amount. The program tracks the result for each hand which reflects the bet amount. For example, consider this Betting Strategy:
(You may use a different Betting Strategy to reflect optimal values for risk of ruin, but tests have shown no difference in the CCBS playing decisions for an optimal set of bet amounts vs. the ones in the talbe above, as long as each uses the same bet range from lowest to highest bet.)
Take 9 v. 2. For six decks, Basic Strategy says hit because the expected value from hitting is greater than from doubling down. The development of Card Counting Basic Strategy considers the result based on the bet according to the count for each hand played. For example, you win more of your double downs at the higher counts, and since you bet more at the higher counts, those wins contribute more to the positive part of the result compared to the losses from doubling down at the lower counts with a smaller bet. For certain decisions, this effect results in a deviation, or modification, of Basic Strategy.
Results of Play All with Card Counting Basic Strategy
For S17, DAS and LS, there are 17 playing decision changes from Basic Strategy. For instance, with Card Counting Basic Strategy you should double 9 v. 2. For 16 v. 10, when you can't surrender, you should stand instead of hit. All the decision differences between Basic Strategy and CCBS are depicted later in the article. The effort required to master CCBS is the same as the effort required for Basic Strategy. And you don't have to learn and recall any indexes.
What if your bet spread is 8 to 1 instead of 16 to 1? I hope you don't use an 8 to 1 bet spread unless you're doing quite a bit of Wonging in/Wonging out. But let's assume you were to use an 8 to 1 bet spread and play all. Compare using Card Counting Basic Strategy developed with a 16 to 1 bet spread vs. Card Counting Basic Strategy developed with an 8 to 1 bet spread—there is no significant difference in win rate.
There is also no significant difference in win rate when using a Card Counting Basic Strategy developed with 83% penetrations vs. a CCBS developed with 75% penetration. This is good news if you were concerned about needing a plethora of CCBS tables in your arsenal.
You might find significant differences in win rates when comparing Card Counting Basic Strategy for extreme measures, such as 50% vs. 83% penetration, or a 4 to 1 bet spread vs. a 16 to 1 bet spread. You can also use the same Card Counting Basic Strategy with a variety of sets of point count values (such as Hi-Lo, K-O, and Red 7).
Let's consider three scenarios for 6-deck, S17, DAS, resplit all pairs up to four hands, late surrender, insurance, with a 16 to 1 bet spread: 1) Hi-Lo for betting coupled with Basic Strategy; 2) Hi-Lo for betting and CCBS for playing decisions; and 3) Hi-Lo for betting and the Top 16 indexes for playing strategy. Here are the results from running simulations of 500 million rounds for each scenario (many of you use a bet unit higher than $5—naturally you would just multiply the dollar amounts listed here by the appropriate factor for your betting):
Card Counting Basic Strategy (Scenario 2) produces a 6% increase in amount won compared to Scenario 1, while using the Sweet 16 indexes (Scenario 3) yields a 10% gain over using CCBS.
Why Use A Special Card Counting Basic Strategy?
Perhaps you use a Count Index Playing Strategy, such as the Top 16 indexes, and are wondering why you should consider Card Counting Basic Strategy when you can wring a higher win rate by varying your playing strategy based on the count. First, you may make enough mistakes in trying to quickly recall whether to deviate from Basic Strategy that you negate the benefit of using count indexes.
But perhaps more significantly, Card Counting Basic Strategy provides potential camouflage. As casino surveillance has advanced to the point of being able to detect when a player correctly deviates from Basic Strategy, the length of your session becomes reduced.
In theory, with Card Counting Basic Strategy, since for quite a few playing decisions (17 decisions in this article's illustration), you can always deviate from Basic Strategy, it may take casino surveillance longer to conclude that you are a skilled player. This should reduce the chance of getting barred. In addition, your table sessions can be longer, and you may have a higher dollar expectation per casino visit compared to using a Count Index Playing Strategy.
Let's say that you are able to get away with playing 45-minute sessions when using a Count Index Playing Strategy. Using Card Counting Basic Strategy instead of a Count Index Playing Strategy, if you were able to extend your session by just five minutes, to 50 minutes per session, due to the camouflage benefit of Card Counting Basic Strategy, your expected dollar win would be the same as using a Count Index Playing Strategy for 45 minutes.
Card Counting Basic Strategy with Wonging In
What happens when you only play if the True Count >=1? The following table provides the results of the same three scenarios as before, with a 16 to 1 bet ratio: 1) Hi-Lo for betting coupled with Basic Strategy; 2) Hi-Lo for betting and Card Counting Basic Strategy for playing decisions; and 3) Hi-Lo for betting and Top 16 indexes for playing strategy.
Using CCBS produces an expected win of $205 more than using Basic Strategy while only giving up $66 to Top 16. Therefore, when you use a Wong-in tactic, CBS gets you very close to the result of the Top 16.
And with the camouflage potential of using CCBS, you should be able to extend the length of your playing sessions. Playing for 16 hours, 22 minutes instead of 16 hours (2% longer), your expected win using CCBS would be the same as it would with Sweet 16. Let's say you could squeeze in an extra two hours of play with CCBS compared to using Sweet 16. Then CCBS would lead to an expected win of $3,311—$302 more than Sweet 16.
When Wonging in, you may want to reduce your bet spread to increase the longevity of your playing sessions. The following table shows the results of an 8 to 1 bet ratio (bet 40 for count >=4).
Using CCBS produces an expected win of $188 more than using Basic Strategy while giving up $49 to Top 16. Here it takes 19 minutes of additional play (a total of 16 hours, 19 minutes instead of 16 hours) for CCBS to yield the same expected dollar win as Top 16. For 18 hours of CCBS play vs. 16 hours of Top 16, CCBS would generate an expected profit of $2,791 vs. $2,530 for Top 16, an increase of $261.
The Card Counting Basic Strategy Playing Strategies
This table depicts the 17 CCBS decisions that differ from the playing decisions in standard blackjack Basic Strategy:
Card Counting Basic Strategy offers a higher win rate for card counters when compared to Basic Strategy because it takes into account the effects on your win rate of using a betting spread. For players who use a Count Index Playing Strategy, such as the Top 16, consider using CCBS for greater session longevity due to the camouflage value of CCBS, and perhaps overall greater longevity in your blackjack playing career.
To do your own CCBS computations, get the Blackjack 6-7-8 Software. For example, using the software, you may wish to analyze different bet spreads and numbers of decks. In addition, you can use various betting constraints, such as never increasing the bet more than twice the prior bet, to see how the different playing strategies compare.
Among the new Blackjack 6-7-8 Strategy Cards, one of the cards represents CCBS—the one titled Blackjack Counter Basic Strategy Card, 4-8 Decks. Each card contains four tables to cover the combinations of H17 & S17, and DAS & no DAS. An item for future study would be to determine whether the playing decisions would change for a CCBS developed for a Wonging in or out scenario, and what the impact on the win rate would be. ♠
Hal Marcus' official laminated Blackjack Counter Basic Strategy Card, 4-8 Decks are now available for convenient reference during your playing trips.
Although Hal Marcus no longer sells his Blackjack 6-7-8 Software, you can run all the strategy simulations you can think of with Norm Wattenberger's Casino Verite Blackjack Software.
For more information on how to win at blackjack with card counting and other professional gambling methods, see Arnold Snyder's Blackbelt in Blackjack.
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