Card Counting Edge
- Card Counting House Edge
- How Much Of An Edge Does Card Counting Give
- Card Counting Edge Calculator
- Blackjack Card Counting House Edge
- Card Counting Player Edge
- Blackjack Card Counting Edge
Advanced blackjack strategy – card counting. I’m sure if you’ve had any experience in the casino, you have heard of what is known as card counting – a system that allows you to gain a positive expectation while playing blackjack putting the house edge in your favor. Simple card counting is a legal way to increase your edge against the house. Last, we have provided a unique Card Counting Trainer to help you improve and hone-in your skills on applying the Hi-Lo Counting method keeping track of the shoe’s count.
- Appendices
- Miscellaneous
- External Links
Rules that give the casino a small enough house edge that card counting can be effective. If the blackjack rules are too crummy, then card counting won’t be enough to beat the game. Things like “Blackjacks pay 6:5” or “No doubling after splits” tend to be too much for card counting to overcome. Adequate Deck Penetration. Just as long as they are aware of the odds that they face and understand the house edge that they are against, card counting is a great skill to have when you tap into blackjack gambling. The Interactive Card Counting Trainer is a software tool that will teach you how to count cards accurately. No experience is required to use the tool, just the desire to want to learn a mathematically proven technique that will give you the advantage over the casino when you play blackjack.
Introduction
Let me say loud and clear that card counting is hard and is not as rewarding as television and the movies make it out to be. If it were an easy way to make money, then everyone would be doing it.
If you do not know the basic strategy, trying to count cards is highly ill-advised. Experienced card counters still play by the basic strategy the great majority of the time.There can be no short cut around learning the basic strategy, those who attempt card counting without a firm foundation in the basic strategy are making a big mistake.
To be a successful counter you have to be able to countdown a deck fast and memorize large tables of numbers as well as make it look like you're just a casual player.Furthermore, with today's rules, a realistic advantage the counter will have is only 0.5% to 1.5%. You will not win money slowly and gradually but your bankroll will go up and down like a roller coaster in the short run. Only in the long run, over hundreds of hours of playing, can you count on winning.
The underlying principle behind card counting is that a deck rich in tens and aces is good for the player, a deck rich in small cards is good for the dealer. When the counter knows the odds are in his favor, he will bet more, and adjust his playing strategy to stand, double, and split in some plays where basic strategy says to stand. All the options the player has at his disposal favor the player even more when the deck is ten and ace rich. Here is a list and a brief reason why.
Standing: The player may stand on stiff totals of 12 to 16, and the dealer may not. In ten-rich shoes, hitting stiff hands becomes more dangerous, favoring the more conservative player strategy.
Insurance: On average, when the dealer has an ace up, the remaining cards in blackjack will be 30.87% tens (based on a six-deck game), making insurance a bad bet. However, if the probability gets above 33.33%, it becomes a good bet. Counters know when the remaining cards are ten-rich, and make powerful insurance bets at those times.
Doubling: Usually, when the player doubles he wants a ten. In ten-rich shoes, the player makes better double downs, getting closer to 21.
Blackjack: Both player and dealer will see more blackjacks, but the player gets paid 3 to 2, and the dealer does not.
Surrender: The alternative to surrendering is much worse in ten-rich shoes. If the alternative is hitting, the player is more likely to bust. If the player would otherwise stand, due to the high count, the dealer is still more likely to get a 10. While the counter will surrender more in high counts, the savings will be greater.
Splits: The player is usually splitting high cards and/or off of a weak dealer card. Either way, a ten-rich shoe helps the player get higher totals, and increases the probability of the dealer busting.
I'm working on an in-depth study of how these effects break down. The contribution to each factor depends on the rules, deck penetration, and bet spread. However, based on average conditions in a six-deck shoe, my initial results break down the benefits of counting as follows.
Why Card Counting Works
| Player Option | Portion of Benefit |
|---|---|
| Stand | 40% |
| Insurance | 34% |
| Double | 9% |
| Blackjack | 7% |
| Surrender | 6% |
| Split | 4% |
The probability for insurance was taken from Don Schlesinger's 'Illustrious 18' list, as found in Blackjack Attack. The rest of the breakdown is mine.
To gauge the richness of the deck in good cards, the player will keep track of the cards the are already played. Strategies vary, but all assign a point value to each card. For example, the hi-lo count assigns a value of +1 to 2, 3, 4, 5, and 6, and -1 to tens and aces. Everything else is 0, or neutral. At the beginning of a deck or shoe, the count is 0. Then the counter constantly adds and subtracts from the count, according to the cards played. This running total is called the 'running count.' A positive count means that a disproportional number of small cards have already been played, which means that the deck is rich in large cards. To determine the 'true count,' divide the running count by the number of decks left to be played, or in some strategies, the number of half decks. This will tell you the relative richness of the deck in good cards.
The true count is used in two ways, to determine how much to bet and how to play your hand. Unless it is obvious, every situation has a line in which you should play one way if the count is above the line and another if below. For example, a 12 against a 6 may dictate that you stand if the true count is -1 or greater and hit if the true count is less than -1. The counter will also bet more when the true count is high, meaning the deck is rich in good cards.
A problem arises when it comes to treating aces. The player should bet more when the deck is rich in aces since they add to the probability of getting a blackjack. However, when it comes to playing your hand, the number of aces left is not nearly as important as the number of tens, so it is desirable, but not necessary, to distinguish between tens and aces. Some card counting strategies keep a side count of aces. In the Hi-Opt I and Revere Plus/Minus aces are counted separately and only considered when making the wager. This is a more accurate and powerful way to play than assigning a negative value to aces and not keeping a side count, as some strategies do. Yet, many people feel that for the beginner it is too confusing to keep two counts. A player is more likely to make mistakes keeping two counts and that costs money. The efficiency of a strategy that does not keep a side count of aces is only modestly less, but you likely will gain more from fewer mistakes made. Different experts fall in various places in the spectrum in terms of what to recommend for the beginner. The Zen Count takes the middle ground and gives aces a value of -1 and tens -2. Personally, I have tried both and would recommend against a count that requires a side count of aces to a person ready to take up card counting. The Uston Advanced Plus/Minus is a good strategy that does not involve an ace side count and can be found in the book Million Dollar Blackjack. How well you know a counting strategy is much more important than which strategy you know.
Legally speaking, the player may play blackjack any way he wants without cheating or using a computer, and the casinos may do anything from making conditions unfavorable to barring, in an effort to stop anyone who they deem has an advantage over the game. Much of the challenge of card counting is avoiding suspicion that you are anything but a normal non-counting player. The most obvious indication that somebody is counting is that they make a substantial increase in bet size after a lot of small cards leave the table. Although the greater the factor by which you can increase your bet the greater your odds of winning, more than doubling your last bet is a fast way to arouse 'heat'from the dealer and pit boss. Usually when casinos employees realize you are counting, they will either shuffle the cards whenever you increase your bet, essentially removing any advantage, or ask you to leave.
This is only scraping the surface of the subject of card counting. I suggest the following pages of mine.
Practice
Practice your card counting skills with our trainer.
Internal Links
- Blackjack main page.
- Hi-Lo Count.
- The Ace-Five Count, possibly the easiest way to count cards.
- Book review section, for suggestions on good blackjack books.
External Resources
- Blackjackinfo - A complete course covering everything from basic strategy to card counting
- BJ21 - By Stanford Wong; A membership based community covering all aspects of card counting.
Card Counting House Edge
Written by: Michael Shackleford- Appendices
- Miscellaneous
- External Links
On This Page
Introduction
The Hi-Lo Count is the most widely written about, and in my judgment, the most commonly used card counting strategy. The High-Low was first introduced in 1963 by Harvey Dubner1. It has since been discussed by just about all the major blackjack writers. In my opinion, the best introductory treatment is in Professional Blackjack by Stanford Wong, and the most detailed coverage is in Blackjack Attack by Don Schlesinger.
How it Works
How Much Of An Edge Does Card Counting Give
Following is a brief explanation of how to use the Hi-Lo.Step 1: Assign a point value to each rank, as follows.
High-Low Point Values
Step 2: Start with a 'Running Count' of zero at the start of the deck/shoe. As cards are revealed, keep adding or subtracting from the Running Count, according to the point system in step 1. For example, if the first ten cards to come out of the shoe were 3, 5, K, 7, Q, A, 8, 5, 4, 2, then the running count would be 1 +1 -1 +0 -1 -1 +0 +1 +1 +1 = +2.
Step 3: Divide the running count by the number of decks remaining, to get what is known as the 'True Count.' This is the part that beginning counters hate. You don?t need to be exact. A rough estimate will do, in my opinion. Let's look at example. The running count is +7 and there are about 4 decks left. The true count would be 7/4 = 1.75. Round that up to 2, to keep it simple. The more you play the more you will be comfortable eyeballing this adjustment, without doing any real division in your head. Usually the right play is obvious. In borderline cases only will you need to do this True Count conversion.
Step 4: The greater the true count, the more you should bet. This is where card counting becomes more art than science. Some blackjack books give rigid rules on how this should be done. However, the casino managers have read these books too, and the patterns recommended in earlier books now set off red flags. How you do this should depend on your own style, and how much heat you are getting. It helps avoid heat to keep the ratio of maximum bet to minimum bet to a limit, known as the ?Bet Spread.? Only increasing bets after a win, only decreasing after a loss, and staying the same after a push, makes play look more natural, but at a cost to profitability.
Step 5: For some hands, you will play according to the True Count and a table of 'Index Numbers,' rather than basic strategy. The greater the count, the more inclined you will be to stand, double, split, take insurance, and surrender. For example, the Index Number for a player 15 against a dealer 10 is +4. This means the player should stand if the True Count is +4 or higher, otherwise hit.
The following tables are known as the 'Illustrious 18' and 'Fab 4' respectively.2 They appear in Blackjack Attack by Don Schlesinger, and are republished here with permission. These are the most important index numbers to remember. Knowing only these will give the counter 80% to 85% of the value of knowing every index number, based on a six-deck game. The difference is more in single and double-deck games. The lists are given in order of value. If you can?t memorize all of them, start at the top, and work your way down.
Illustrious 18
| Order | Play | Index |
|---|---|---|
| 1 | Insurance | +3 |
| 2 | 16 Vs. 10 | +0 |
| 3 | 15 Vs. 10 | +4 |
| 4 | 10,10 Vs. 5 | +5 |
| 5 | 10,10 Vs. 6 | +4 |
| 6 | 10 Vs. 10 | +4 |
| 7 | 12 Vs. 3 | +2 |
| 8 | 12 Vs. 2 | +3 |
| 9 | 11 Vs. A | +1 |
| 10 | 9 Vs. 2 | +1 |
| 11 | 10 Vs. A | +4 |
| 12 | 9 Vs. 7 | +3 |
| 13 | 16 Vs. 9 | +5 |
| 14 | 13 Vs. 2 | -1 |
| 15 | 12 Vs. 4 | 0 |
| 16 | 12 Vs. 5 | -2 |
| 17 | 12 Vs. 6 | -1 |
| 18 | 13 Vs. 3 | -2 |
The player should stand/double/split if the True Count equals or exceeds the Index Number, otherwise hit. The player should take insurance if the True Count is +3 or greater.
Fab 4 Surrenders
| Order | Play | Index |
|---|---|---|
| 1 | 14 Vs. 10 | +3 |
| 2 | 15 Vs. 10 | +0 |
| 3 | 15 Vs. 9 | +2 |
| 4 | 15 Vs. A | +1 |
Card Counting Edge Calculator
The player should surrender if the True Count equals or exceeds the Index Number.
A full table of all index numbers can be found in Chapter 3, and Appendix A, of Professional Blackjack by Stanford Wong.
The next table shows some statistics using the High-Low. The blackjack rules this table is based are liberal Vegas shoe, as follows:
Six decks
Dealer stands on soft 17
Surrender allowed
Double after split allowed
Player may resplit to four hands, including aces
To avoid setting off red flags, the simulation increased the bet after a win only, decreased after a loss only, and always stayed the same after a push, except resetting to a minimum bet after a shuffle. The simulation rounded the remaining decks to the nearest half deck, otherwise playing perfectly.
High-Low Statistics
| Spread | Penetration | Index Numbers | Player Adv. | Std. Dev. | Avg.Bet |
|---|---|---|---|---|---|
| 1 to 5 | 4 | I18+F4 | 0.157% | 1.50 | 1.35 |
| 1 to 10 | 4 | I18+F4 | 0.368% | 2.04 | 1.57 |
| 1 to 15 | 4 | I18+F4 | 0.578% | 2.67 | 1.73 |
| 1 to 5 | 4.5 | I18+F4 | 0.300% | 1.60 | 1.41 |
| 1 to 10 | 4.5 | I18+F4 | 0.587% | 2.27 | 1.68 |
| 1 to 15 | 4.5 | I18+F4 | 0.834% | 3.06 | 1.90 |
| 1 to 5 | 5 | I18+F4 | 0.469% | 1.70 | 1.47 |
| 1 to 10 | 5 | I18+F4 | 0.837% | 2.52 | 1.80 |
| 1 to 15 | 5 | I18+F4 | 1.147% | 3.49 | 2.10 |
| 1 to 5 | 4.5 | All | 0.313% | 1.61 | 1.41 |
| 1 to 10 | 4.5 | All | 0.608% | 2.29 | 1.68 |
| 1 to 15 | 4.5 | All | 0.862% | 3.10 | 1.91 |
| 1 to 5 | 5 | All | 0.494% | 1.71 | 1.47 |
| 1 to 10 | 5 | All | 0.857% | 2.55 | 1.81 |
| 1 to 15 | 5 | All | 1.182% | 3.54 | 2.11 |
Blackjack Card Counting House Edge
Explantion of columns
Spread: This is the ratio of the player?s minimum bet to maximum bet. The bigger the range, the greater the player?s advantage, and bankroll volatility. A wide bet spread also sets off a red flag. In a six-deck game, I think a 1 to 15 spread is about the most aggressive the player should get. The simulation played one betting spot only.
Penetration: How many decks played before reaching the cut card. In a six-deck shoe, 4.5 is the norm.
Index Numbers: I already explained index numbers above. Simulations were run using both the Illustrious 18 and Fab 4 (I18+F4) above, and with the full table. The difference is not much, which shows that knowing the top 22 gets you most of the benefit of knowing all of them.
Player Advantage: This is the ratio of net player win to total initial bets. For example, in the last row, the player could expect to win 1.182% of his total initial bets.
Standard Deviation: This is a term for the volatility per initial bet.
Average Bet: The average final bet per hand, compared to the lowest bet For example, in the last row, if the player?s minimum bet were $100, his average bet would be $211. This includes additional money bet due to doubles and splits.
This table was created using CVCX Blackjack Analyzer by Casino Vérité. This software produces hundreds of different statistics for just about any set of rules, betting strategies, and playing strategies. For the player who wants to run these tests, this software is the best there is, in my opinion.
Footnotes
- Professional Blackjack by Stanford Wong, page 31, 1994 ed.
- Blackjack Attack by Don Schlesinger, page 62, 2004 ed.
Acknowledgments
Don Schlesinger: For his permission to reprint the Illustrious 18 and Fab 4 tables from his book, Blackjack Attack.
Norman Wattenberger: For his complimentary use of CVCX Blackjack Analyzer by Casino Vérité.
Practice
Card Counting Player Edge
Practice your card counting skills with our trainer.
Further Reading
- Card Counting Introduction.
- Wizard Ace-Five Count: Very easy and simple card counting strategy.
- '21' Movie Review: Truth and fiction about the movie about the MIT card counting team.
- Blackjack book reviews.
- Main blackjack page.