If you only read one section of this file, and you don't already know what Basic Strategy is, then this is the section you should read. Knowing Basic Strategy is critical to you gaining an advantage over the house.
The Basic Strategy for a particular set of rules was developed by intensive computer simulation which performed a complete combinatorial analysis. The computer "played" tens of thousands of hands for each BlackJack situation possible and statistically decided as to which play decision favored the player. The following three charts are the results of this analysis.
|Download the Grande Vegas Casino Software|
It's possible for a blackjack player to gain the long-term advantage over the casino. This means you will win more money than lose over time. To do so, you must bet more when the odds of winning a hand are in your favor and less when the odds shift to the dealer. In order to know when the odds shift from dealer to player you must keep track of the cards as they are played. This technique, known as card counting, does not require a photographic memory (that's a misconception).
First off, you must understand that the probability of winning a hand in blackjack is very dependent upon the mix of cards remaining to be played. If this mix happens to contain an abundance of large cards like 10's, picture cards and aces, then your chances of winning improve. On the other hand, if the mix of unplayed cards contain an abundance of small cards like 2 though 6's, then the odds shift in favor of the dealer.
Here are some of the reasons why large cards favor the player and small cards the dealer. When you have a mix of unplayed cards that contain an abundance of large cards there will be more blackjacks dealt. Yes the dealer has just as much chance of getting a blackjack as a player but the player gets paid a bonus on a blackjack hand (3 to 2 payoff). Also, when the dealer has a stiff hand (like 12 to 16) he must draw. If the deck is rich in large cards, the dealer will most likely bust. Unlike the dealer, the player does not have to draw on a stiff hand.from a deck rich in large cards. Also players will profit more when doubling down in a mix rich in large cards. Likewise if a player has a pair, he can split the pair into two hands, a sometimes lucrative play when the dealer shows a weak face card. The dealer on the other hand will usually make good when he holds a stiff hand and draws from a mix of cards containing an abundance of small cards.
How does a player know when the unplayed cards are either rich in large or small cards? You must keep track of the cards as they are played because with this information you can deduce whether the unplayed cards are rich in small or large cards.
In order to keep track of the cards you must assign a tag to each card for card counting purposes. The dealer favorable small cards - 2, 3, 4, 5, 6 - have a tag of +1 (plus one). The player favorable large cards - 10, J, Q, K Ace- have a tag of -1 (minus one). The remaining cards - 7, 8, 9 - have a tag of 0.
Card counting is simply adding of the tags for each card that is played. For example after the shuffle, your starting count is 0 (this indicates an equal number of large and small cards). As the first round of play begins and cards are faced, you must add the tags of each card. If player #1 shows a 4 and 6 your count is +2 (sum of +1 tag for the 4 and +1 tag for the 6). Continue to add the card tags for every card that you see. If it's a small card you increase you count by 1. If it's a large card you decrease your count by 1. At the end of the first round your count will be either a plus or negative number. If your count is positive it means that there were a lot more small cards than large cards played in the previous round. That means the reverse must be true for the unplayed cards - namely the unplayed cards contain a slight excess of large cards over small cards. This is precisely the point at which the edge swings to the player on the next hand and therefore the player should make a larger bet. Likewise when the count is negative, the edge is with the
dealer and the player should bet the minimum.
To learn how to count, get a deck of cards, shuffle them, and then turn one card over and recite the tag for that card. For example if your first card is a 6, recite "plus 1". If the next card is a queen recite "minus 1". Continue to do this for the entire deck of cards to help you associate the tag for each card.
Next take the same deck of cards and flip the cards over one-at-time and keep the running count. For example if the first card is 5, you count is "plus 1". If the next card is a 3, your running count is "plus 2". Assume the next card is a 7. Your running count is still "plus 2". Continue to flip each card and add the tags. When you are finished counting a deck of cards your running count should be 0 (this is how you can check the accuracy of your counting).
Now you are ready to cancel the tags of a group of cards to make counting even easier. Instead of flipping over one card at a time, flip 2 or 3 cards at one time. Glance at the cards and cancel every high card and low card. When you learn this technique you won't have to count every single card that you see on the layout.
Keep practicing card counting with your deck of cards until you can count down a deck accurately in 30 seconds or less.
In part 2 of this series on Advanced Blackjack Strategies I'll show you how to bet based on your running count.
In Part 1 of this series we showed how a blackjack player can gain the long-term advantage over the casino by card counting and showed how card counting works. Here, we'll show you how you can use the information to beat the single deck blackjack games.
The single deck blackjack game has an inherent advantage over multiple deck blackjack games. First, the casino's edge against a basic strategy player is close to 0. Secondly, you will experience positive counts more often therefore you do not need a very large bet spread to beat this game (a 1-4 bet spread will do just fine). The only negative aspect of a single deck game is that it generally draws more attention from pit bosses because they know card counters can beat single deck games more readily compared to multiple deck games.
The first thing you must do is evaluate the rules of the single deck game because some games have good rules and other not so good. By referring to the table below, you will get an idea of how the mix of rules effect the casino's edge (CA) in single deck games and a list of some of the casinos that offer these games. The worst rules for single deck games occur when the casino restricts doubling to a two card 10 and/or 11. The best rules allow unrestricted doubling or replace the double down rule with resplitting of aces. Better yet are casino's that offer single deck games in which the dealer stands on soft 17 rather than hit (you can actually have the edge without card counting in a single deck game where the dealer stands on soft 17).
As a general rule, you'll find more single deck games with favorable rules in Las Vegas than elsewhere.
Another very important variable that determines whether a single deck game is worth your time is the penetration or percentage of cards that are dealt from the deck prior to the shuffle. Some casinos offer single deck games but shuffle after one or two rounds. Forget these games. You want at least 50 and ideally 75% of the cards to be dealt. The more cards that you see prior to the shuffle, the greater will be your advantage with card counting. This is very important so shop around for the best penetration.
For camouflage purposes do not increase your bet from 2 to 4 units unless you also won the hand. Also do not increase or decrease your bet size following a push. These are important betting rules if you are a green ($25) or black ($100) chip bettor since you will get more scrutiny from the casino bosses compared to a player betting red ($5) chips. If you are a $5 minimum bet player your betting spread would be $5 to $20. Likewise for a $25 player it would be $25 to $100.
To withstand the normal short-term fluctuations in your bankroll that will occur when you play blackjack, you should have a bankroll equal to 125 times your maximum bet. That's $5,000 if you spread $5 to $20 and at least a $12,000 if you spread $25 to $100.
Another advanced strategy is how to compute the true count. You will use the latter to vary the size of your bets in single and multiple deck games and also when to deviate from the basic playing strategy.
Why do you have to convert your running count to a true count? Because the running count doesn't take into consideration the number of unplayed decks of cards and therefore you can overestimate your advantage. For example, a running count of +6 with 2 decks unplayed in a 6-deck shoe game is a greater advantage for the player than the same running count with 5 unplayed decks of cards. To compensate for this difference, we normalize the running count by dividing the number of unplayed decks in order to get a true count per deck.
Mathematically, true count is the running count divided by the number of decks unplayed. Suppose your running count is +6 after the first round in a six-deck shoe. There is essentially 6 decks left unplayed so the true count is +1. If instead there were only 2 unplayed decks, your true count would be +3.
You can determine how many unplayed decks of cards there are in a multiple deck game by eyeballing the number of decks of cards in the discard tray. For example, if you are playing in a 6-deck shoe game and you estimate 3 decks of cards in the discard tray, then there must be 3 unplayed decks left in the shoe. Likewise, if 2 decks are in the discard tray, then there must be 4 uplayed decks in the shoe.
You don't have to be super accurate in estimating the number of decks in the discard tray. In fact if you practice at home, you'll see it's not that difficult to estimate the number of decks in a stack of cards.
Remember that you will be converting your running count to a true count just for a split second so you know how much to bet then you revert back to keeping the running count of the cards.
The more positive the true count, the greater will be the counter's advantage on the next hand. As a general rule, each additional unit of the true count will add 0.5% advantage to the player. In a typical 6 deck game, the casino's edge after the shuffle is about 0.5% (that's equivalent to a true count of 0 or a neutral deck). When the true count is +1, the player is playing even against the casinos and when the true count is +2, the player has a 0.5% edge and at a true count of +3 the counter has about a 1% edge.
In Part 2 of this series we described how you could use the running count in single deck games to vary your bets. It's also possible to compute a true count in single deck games
(which you will need in order to vary your playing strategy). The equation is running count divided by the number of unplayed cards. However, an easier way to do this conversion in single deck games is as follows:
Running count = true count during the play out of the first quarter deck
Multiply the running count by 1.5 for the play out of the second quarter deck
Multiply the running count by 2 for the play out of the third quarter decks.
Notice that in single deck games the true count is always greater than the running count whereas in shoe games it's the other way around.
Let's try an example so you see how easy this is. If you are playing in a single deck game and during the play out of the second quarter deck your running count is +2, your true count is +3 (+2 running count times 1.5). If your running count is +2 during the play out of the third quarter deck your true count is +4 (+2 running count times 2).
In single deck games a bet spread of 1 to 4 units is sufficient to gain the edge. A suggested betting scheme is to bet 1 unit when the true count is 0 or negative, 2 units at true count +1, then bet 3 units when the true count is +2, and 4 units when the true count is +3 or more.
For double deck games, I would suggest a 1 to 5 bet spread using the above betting schedule except bet 5 units when the true count is +4 or more.
For 6 deck games, you will need at least 1 to 8 and preferable 1 to 10 betting spread. For 8 deck games your betting spread should be 1 to 10 or 12. An easy to remember betting schedule for 6 deck games is to just bet two times the value of the positive true count. If your true count is +1, bet 2 units, at a +2 true count bet 4 units, at +3 bet 6 units and +4 bet 8 (or 10) units. For an 8 deck game I'd suggest a slightly more aggressive betting schedule with a top bet of 12 units (+1 bet 3 units, +2 bet 5 units, +3 bet 8 units and +4 or more bet 12 units).
The above betting schedule is not absolute. The key point is that your big bets need to be larger than your small bets because the very positive true count situations do not occur that often especially in shoe games. In fact most of the times you will be playing at a disadvantage making small "waiting" bets until the advantage turns in your favor and then should bet more.
Another more practical and easier way to bet using the true count is to parlay your bet when you win and have the advantage. In fact this method of betting helps disguise the fact that you are card counting. I'll discuss this point more in part 4 of this series along with another important variable, the penetration or the percentage of cards that are played prior to the shuffle.
In the previous three articles in this Advanced Blackjack series I described in detail how it's possible to gain a positive expectation playing blackjack by learning how to card count. However, it's important that you just don't jump in and play any old blackjack game. You've got to know what are the most important factors that make a blackjack game "beatable" or not.
The most important criteria for card counters is the penetration or the number of cards that will be dealt before the dealer shuffles. No casino will deal every single card before shuffling because a counter would have a tremendous advantage on the last few hands. Therefore just about every casino will deal only a certain percentage of the cards.
We have studied the effect of penetration on a counters advantage in great detail. In one study, using typical Las Vegas playing rules and a 1 to 4 bet spread in a 2-deck game, a counter playing heads up with the dealer would have a 1.0% advantage if 70% of the cards were dealt. If 90% of the cards were dealt, the counter's advantage would increase by 80% to 1.8%. If instead only 50% of the cards are dealt, the counter's edge would decrease by 50% to only 0.5%.
There have been many other computer studies by scores of other blackjack theoreticians that have proven this fact over-and-over, namely that the penetration has a major effect on your winnings.
Most counters will not make a single bet unless the penetration is 75% or more. This means in a typical 6-deck game, the dealer cuts off only 1.5 decks of cards. Likewise you are wasting your time and money trying to count in a game with only 50% penetration.
Most casinos are fairly strict about the placement of the cut card by the dealer after the shuffle and cut. Many have a measuring device on the side of the dealing shoe that indicates to the dealer where to position the cut card. However, there are still many casinos that only give guidelines to the dealer as to how many decks to cut off. It's possible therefore to find a dealer who gives a more liberal cut, say cutting off only 1 deck instead of 1.5 decks in a 6-deck game.
Another important criteria that card counters use to evaluate a blackjack game are the playing rules. For example, the fewer the number of decks of cards the greater will be the edge to the player. Also rules that allow doubling after pair splitting, late surrender, and the dealer standing rather than hitting on soft 17 are favorable for players. But a word of caution is in order. Some games with marginal rules can still be beaten if the penetration is good. For example most counters shun an 8-deck game but if the rules are decent and the penetration is 75% it would be a better game compared to say a 6-deck game with similar rules but only a 50% penetration. Likewise a single deck game with bad rules but 70% penetration is more profitable than one that deals less than 50% of the cards with good rules.
It's to a counters advantage to play at tables which are not crowded with other players. The best is playing head up with the dealer. This allows you to see more cards before making your playing decision. Also, when the count gets high, you will have just as much chance as the dealer of getting the aces and tens. Counters can also spread to 2 hands in high-count situations giving them an even greater chance of drawing the aces and tens. Playing at less crowded tables will increase the number of hands per hour dealt and a counters win rate.
Another important point is whether or not the pit boss will allow a decent bet spread. In single deck games you'll need to spread at least 1 to 3-4 betting units and in 6-deck games, 1 to 8-10 betting units. If you are limited in your bet spread by a nervous pit boss that gives you "heat" every time you make a large bet, then your profit potential decreases.
As you can see, learning the theory of card counting is one matter, but applying it to generate winnings is quite another task. Finding good playing conditions is very important. But there are other skills that must be mastered like balancing profits with risk, disguising your skills when you play, and knowing the typical countermeasures that casinos employ against counters. I'll cover these other important topics in future articles in this series. Until then, go out and get a blackjack.
In the previous series on advanced blackjack playing strategies I explained how to use card counting to vary your bets and gain the edge over the casino. In essence you bet more when the count tells you have the advantage and bet less when the count indicates the dealer has the better of it.
Besides using card counting to vary the size of your bets, you can also use it to vary the basic playing strategy. When you think about it, it makes sense. If your count tells you that the remaining unplayed card are rich in ten value cards, then hitting a hard 16 when the dealer shows a 10 face card might not be the best play in this situation. Likewise, taking insurance when the dealer shows an ace upcard might also make sense in this situation (since you are betting that the dealer has a ten in the hole).
Blackjack computer software can be used to determine the value of the true count that a player should deviate from the basic playing strategy. These values, called indices, have been published in a host of blackjack books including my Blackjack: Take The Money & Run.
When just starting to play blackjack, people spend weeks memorizing tables of indices. For every hand and dealer upcard an index was listed. For example for the popular Hi/Lo card counting system, the index number for hard 12 vs. 2 was +3. Normally the basic strategy play is to hit a hard 12 if the dealer shows a 2 upcard. But the index number of +3 tells you that when your true count is +4 or higher you should deviate from basic strategy and stand. The reason of course is that with a true count of +4, the unplayed cards are rich in tens and if you drew a card you would have a high probability of busting. There are no guarantees you will win if you stand but you will win more money in the long run if you stand when the true count is +4 or higher (likewise you should hit if it's +3 or less).
Memorizing 50 or so of these strategy indices was no fun. Worst I was making a lot of mistakes while I was playing because I would forget the right index number. Then some thing wonderful happened that changed everything. Don Schlesinger (author of Blackjack Attack) published an article in Blackjack Forum in which he calculated that it was not necessary to learn 50 or so indices. In fact, you'll realize about 90% of the potential gain by just learning a handful of plays.
The table at the end of this article summarizes the true count index for these plays (Hi/Lo count). You should use the basic strategy play for all other decisions. Here are some examples of how to use the information in the table.
Suppose you are dealt a 7,4, the dealer shows an ace, and your true count is +4. The dealer will first ask if you want to take insurance and you would since your true count is above the insurance index number where taking insurance is profitable in the long run. In the unlikely event the dealer doesn't have the ten in the hole, you would have to play out your hand. The basic strategy play for hard 11 against a dealer ace upcard is to stand. However, the index for this play is +2 (see table) which means you should double down if your true count is greater than +2.
If you still find the task of learning 16 indices to daunting, then I'd recommend you try learning this simplified version which groups the strategy changes by true count. I've simplified things a bit by combining some plays under the same true count number. The error in doing this is very small and you'll still be benefiting from most of the gain.
Here are some examples of how to use the above information. Suppose you are dealt a 9,3 (12) and the dealer shows a 6 with a true count of -1. In this case you would vary your basic strategy and hit rather than stand. Likewise if you are dealt a 6,4 (10) against a 10 and your true count is +5 you should double down.
As a general rule strategy changes are more valuable (important) in single deck games compared to multiple deck games. It's possible, in fact, to get the edge in single deck games by just flat betting and varying your basic strategy based upon the count (although I recommend you also vary your bets in single deck games as well).
Take insurance when:
True count is 3 or higher (2.5 or higher in double deck games and 1.5 or higher in single deck games)