When a player decides he wants to beat a casino fair and square, the first attempt is almost always ordinary blackjack card counting. There are many reasons for this obsessive misdirection, not least of which is the sheer bulk of movies, books and websites devoted to the topic. Conversely, there is very little information available to show the would-be AP that he is completely misguided. Blackjack card counting is tough. The profit potential is small. The bankroll needed for even a modest win-rate is enormous. The swings can be brutal.  If the blackjack card counter manages to get over these hurdles, then he must get away with it against casino staff who are very well-trained at spotting guys just like him.

In the world of serious table game advantage play, blackjack card counting occupies a position at the very bottom, with most professional APs considering it somewhere between death and taxes. Were it not for the large table maximums and high-roller perks that some casinos offer, there would be no pure professional blackjack card counters at all. However, this does not mean that card counting is a dying art. Indeed, it is an extremely powerful arrow in the advantage player’s quiver. With the right game-target, card counting can be an extraordinarily lucrative endeavor.

Card counting works for those games where multiple rounds are dealt between shuffles. The AP is looking for a  proprietary game or side bet where there are cards that are good for the house and cards that are good for the player. Right after the shuffle these cards are in balance, giving the baseline house edge. However, as cards are dealt, the relative balance of good cards and bad cards changes, altering the house edge with each new round. Sometimes this change is enough to throw the edge toward the player side. That’s when the card counter strikes. His counting system allows him to identify these advantageous situations. Armed with this knowledge, he can choose to play a side bet or he can choose to raise his wager in the main game.

To understand how card counting works I am going to review its use against blackjack. In this case, the cards that are good for the house are 2, 3, 4, 5 and 6 (the low cards) and the cards that are good for the player are the high cards (T, J, Q, K, A). When there is an abundance of high cards, the player will get more blackjacks, will get better cards on his double downs, and the dealer will bust more often when drawing to a stiff hand. When there is an abundance of low cards, the player will get fewer blackjacks, will get worse cards on his double downs, and the dealer will make more of his stiff hands. The secret of blackjack card counting is knowing whether the remainder of the deck is rich in high cards (good for the player) or low cards (good for the house).

To keep track of this ratio of high and low cards, a card counting system is used. The most commonly used counting system for blackjack is called “High-Low.”  In this system, each of the low cards 2, 3, 4, 5, and 6 are assigned the tag +1. Each of the high cards T, J, Q, K, and A are assigned the tag -1. Finally, the neutral cards are 7, 8, and 9. Each of these is given the tag 0. Note that the suit of the card does not matter. I collectively refer to any of the cards T, J, Q, or K by the letter “T”. The following table gives a summary of the High-Low card counting system.

High-Low card counting system

I will use the notation (-1,1,1,1,1,1,0,0,0,-1) to describe the tags for this counting system. Whenever I use this type of notation, the cards are always listed in the order A, 2, 3, 5, 6, 7, 8, 9, T. One feature of this system is that the tags add up to zero (recall, each of T, J, Q and K have the value -1). This makes High-Low a “balanced” card counting system. Balanced systems are most frequently used for card counting, but unbalanced systems can be useful as well.

To “count cards” in blackjack, the counter starts with a running count of 0 with a newly shuffled deck.  As each card in the deck is dealt or exposed, he takes its value, 0, +1, or -1, and adds that to the running total he is keeping.  This gives the current running count (RC).

For example, assume that the first few cards dealt out are: 2, 7, 9, T, T, A, 3, 5, 8, T. The following table shows the card tags and the running count after each card is dealt:

card tags and the running count after each card is dealt

The card counter usually goes one step further and computes the “true count.” He obtains the true count (TC) by dividing the RC by the number of decks (ND) remaining to be dealt.  Thus,

TC = RC / ND

Here are some examples.

In a six-deck game where two decks have been dealt out to the players, and the running count is RC = +12, then the number of decks remaining to be dealt is ND = 4.  In this case,

TC = 12 / 4 = 3.

If the fraction doesn’t come out even, the convention is to round down to the lower number. Thus, if RC = 11 and ND = 2 then

TC = 11 / 2 = 5.

With a negative RC, the convention is also to round down to the lower number. Thus, if RC = -11 and ND = 2, then

TC = -11 / 2 = -6.

Any time the TC is larger than 1, the blackjack card counter has the edge over the casino. The higher the true count, the greater the counter’s edge. If the counter raises his wagers with a positive count and lowers his wagers with a negative count, he will beat the house. It’s that simple. Unfortunately for the AP, in blackjack, the win rate is extremely low (see this post and this post). A $10,000 bankroll will likely earn the counter under $20 per hour in expected profit.

The same principles that create the opportunity to beat blackjack apply to every other game or side bet where multiple rounds occur between shuffles. No game is immune. Every multiple-round game can be counted. But for each game, a new card counting system must be developed, one that relies on the good and bad cards specific to the game. Here are some examples.

Consider the Dragon 7 side bet for EZ baccarat. This side bet in baccarat pays 40-to-1 if the Banker’s three-card 7 beats the Player hand. Intuitively, natural 8’s and 9’s end the hand before a third card is drawn. It therefore benefits the Player when 8’s and 9’s are removed from the shoe. On the other hand, when a third card is drawn by the Banker, the draw cards that are most likely to bring the Banker’s total to 7 are 4, 5, 6 or 7, making these the good cards. The card counting system that best suits the Dragon 7 bet is the balanced system (0,0,0,-1,-1,-1,-1,2,2,0). The win-rate for the Dragon 7 using this count is roughly twice that of ordinary blackjack. (blog article).

Another game that is intuitively easy to understand is the Lucky Lucky blackjack side bet. This bet wins for the player if the total of the player’s two cards and dealer up-card is 19, 20 or 21, with bonuses for the hands 678 and 777. Aces can count 1 or 11. Clearly 6, 7 and 8 are good cards for the player. Not only do they help create the premium winning hands, they also yield the greatest number of winning hands in combination with other cards. Aces are also good because they can be two different numbers. Meanwhile, ten-valued cards are too large, tending to give hands that exceed 21, while 2 and 3 are too small, forming hands that have values less than 19. In other words, the bad cards are 2, 3 and 10. The card counting system that best suits the Lucky Lucky side bet is the balanced system (-1,1,1,0,0,-1,-2,-2,0,1). The win-rate for counting Lucky Lucky is roughly four times that of ordinary blackjack (blog article).

Card counting systems don’t always have to assign tags to card ranks. For example, the Red Flex side bet pays based on the number of red cards that occur consecutively in the dealer’s hand. Clearly the good cards are the red cards, the bad cards are the black cards. The count is therefore, red = -1, black = +1. The win-rate for counting Red Flex is roughly ten times that of ordinary blackjack (blog article).

Not every card counting opportunity will be lucrative. As Richard Munchkin has bent over backwards to point out (see this post), the 21 + 3 side bet is such a wager. This bet wins for the player if the player’s two cards and dealer up-card form a straight, flush, straight-flush or three-of-a-kind. There is no natural card counting system based on good and bad cards. However, situations can be identified by card counting when the remainder of the shoe is rich in one particular suit, making flushes more likely. In this case, the counter takes the difference between the most abundant and least abundant suit for his “running count.” The win-rate for counting 21 + 3 is just under half that of ordinary blackjack (blog article).

Card counting is not “one size fits all.” Just because the ten count (0,1,1,1,1,1,1,1,1,-2) works for Lucky Ladies does not mean that same system will be good for the Dragon 7 (good cards are 4, 5, 6, 7). The system must align with the good and bad cards for the wager it is used against, otherwise it is worthless and all claims made about it are bogus (see this post). A vulnerable wager demands a card counting system that targets its specific weaknesses. Use your common sense and you can see right through the hucksters who preach the "one system" nonsense.

Likewise, there are some games that can be counted, but there is simply not much there, no matter how diligent the counter is willing to ply his trade. Foremost among these games are ordinary baccarat and the baccarat Tie bet. You can’t squeeze water from a rock. Baccarat will earn the counter about a cup of coffee a week. The Tie bet will yield slightly more, but is still a pitiful attempt (see this post and this post).

One of the most surprising counting opportunities is the pair bet in baccarat. Beating this bet requires the highest level of mental acuity, unless you happen to be in Macau, in which case you can just use a cell-phone app (see this post). The pair bet will give you about the same win rate as a very good blackjack card counting game. In Macau, where the limits are quite high, the pair bet has become a significant game protection problem.

The win-rates for some of these non-traditional card counting opportunities can be extraordinary. For example, the Slingo Bonus Bet 21 can earn a team of five counters over $8000 per 100 hands, playing $100 wagers (see this post). In baccarat, a team of five counters can beat the Super Pay Egalite side bet out of close to $4000 per 100 hands, playing $100 wagers (see this post).

If you would like to find out more about how I carry out my card counting analysis, see this post. It's a bit math heavy, but worth it if you really want to get into the details. If you are interested in the card counting win-rates for the full spectrum of games I've analyzed, see this post.

Every game where multiple rounds are dealt between shuffles can be card counted. This includes the myriad of blackjack variants, including games like Spanish 21 and Blackjack Switch. Some of these games are more vulnerable to card counting than ordinary blackjack, for example Triple Attack Blackjack. Others are safer, for example Super Fun 21. However, most APs are no more interested in these games than they are in card counting ordinary blackjack.

Like many aspiring new players, I put my faith in card counting ordinary blackjack when I started out. Today, card counting has become an opportunistic endeavor. Worldwide, there are teams playing against the Dragon 7 bet. Recently, a player confessed to me that he has been targeting the Red Flex bet for years. Slingo was demolished by card counters at several different casinos. Smart phones are being used to pummel the pair bet. Lucky Ladies is still a big target. It goes on. While it is true that casino management should not sweat the small stuff (e.g. 21 + 3, Royal Match, Bet the Set), it is certainly not all small stuff.

Whatever games you offer in your casino, the key is to educate yourself. Knowledge is power. You can only learn about something if information is available and you seek it out. I have made the information available in this blog. You know your games. You know your side bets. It’s up to you to take the next step.

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received his Ph.D. in Mathematics from the University of Arizona in 1983. Eliot has been a Professor of both Mathematics and Computer Science. Eliot retired from academia in 2009. Eliot Jacobson