Blackjack Card Counting – Card Counting Systems and Strategy
Depending on whom you consult – players or casinos – blackjack card counting to win is either a subtle strategy or a downright cheat. Whether viewed as a winning blackjack strategy or a cheating strategy, card counting in blackjack has a rich and colorful history. Unlike other gambling “systems,” card counting remains one of the few mathematically based strategies to give players an edge over the casino in a game that heavily favors the house.
If you’d prefer to skip the history review, you can use the menu below. It will also take you straight to the different methods used to count cards in blackjack.
Card Counting History & Systems
Card Counting History
Card counting has found its way into the movies dozens of times. Perhaps the most famous episode can be seen in Rainman, the 1988 Oscar®-winning film starring Dustin Hoffman and Tom Cruise. In one of the film’s turning points, Charlie Babbitt (Cruise) takes his autistic older brother, Raymond (Hoffman), to Las Vegas to exploit Raymond’s talent for seeing and remembering numbers.
Charlie teaches Raymond the game of blackjack so that Raymond can understand how to count the cards. The pair wins thousands of dollars before casino authorities intervene and ban the Babbitt brothers.
“We know you’re counting cards,” the security chief tells Charlie. “We don’t know how you’re doing it, but we know you’re doing it.”
While Raymond Babbitt was an autistic savant who could count blackjack cards as easily as he breathed, the truth is that any player with persistence and patience can learn to count cards. Several leading experts going back more than half a century have already performed the hard work of figuring out the mathematics of card counting.
Card counting can be defined as a mathematical system of probabilities, tracking each card dealt in blackjack in order to know which cards remain to be played. In general, all card counting strategies are based on a theory that assigns values to high or low cards in order to track them similar to betting systems.
Considering that blackjack typically pays out 3 to 2 in casinos, raising the bet when counting indicates that a blackjack is likely gives players an advantage over the long term. Card counting also can indicate to the player when there’s a greater chance that the dealer will bust on a stiff hand if the deck has lots of high cards. It’s also to the player’s advantage to count cards in order to know when lots of high cards remain to be played, a situation in which doubling down a wager becomes less of a chance and much more of a sure thing. Is it any wonder that casinos have been opposed to modern card-counting strategies since they first emerged in the early 1960s?
In the movie Rainman, the conflict between the Babbitt’s and the casino points out one of the key factors for players that wish to use card counting when they play blackjack: Don’t let the casino know what you’re doing.
After all, successful card counting can significantly cut the casino’s revenues, which gambling experts say can range as high as 6 percent on top of whatever the house percentage is on single-deck blackjack. There are plenty of variables to be factored in, as we’ll discuss later on, but blackjack is definitely one of those games that can be a money-spinner for casinos.
To keep card counting a hidden strategy requires that blackjack players practice whatever method they choose until they can do it with consistent success. Most of all, players should practice in front of a mirror or with a partner so they can eliminate any “tells” of voice or facial movement that will clue a dealer or pit boss to what they’re doing.
A brief history of the development of card counting methods helps players understand why this blackjack strategy is considered to be so controversial.
Arguably, the father of modern blackjack card counting is a former mathematics professor named Edward Oakley Thorp. Today the CEO of an investment strategy firm based in Newport Beach, California, Ed Thorp didn’t invent card counting. He wasn’t even the first player to try using card counting to gain an advantage over the casino.
Thorp’s genius was to apply mathematical theory to the calculate the probability of certain cards appearing in blackjack hands, based on assigning numeral values to the cards. Thorp’s 1962 book, Beat the Dealer, is often cited as the book that started the modern craze to develop card counting systems for blackjack. An earlier book, Playing blackjack to Win, was published in 1957, but its method was too crude to give players a genuine edge for winning.
Among other predecessors in card counting, Thorp mentions colorful professional gamblers such as “Greasy John” and “System Smitty,” who often claimed to have methods to beat blackjack. Two of Thorp’s predecessors who tried card counting included Jess Marcum, a nuclear physicist for the Rand Corporation who quit his high-security job in the 1950s to become a professional gambler, and former Reno, Nevada, casino owner Harold Smith Sr., author of I Want to Quit Winners published a year before Thorp’s book.
However, Ed Thorp’s Beat the Dealer offered the first mathematically verified system for beating blackjack. As a result, Thorp became an instant celebrity who was at the same time criticized and even derided for his card counting system. The funny thing is, Thorp’s Ten-Count method really isn’t a pure card counting system at all. At best, card counting using the Thorp system will cut the casino’s edge from about 6 percent to around 4 percent, but it doesn’t give a player a foolproof method of winning at blackjack. What’s more, Thorp’s Ten-Count has been supplanted by later more effective card counting methods, as we shall see.
Nonetheless, Thorp’s achievement was sufficient to earn him the honor of being among the first seven gambling greats inducted into the blackjack Hall of Fame in San Diego, California, in 2002. TOP
When Professor Thorp published Beat the Dealer in 1962, he took direct aim (knowingly or not) at a man named John Scarne, then considered the greatest U.S. expert and author on gambling. Scarne often was called The World’s Foremost Gambling Authority based in part on the dozens of books he’d written on the topic since 1945.
Scarne was everything that Thorp wasn’t. Scarne was a showman in the P.T. Barnum mode. He consulted with casinos on five continents. He was a noted sleight-of-hand magician, famed especially for his card tricks. Scarne even testified before the U.S. Senate committee on organized crime and gambling in the 1950s.
On the other hand, Thorp was a mild-mannered mathematics professor who, after his book gained him notoriety, took to frequenting casinos in disguise in order to test his methods. Scarne might have been able to blow off the newcomer Thorp had it not been for three things:
- Thorp’s Beat the Dealer became so popular that it undermined Scarne’s standing as the world’s foremost gambling authority.
- Thorp’s book revealed that the blackjack strategy Scarne recommended in his New Complete Guide to Casino Gambling was inaccurate.
- Thorp also documented in Beat the Dealer that Scarne wasn’t the first to use strategy analysis for winning at blackjack as Scarne had claimed, and included several examples of other strategists who preceded Scarne.
The final straw was when Thorp acknowledged the assistance of another gambling expert, Mickey McDougall, with whom Scarne had a long-running feud.TOP
As more and more players began to try Thorp’s card-counting methods, Las Vegas casinos began to fear that the professor was actually teaching droves of people how to beat the house at blackjack. In 1964, the Las Vegas Resort Hotel Association, responding to their own anxieties, altered blackjack rules for all Las Vegas casinos. The changes forbid players from splitting aces into two blackjack hands, and limited the “double-down” bet to only two-card totals of 11. Players were so outraged by these new rules that blackjack play fell to almost nothing, forcing the casinos to revert to the old rules within three weeks.
Next the casinos turned to John Scarne. Along with his backer, the famous Sands Hotel and Casino owned in the mid-1960s by billionaire Howard Hughes, Scarne challenged Thorp to a blackjack freeze-out for $100,000, with Scarne as dealer. Ed Thorp might have been a retiring character, but he was no fool. He knew better than to play blackjack with a magician famed for his “card mechanics,” and declined the face-off.
The Scarne/Sands challenge responded to a wager that Thorp had made to the casinos in Beat the Dealer. Thorp proposed a $10,000 bet of his own money, winner take all, against any casino that would play by standard Vegas blackjack rules, with some additional restrictions to keep the casino from cheating (see “Cheating at blackjack”). No gambling house ever took up Thorp’s challenge.TOP
Card counting to win at blackjack continued to rise in popularity. In 1966, Ed Thorp brought out a new edition of Beat the Dealer with a strategy that’s now called the “Hi-Lo Count.”
Not only did Thorp’s latest book throw down a new gauntlet in Scarne’s direction, Scarne began to tarnish his own reputation with inconsistencies in his newly published autobiography, The Odds Against Me. In this book, Scarne claimed that he had boasted to the late mobster Benjamin “Bugsy” Siegel, considered the father of Las Vegas gambling, back in 1947 that he could use card counting to beat blackjack. Since Scarne had been asserting passionately that card counting wouldn’t beat blackjack, people began to doubt his credibility.
Scarne kept open his $100,000 challenge, aiming now for the new generation of card counters who had emerged since Beat the Dealer was published. These included experts such as Julian Braun, Lawrence Revere and Allan Wilson. However, the opponents could never agree on the rules. Scarne died in 1985 without anyone ever taking up his wager.TOP
Card counting became so popular among blackjack players that casinos again changed operations in an attempt to defend against the strategy. Learning from their earlier mistake, casinos didn’t alter the standard blackjack rules. Instead they tried to make it harder to count cards, instituting two-deck and four-deck blackjack games that are much harder to count. Thorp’s system, based on single-deck blackjack, remained difficult to learn for most players and didn’t adapt well to multi-deck play. Thus the casinos continued to turn tidy profits on blackjack.
However, Beat the Dealer had broken open floodgates for card-counting schemes. Many of these “systems” were hideously overpriced, inaccurate or just plain foolish. Nonetheless, Thorp’s success prompted other math whizzes to try their hands at creating legitimate card counting techniques to offset the casino’s edge. Among those who rose to prominence were nuclear physicist Allan Wilson, author of The Casino Gambler’s Guide; computer programmer Julian Braun; and computer scientist Harvey Dubner.
The preponderance of computer scientists in blackjack strategies hinged on the fact that this period marked the growth era of computer science. Thorp himself, along with his students, tried to develop a personal computer that would calculate the odds on every blackjack hand. They were only marginally successful, in part because the machines failed more than the worked and were cumbersome to wear, being easily spotted by casino security. (Although the microchip had been invented by Jack Kirby of Texas Instruments by this time, this was long before computer scientists figured out how to program microprocessors to run personal devices).TOP
Just as casinos were have conniption fits over card counting in the late1960s, a Las Vegas investigator, Robert Griffin, had a brainwave: He assembled a book containing mug shots of gambling cheats, including controversial card counters. In the 40 years since, Griffin’s inspiration became a multi-volume series and an online database known as Griffin Books.
His company, Griffin Investigations, Inc., was the premier agency conducting surveillance and investigations for Las Vegas casinos between 1967 and 2005. Being “outed” by Griffin as card counters caused many experts to begin disguising themselves in order to play blackjack in Las Vegas casinos. The agency has since incorporated biometric techniques in order to identify card counters even when disguised.
Griffin filed for bankruptcy protection in 2005 after being successfully sued for defamation by card-counting blackjack players James Grosjean and Michael Russo, who were arrested as gambling cheats based on their profiles in the Griffin Books. The damages they won in their lawsuit, along with legal costs, led to Griffin’s bankruptcy.
In addition, the Grosjean-Russo case stressed once again the different understandings of card counting: Players see the technique as a blackjack strategy, while casinos continue to view card counting as a method of cheating.TOP
Unlike Raymond Babbitt, whose genius was such that he could mentally track every card, most methods don’t involve counting all cards played. Instead, a system assigns a value to certain cards, usually +1 or -1. The player then mentally keeps a running count. The more complex the system, the more accurate the results. However, the more complex the system, the harder it is to learn and practice. That’s why so few amateur blackjack players – or many professionals, for that matter – get to be expert card counters; it requires high levels of discipline and perseverance.
Many blackjack card counters suggest that beginners start with the Hi-Lo System, since it’s one of the easiest to learn and perform. A single-level system for counting, Hi-Lo works like this:
|Hi-Lo Card Point Values|
|2 3 4 5 6 7 8 9 10 A|
|+1 +1 +1 +1 +1 0 0 0 -1 -1|
Each time one of the cards listed in the Hi-Lo table appears, count its value according to the table. By the time you go through a 52-card deck, the final value should be zero.
Whatever system a player chooses, however, the key to card counting is to practice constantly until one’s counting is number-perfect and invisible to others. This is the only way a player can use card counting to his or her advantage.
The first step is to learn how to count one’s way through an entire deck, turning over one card at a time. The next step is to start learning how to count two-card deals. Furthermore, newbies are often told not to start their two-card counts until players get their second cards, because many two-card combinations cancel out each other. By waiting until the second card, players will have to count fewer cards.
Once two-card counts are mastered, players should move on to counting three- and four-card combos. When deals of this complexity are mastered, blackjack students will be able to start timing themselves, and counting out an entire deck fanned out face-up on a table. The goal here is to reach professional skill level. Professional level requires a blackjack student to count cards with 100 percent accuracy within 40 seconds.TOP
Can you see why card counting to win at blackjack is such a difficult technique to master?
Here are examples of other card counting systems. Some of these are explained in greater detail elsewhere on this website.
The Wizard’s Ace-Five Count.
Former computer scientist and mathematician Michael “The Wizard of Odds” Shackleford has come up with a blackjack card counting system he calls The Wizard’s Ace-Five Count. With this method, the count starts at 0, and each ace counts a -1 and every five counts as a +1. When the count is zero or negative, bet one unit. When the count is positive, bet two units times the amount of the count, so a count of +1 means betting two units, a count of +2 bets four units, and so on. This strategy works best in a six-deck game, in which the rules allow the dealer to stand on a soft 17, players may re-split aces, and late surrender is permitted. where the dealer stands on a soft 17, late surrender is allowed, and the player is allowed to re-split aces. Wizard’s Ace-Five’s advantages are its simplicity and ease of use.
The Knockout Count, or KO Count.
Ken Fuchs and Olaf Vancura introduced the KO Count in 1998 in their book, Knockout blackjack. It has the prestige of an endorsement from Edward Thorp. The KO Count is called an “unbalanced” system of card counting because it doesn’t total 0 when an entire deck is counted. KO was devised to be simple, eliminating a need to figure a true card count from a running count. It’s almost the same as Hi-Lo except that it factors in the 7 as +1’s. The starting number for the count is determined by the number of decks being played, i.e., with a single deck, the starting count would be 1, with additions and subtractions according to what follows.
The Hi-Opt I Count.
Charles Einstein created the Hi-Opt I Count in 1968. “Hi-Opt” is short for “Highly Optimum.” This system also has been called “The Einstein Count.” The Hi-Opt 1 system works like Hi-Lo Count, except that 2’s and aces count as O. Hi Opt I requires keeping a separate count of aces, which is used to derive multiple variations on the basic strategy. This makes Hi-Opt I a multi-level counting system. Lance Humble and Julian Braun refined the system in the 1970s, and made it popular through Humble’s book, The World’s Greatest blackjack Book.
The Hi-Opt II Count.
Along with popularizing Einstein’s Hi-Opt I system, Humble created a variation known as Hi-Opt 2, consider the most accurate and powerful card counting method through the late 1970s. The Hi-Opt II system keeps separate side counts of 8’s, 9’s and aces, making this a multi-level counting method. This also makes Hi-Opt II much more difficult to learn.
The Red Seven Count.
Arnold Snyder devised the Red Seven Count in his book, Blackbelt in blackjack. Similar to the KO Count, Red Seven is considered an unbalanced system that gets its name because only red sevens are counted as +1 in this method; black sevens count as zero. Like the KO Count, Red Seven’s goal is to avoid the necessity of converting the running count into a true card count for betting purposes.
The Zen Count.
Snyder also outlines his Zen counting system in great detail in Blackbelt in blackjack. As might be expected, this method is much too “zen” to be explained briefly.
The Omega II Count.
Bryce Carlson came up with the Omega II count in his book blackjack for Blood. This advanced counting strategy is too complex for beginners, but have been proven to be highly accurate.
The Uston Advanced Point Count
The late Ken Uston put forward his system, also known as the Uston APC, in his book Million Dollar blackjack. Uston’s system is one of the most complex, and therefore most accurate and most difficult, of card-counting strategies for multi-deck blackjack games. Uston’s strategy includes the use of plus-or-minus three counts on fives and tens. Not recommended for beginners.
The Revere Advanced Point Count.
The late Lawrence Revere, author of Playing blackjack as a Business, invented his own strategy that involves using more positive counts and fewer negative counts. Once again, this is a method that works at multiple levels, increasing both its accuracy and its difficulty.
- No matter which of these methods – or others – a player prefers, remember these basic rules about card counting to win at blackjack:
- Practice until counting is both 100 percent accurate and invisible to others.
- Start with counting one deck, then move on the multiple decks.
- Don’t even think of counting cards in a casino game of blackjack until you’ve reached professional level, namely counting cards with 100 percent accuracy in 40 seconds or less.
Most of all, don’t let the casino know that you’re counting cards. You’ll be bounced faster than Raymond “Rainman” Babbitt can add up spilled toothpicks.