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The Men Who Beat Las Vegas Blackjack
1950's - Roger Baldwin
In 1956, the Journal of the American Statistical Association published a paper entitled The Optimum Strategy in Blackjack by Roger Baldwin. Although the title of the paper was Optimum Strategy, it required a computer to implement this strategy system.
Together, Wilbert Cantey, Herbert Maisel, James McDermott and Roger Baldwin created the framework for blackjack Basic Strategy. Their mathematics proved that of all casino games, blackjack offered the best odds of winning if the player followed certain rules. This strategy was later improved upon by Edward Thorp.
1960's - Edward O. Thorp
One of the most famous mathematicians who developed a lifelong fascination with the game of blackjack and the mathematics of risk was Edward Thorp. In 1961 after receiving his PhD. in mathematics, Thorp was hired as a lecturer at MIT. His credentials included an M.A. in Physics, as well as teaching mathematics at UCLA, MIT, NMSU and UC Irvine. He also taught Quantitative Finance. Thorp wrote a paper titled Fortune's Formula which he presented at the American Mathematical Association's yearly meeting. This paper described some of Thorp's early blackjack simulations which he ran on an IBM 704.
These blackjack simulations included Basic Strategy and Card Counting. He considered the effects of all the different cards when removed from the deck. He assigned a positive value to the cards that had a positive effect and a negative value to cards that had a negative effect. Of course these values were all different because the cards had different effects. You then added these values as the cards were exposed during game play. This was called the running count. When your running count was positive it meant that the total effect of removed "bad" cards was bigger than the total effect of the removed "good" cards, so the blackjack player had the edge. This was known as the Thorp "Ten Count" blackjack system which was detailed in his 1962 book, Beat the Dealer.
To test his blackjack theories Thorp joined forces with Emmanuel Kimmel, a New York businessman, to undertake a financial blackjack adventure. The two took a trip to Reno, Nevada, to play blackjack using card counting techniques never before heard of. They started with a $10,000 bankroll. By the time Thorp and Kimmel finished their great blackjack adventure, they had more than doubled their money. This was a pivotal moment in history for the game of blackjack. The seeds of card counting were sown.
In 1962 Edward Thorp published a book titled Beat the Dealer* which shook the casino industry to its very foundations. Thorp's book took some earlier works on probability statistics and applied them to the game of blackjack to create a method of winning at blackjack called "card counting". The book became wildly popular, reaching the New York Times bestseller list and sending the casino industry into a panic.
Prior to the publication of Thorp's book, blackjack was a side game for the casinos and the blackjack patrons were primarily female - the wives of veterans from World War II and the Korean War. When Beat the Dealer came out complete with a set of blackjack strategy cards, suddenly the game of blackjack was catapulted into the gambler's spotlight. People who had before given no thought to the game of blackjack suddenly took notice. And the casinos panicked, afraid that Beat the Dealer* would create a slew of blackjack winners to eat away at the casino profits.
To tip the odds back into their favor, many casinos changed their blackjack rules. And the war escalated. Players countered by boycotting the casinos. Players stopped playing the game of casino blackjack. The casinos quickly relented and reinstated the original blackjack rules, though some of the subtler changes remained. These changes included Preferential Shuffling, where the dealer shuffled the cards when the cards favored the players, and Multi-Deck games, dealing from multiple decks stored in a shoe.
After all the panic by the casinos however, card counting ended up being much ado about nothing. Thorp's blackjack book actually increased the profits of the casinos as thousands of people flocked to the blackjack tables, convinced that they could "Beat the Dealer" by card counting.
However, Thorp's system was difficult to master and required a great deal of practice to gain even basic proficiency at card counting in blackjack. As a result, most people lost at an even greater rate than before.
Nevertheless, a very small number of card counting experts did take the time and effort to learn and apply card counting and were successful enough that dozens more books and blackjack systems were developed and continue to flourish today. Thorp himself however, rarely played the game of blackjack. He was not able to win using his own blackjack techniques. It was not uncommon for blackjack dealers in the 1960s to cheat, and Thorp with all his mathematical genius was unable to spot a cheating blackjack dealer. Dealers would often switch their hole cards when they checked for blackjack and found a stiff hand. Dealers would flip the deck over to redeal cards that had just been played when those cards were unfavorable to players. In those early years there were many underhanded techniques employed by both blackjack players and blackjack dealers to turn the tables in their favor.
1960's - Julian Braun (deceased 2000)
Once Thorp's method was published, several scientists and mathematicians began developing "point" count systems based upon his work. The most notable was Harvey Dubner who, in 1963, created a crude version of what he called the High-Low point blackjack system.
After reading Edward Thorp's book, IBM computer programmer Julian Braun became fascinated with the mathematics of blackjack. Julian had access to some of the highest speed computers of that time and he wrote to Thorp requesting a copy of the blackjack computer program. The program was written in Fortran and Julian soon figured out how it worked.
It was a complex program which produced ten pages of information for each potential dealer up-card. Every possible choice was analyzed in detail with a summary at the bottom of the page giving the best blackjack strategy. Julian Braun refined the strategies detailed by Thorp and tested them with an IBM 7044 mainframe computer. He ran 9,000,000,000 blackjack simulations. His blackjack simulations included both fixed blackjack strategies and varying blackjack strategies.
Julian improved on the program and the result helped to create the Hi-Opt blackjack strategies and the Hi-Lo blackjack strategies. His thousands of lines of computer code and hours of blackjack simulation on IBM mainframes resulted in The Basic Strategy as well as a number of card counting techniques. His conclusions were used in a 2nd edition of Beat the Dealer, and later in Lawrence Revere's 1977 book Playing Black Jack as a Business.
The conclusion was that a deck rich in high cards, such as Nines, Tens and Aces, favored the blackjack player. A deck rich in low cards favored the casino. Think about it... how can the dealer bust if he keeps drawing low cards?
Braun's work was noticed by a college professor who used the pseudonym "Lance Humble". Lance contracted with Braun to perfect a blackjack system which had been published by Charles Einstein in his 1968 book, How to Win at Blackjack. The Einstein count did not assign a point value to the Ace nor did it count the 2,7,8, or 9, so the count remained "balanced". (When the point count of all cards in the deck are added together, the total is zero. Therefore it is a "balanced" count system. More recently, unbalanced count systems have emerged.)
Braun's development of this Ace-neutral count resulted in the Hi-Opt I blackjack count which was originally sold privately, then published in a book called The World's Greatest Blackjack Book in 1980. Braun's work was used to develop Hi-Opt I and II, Thorp's Ten Count, Hi-Lo, Revere's Point Count, Revere's +/-, and Revere's Advanced Point Count blackjack systems.
Knowledge is power, and armed with the new knowledge put forth in Beat the Dealer, the odds of winning the game of blackjack changed. Where the casino's profit from a blackjack game was once 18 percent, with the new generation of knowledgeable blackjack players the profit fell to 14.5 percent. More recent refinements have further reduced the house edge to 12 percent, and some claim that with the right table rules and blackjack strategy, the house edge can be as low as .5 percent.
An interesting fact to note, even the blackjack experts do not always agree on the best blackjack strategy. For example, if the dealer is showing a 3 and the player has a 2-2, the recommendations are as follows:
Stanford Wong - hit
So who is correct? The key lies in which blackjack strategies are successful with the current blackjack conditions. What was successful ten years ago may not be as successful today. But one thing is for certain, most of the blackjack experts of today built upon the work done by Julian Braun.
Lawrence Revere (deceased 1977)
Revere was a genuine Las Vegas card shark. A hustler who traveled under many names: Griffith K. Owens, Leonard Parsons, Specs Parsons, and Lawrence Revere were various personas of the same man. It is said that Revere made more money from teaching card counting than from playing blackjack. He allegedly would remove a card from the deck causing his students to come up with the wrong count, thereby ensuring they would pay for more blackjack card counting lessons. It is also alleged that the casinos paid him to point out his own students.
Lawrence Revere brought the game of blackjack to the average player. He created a series of color-coded charts based on the work done by Thorp and Braun that gave the exact play for every blackjack hand. It's design was so perfectly simple that anyone could understand it.
1970's - Ken Uston (deceased 1987)
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If the first round of a single-deck game is dealt and all four aces appear, the chances of a blackjack on the next hand are zero. Conversely, if no aces or ten cards are dealt in the first round, the chances of a blackjack occurring in the second round are much higher. When the odds favor the blackjack player he can place bigger bets. When the odds favor the casino, the player can bet less. This strategy gives the blackjack player an edge over the house and is known as Progressive Betting. Be aware that this is a grossly oversimplified illustration.
Ken's endeavors were so successful that he soon left his job as Vice President of the Pacific Stock Exchange and began playing blackjack full time. After enjoying several years of success throughout the world's casinos, Ken encountered Keith Taft, an electronics engineer who had developed a tiny computer that played a perfect game of blackjack and could be worn without detection. This computer became the prototype for a device named George, one of Keith's many unique gambling inventions.
George consisted of a microprocessor, memory and a stored program crammed into a plastic box the size of an eyeglass case. After calculating the house advantage for the next hand, George would calculate how much the blackjack player should bet to the nearest $10. George also kept track of all cards played and told the player precisely what to do with his hand (whether to hit, stand, double down or split pairs). This contributed to the concept of blackjack Basic Strategy and was used in conjunction with card counting for optimal success.
A pocket-size device with four switches activated by each of four fingers gave George information on blackjack game play. The switches worked on a binary code, with values from 1 through 15 to indicate cards played. George's output device was a little tapper that vibrated, using a series of Morse-like dots and dashes, encoded to tell the blackjack player how much to bet and how to play his hand. A separate battery-pack powered the entire system. George's components were wired together and scattered among various hidden parts of the blackjack player's body. The concept was ingenious and very successful for the player while it lasted.
On February 1, 1977, Ken and George started their partnership at the Golden Gate casino in downtown Las Vegas. This was the first time a blackjack computer had been successfully used in a casino. Previous attempts by others had been unsuccessful. After several hours of blackjack game play, Ken concluded that George was a success. This was just the beginning. From the loins of George sprouted one of the most successful gambling forays in the history of the game of blackjack.
Ken and Keith began training "computer operators" - people who pushed the buttons as they kept up with the cards that were dealt. To prevent detection from the pit bosses, Keith devised a unit that made it possible for a computer operator to send signals via a small radio transmitter to another blackjack player known as the Big Player, or BP. All the Big Player had to do was stand at the blackjack table, betting and playing his hand according to the signals he received from a "tapper" hidden in his shoe.
Condominiums in Las Vegas were transformed into blackjack training rooms complete with flash cards, tables, charts, and electronic workshops. The rooms were filled wires, battery chargers and "magic" shoes filled with electronic gear. Ken's job was to recruit and look after the blackjack team. Keith handled the electronics. Their blackjack team soon grew to sixteen people: eight computer operators and eight Big Players.
Soon it came time to test the blackjack teams at a real casino. Over the next three weeks they won approximately 80 percent of the time, which was far better than the average of 60 percent playing a "manual" blackjack game. After five weeks of blackjack play the teams were up $110,000.
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At first the casinos loved the Big Players whom they viewed as high-rolling suckers bound to lose a bundle. The Big Players were simultaneously "comped" (given free services) at the MGM, Caesars Palace, the Stardust and the Sahara. The Big Players were living quite well in the most lavish suites and enjoying ringside show tickets and gourmet meals "on the house." They were a smashing success and the darlings of the casinos.
The blackjack teams kept winning and eventually started getting "heat" from the pit bosses. Casinos become suspicious when a player is on a big-time winning streak. Agents began to follow the Big Players out of the casinos and the blackjack teams had to split up and take several cabs in different directions before returning to base camp. They decided not to tempt fate and moved their successful blackjack operation to Lake Tahoe. This was the Big Mistake that brought the whole gambit crashing down upon their heads.
Blackjack teams were sent to the Sahara casino, Harrah's casino, and Harvey's Wagon Wheel casino in Lake Tahoe. Placing $1,000 blackjack bets in Lake Tahoe drew far more attention than it would in Las Vegas and the pit bosses in Tahoe immediately became suspicious. The Big Player at Harrah's was whisked away into a back office by two burly security guards. They stripped him and found him covered with wires and electronic devices. They must have sent word to other casinos because two other teammates were also arrested. The gig was up.
The police apprehended the suspicious players and charged them with "bunko steering" - luring an unsuspecting individual into an illicit gambling game. That was the best charge they could trump up.
Unfortunately, one of the people arrested was Keith's son. Keith's wife had been pressuring him to stop playing blackjack. She urged him to choose a more legitimate profession. The arrest of their son clinched it. Keith quit playing blackjack and Ken cooled his heels for awhile, backing away from the concept of team play but continuing to play blackjack without the assistance of devices.
The confiscated computers were shipped to the FBI in Washington for analysis. Five months later the FBI sent them back saying that in their opinion the computers were not "cheating devices." All charges against the blackjack teams were dropped. Keith invented many devices for use in casinos, some of which are on display at the Blackjack Hall of Fame Museum at the Barona Casino in Lakeside, California.
Ken believed that if the team had not been greedy and settled for winning $10,000-$20,000 per week, chances were they'd still be playing blackjack. On the flip side, Ken's philosophy in playing blackjack was to capitalize on opportunities immediately and to the fullest.
Ken's blackjack team had won hundreds of thousands of dollars in Las Vegas and millions in Atlantic City before being barred from the casinos. Soon after, the ruling of the New Jersey Supreme Court assured the right of card counters to play in Atlantic City casinos. Ken was one of the leaders of this long and costly court battle and was featured on Sixty Minutes in 1981.
Before his death in 1987, Ken authored a book entitled Million Dollar Blackjack*. It is considered to be one of the most definitive books on the game of blackjack. The book details blackjack Basic Strategy and progressive betting techniques. Ken Uston died at the age of 52. He was found dead in his apartment in Paris. In spite of the many enemies he had among the casino industry, his death was considered accidental. No investigation was performed as no foul play was suspected. He is said to have died of a heart attack.
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To this day card counting is not considered illegal though most casinos frown on it and will still ban suspected card counters from playing blackjack. Casinos are wise to the concept of blackjack team play, and the rule of No Mid-Shoe Entry was designed to prevent a Big Player from entering a blackjack game at a strategic time. As for Keith Taft, he eventually became the 8th inductee into the Blackjack Hall of Fame.
Peter Griffin injected his mathematical genius to analyze the effect of card counting on the game of blackjack. He broke it down into two primary factors: Betting Correlation (BC) and Playing Efficiency (PE). These two factors allowed an accurate estimation of a blackjack count system's potential win rate without using computer simulations. His methods have been widely used by blackjack researchers to compare count systems.
His book, The Theory of Blackjack, has been revised many times since it's first debut in 1978. His many technical publications have appeared in mathematical journals and academic conferences.
Stanford Wong continued where Thorp left off, further expanding on the theories of the blackjack gurus who came before him. He is oft referred to as the Godfather of Blackjack, and was inducted into the Blackjack Hall of Fame. He is considered an authority on casino casino blackjack tournement play. The term "wonging" as it relates to card counting stemmed from Stanford Wong and his many years of blackjack success.
Wong / Wonging (blackjack)
1.To back count the cards dealt at a particular table and to then join play only when the count indicates the game has swung to the player's advantage, and then to leave when the count indicates the game has turned unfavorable.
2. Playing in any favorable situation in a number of different games. It is named after blackjack author Stanford Wong, who popularized this method of play.
Wong was one of the first to beat the Continuous Shuffle Machines (CSM's). When the first generation of Continuos Shufflers were introduced at the Mirage, two teams of professional card-counters, one led by Stanford Wong, beat the casinos, making off with tens of thousands of dollars before the casino removed the machines. Needless to say refinements have been made to the Continuous Shuffle Machines since then. Many believe they are still beatable, however, if you learn their shuffle patterns.
The Hi/Lo count was refined by Stanford Wong in his 1975 book, Professional Blackjack, but even more importantly, Wong gave the reader the information needed to actually put it all into use. The book includes the most complete charts for a wide variety of blackjack game rules.
His book Basic Blackjack is one of the most comprehensive blackjack books dealing with Basic Strategy. Novice blackjack players will appreciate the most complete description of blackjack Basic Strategy available anywhere. Blackjack experts will appreciate the wealth of information on unusual blackjack rules. Advice and discussion of proper play for all blackjack rule variations are included. Basic Blackjack* also contains the best of Winning Without Counting.
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Wong, who holds a Ph.D. in finance from Stanford University, played blackjack for a living in Las Vegas in the early 1960's. Unlike Uston who came before him, he kept his bets low and stayed under the radar in order not to draw attention from the pit bosses. He believed you have to be hungry to win at blackjack. You must frequent casinos in the early morning hours when the blackjack tables are empty.
Today Wong, a grandfather who lives in La Jolla, California, plays very little blackjack. He prefers to bet on sports, wagering $25,000 a week on NFL games.
In gambler's parlance, two forms of advantage play are known as "Wonging." The first involves back-counting a game of Blackjack from behind the table and then jumping in when the deck favors the player. The second involves betting a football "teaser" card when the increased point spread covers a win by either a field goal or a touchdown.
Of his many books one of the rarest is called Blackjack in Asia, priced at a whopping $2,000 and highly sought after by collectors. The book included underground advice for exchanging currencies in the black market and detailed his own difficulties in dealing with custom's agents when trying to take his winnings out of the Philippines.
Another collector's item is his book Winning Without Counting, priced at $200. It details hole card techniques, spooking, warp play, and many illegal methods of gaining an edge over the casinos. The techniques include bet capping, card switching, and card mucking.
According to blackjack afficionado Al Francesco, an inexperienced blackjack dealer might inadvertently expose their hole card while checking for blackjack, tipping it up just a bit too far where an eagle-eyed player could see it. Players sitting at first base were the most likely to see the exposed card. A dealer overly worried about their hole card might bend the card too much while peeking, causing a permanent bend in the card which could later be used by a player to identify the card. A dealer might also expose their hole card after checking for blackjack, while sliding the hole card under the upcard. Another technique to view a dealer's hole card was to use a Spook: a person located somewhere behind the blackjack dealer who would spy out the hole card and signal it to a player at the table. Mirrored and electronic card readers were invented and have virtually eliminated this particular form of improving your odds. Needless to say neither Wong nor Francesco were darlings of the casinos, though Wong is still sharing his blackjack teachings today.
In the 1990's a team of MIT students took on the Las Vegas casinos and walked away with millions of dollars. Engineering students by day, they became high-rolling gamblers on the weekends. The MIT Blackjack Club was borne.
The team was headed by Micky Rosa, a man of dubious background who trained the students in mock casinos and underground warehouses in and around Boston.
The game was blackjack, and the students were from the world-renowned Massachusetts Institute of Technology (MIT). Their incredible blackjack winnings marked the climax of an arms race between casino and blackjack player that began 40 years earlier with the discoveries of Roger Baldwin. He realised that the one feature of blackjack that made it different from other casino games also made it possible to beat.
The MIT whiz kids had more resources, training and attention to detail than the casinos had ever before encountered. The original three students who joined the MIT Blackjack Club were Semyon Dukach, Katie Lilienkamp and Andy Bloch. They were all studying at MIT when they heard of blackjack card counting as a way to make extra money. MIT had a history of card counting. Indeed, Edward Thorp himself had developed the original blackjack card counting system while at MIT, using one of the most powerful computers in the world at that time. Card counting had come full circle.
Soon after, other students joined the Blackjack Club. The MIT students played in blackjack teams, usually of three or more. Each student was given a specific role. Some would simply watch the blackjack tables and wait for favorable situations to appear. They were known as The Back Spotters. Others actually played at the blackjack tables, counting cards but not exhibiting the wide betting spreads common to card counters. They were known as The Spotters. The various Spotters would report to the strategist they called The Controller, who would determine exactly when the optimum moment came to play, and how much to bet according to the cards being played. The Controller would secretly signal to a Gorilla, who would then join a table and place a massive bet at exactly the right moment.
The key was that by only betting when the odds were in the Gorilla's favor, the Gorilla could maximize his profit and avoid being spotted as a card counter. By watching a number of blackjack tables at any time, the blackjack team could select only those with the greatest promise of a good return. The Gorilla simply looked like a rich, arrogant young gambler who got lucky on a single bet. The ploy was wildly successful, just as it had been decades before with the Uston blackjack teams.
The MIT players went to great lengths to conceal both their own identities and their blackjack team play. They would work relentlessly to exploit any edge they could find: inexperienced dealers, poor shuffling or weak security.
The team also recorded exactly how much profit they made from each situation and honed their skills to almost perfect blackjack strategy play. The trio played blackjack profitably all over the world throughout most of the 1990's. Their exploits came to an end when Griffin Investigations, a private agency hired by the casinos, identified the members of the MIT teams after months of surveillance. After that a known blackjack team player even entering a casino would be immediately ejected.
The story of the MIT Blackjack Club is the basis for the book and movie, Bringing Down the House. The team created the popular DVD called 60 Minutes to Winning Blackjack. They were also featured in a documentary by the History Channel in 2004 called Breaking Vegas.
The Blackjack Hall of Fame came into being in 2002. Afficionados of the game made up of blackjack players, publishers, and casino personnel nominated 21 blackjack experts, professional blackjack players and highly respected authors into the Blackjack Hall of Fame. For a period of one month, public voting took place on the internet, narrowing down the list of potentials. In January 2003, the final voting took place at the Blackjack Ball, and event open only to the most highly ranked professional blackjack players. These blackjack players who used the knowledge provided by others to consistently win at blackjack were the best to know whose advice and information was truly valid and most useful, and hence became the final judges.
The original inductees were:
Al Francesco and Tommy Hyland are not as prominently known to the public, but well known to both professional blackjack players and casino personnel for their very successful blackjack team play in the casinos. Max Rubin is known for his exploitations of casino comps, which he detailed in a book called Comp City. Arnold Snyder discovered the importance of deck penetration and its effects on blackjack card counting.
Later additions included:
Today it is the current Hall of Famers who select potential candidates, and then choose their final seven selections by voting amongst themselves. Biographies are posted during public voting which highlight the particular achievements of each candidate.
In 2003, the Barona Casino created the physical Hall of Fame. Each Hall of Famer has their own plaque with a photo and brief notation regarding their contributions and accomplishments to the game of blackjack, along with a lifetime offer of free food and beverage, and free rooms in exchange for the Famer's agreement never to play blackjack at the casino's tables. There is also a museum of cheating devices with marked cards, computer shoes, gizmos for card-swapping, and other gizmos.
Casinos have gone to great lengths to undermine the efforts of blackjack card counters, and there is more to successful card counting than just learning a few numbers. Even the experts had their losing streaks, and not all of their tactics proved successful.
For starters there is the issue of deck penetration, which is the percentage or number of cards that are dealt before the dealer reshuffles the cards. Most card counters will never play in a blackjack game unless the penetration is at least 75%. This means that in a 6 deck blackjack game, only 1.5 decks of cards are cut out of play. When 75% of the cards have been dealt from the decks, the cards are shuffled. Playing in a game with poor deck penetration (less than 75%) would lower the blackjack player's odds to an unacceptable level.
Another important criteria for card counters are the Table Rules for a blackjack game. This is also called House Rules or Casino Conditions, and refers to the specific rules in place at a particular blackjack table.
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For example, the fewer the number of decks of cards, the better the odds for the blackjack player. Rules that allow doubling after splitting pairs, late surrender, and the dealer standing rather than hitting on soft 17 are also favorable for blackjack players. For a more detailed list of rules and how they affect blackjack game odds, see Odds of Winning. However, it is possible to beat a blackjack game with marginal rules if the deck penetration is good. Most blackjack card counters avoid an 8 deck game but if the rules are excellent and the penetration is 80% it would be a more favorable blackjack game compared to a 6 deck game with similar rules but only 50% penetration.
One of the most common methods for stopping blackjack card counters is the Continuous Shuffle Machine (CSM). After every hand the cards are put back in the machine and are reshuffled back into the decks. Counting becomes useless and blackjack Basic Strategy becomes even more critical to the player's success.
Shuffle Master, one of the manufacturers of Continuous Shufflers, has offered a $100,000 challenge to advantage players. If a player can show the machines can be beaten by legal card counting or shuffle tracking techniques, the machine's manufacturer will give that player $100,000. Would such a player actually claim the prize? Or would they quietly beat the machine for as long as they could? Only such a true blackjack player would know the answer...
* Note: While these books are still considered to be essential background for anyone interested in maximizing their winnings in blackjack, they may not reflect the current conditions of most casinos today. They will, however, offer you a solid foundation of blackjack knowledge and theory to build upon.
Some of the more recent blackjack books from highly respected authors include:
Note that we (Gypsy King Software) do not personally endorse any blackjack book or method, nor do we proclaim to know the best method of winning at blackjack. We simply offer a blackjack game that mirrors what you would find in a real casino, and that allows you to play blackjack at home and test your own blackjack strategies. We have provided these blackjack pages for information purposes only, and because we find the history of the game of blackjack fascinating.
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