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Card counting is a card game strategy used to determine when a player has a probability advantage. The term is used almost exclusively to refer to the tracking of the ratio of high cards to low cards in blackjack and its derivatives such as Spanish 21, although it is sometimes used to refer to obtaining a count of the distribution or remaining high cards in trick-taking games, such as contract bridge or spades. This article deals only with card counting as it applies to blackjack and its derivatives.

Contents 1 Card counting in blackjack 1.1 Basics 1.2 Basic system 1.3 More advanced counting systems 2 Running counts versus true counts in balanced counting systems 3 Unbalanced card-counting systems 4 Back-counting 4.1 Advantages 4.2 Disadvantages 4.3 Group Counting 5 Ranging bet sizes and the Kelly Criterion 6 Expected profit from card counting 7 Card counting devices 8 Legal status of card counting 9 Countermeasures against blackjack card-counters 10 Detecting card counters 11 Technology for detecting card counters 12 History of card counting 13 References

[edit] Card counting in blackjack

[edit] Basics

The principle of counting cards in blackjack is that a deck of cards with a high proportion of high cards (ten-valued cards and aces) to low cards is good for the player, while the reverse (a deck with a high proportion of low cards to high cards) is good for the dealer. There are many reasons for this: blackjacks become more common (and they offer a higher payout than other winning hands), the dealer is more likely to bust a stiff hand, double-downs are more successful, and insurance becomes profitable. ^[1]

Contrary to the popular myth, card counters do not need savant qualities in order to count cards, because they are not tracking and memorizing specific cards. Instead, card counters assign a heuristic point score to each card they see and then track only the total score. (This score is called the "count".)^[2] The myth that counters keep track of every card was portrayed in the movie Rain Man, where the savant character Raymond Babbitt counts through six decks with ease and a casino employee comments that it is impossible to count six decks. Also, in the movie 21 card counting is portrayed as an intellectually difficult task which can only be undertaken by high-IQ top level students. In fact, card counting requires little more than simple addition, and possibly division, depending on the system being used. It also requires the ability to perform these tasks while also concentrating on playing the game correctly.

[edit] Basic system

Basic card counting assigns a positive, negative, or zero value to each card.

[edit] More advanced counting systems

The High-Low system is considered a single-level or level-one count, because the count never increases or decreases by more than one. A multilevel count, such as Zen Count or Wong Halves, makes finer distinctions between card values to gain greater play accuracy. Rather than all cards having a value of +1, 0, or −1, an advanced count might also include card ranks that are counted as +2 or −2. Advanced players might additionally maintain a side count of specific cards, such as a side count aces, to deal with situations where the best count for betting accuracy differs from the best count for playing accuracy.

Many side count techniques exist including special-purpose counts used when attacking games with nonstandard profitable-play options such as an over/under side bet.^[3]

The disadvantage of higher-level counts is that keeping track of more information can detract from the ability to play quickly and accurately. A card-counter might earn more money by playing a simple count quickly—more hands per hour played—than by playing a complex count slowly.

The following table illustrates various ranking systems for card counting.^[4]

Card Strategy	2	3	4	5	6	7	8	9	10	J	Q	K	A
Wizard Ace/Five	0	0	0	1	0	0	0	0	0	0	0	0	−1
KO	1	1	1	1	1	1	0	0	−1	−1	−1	−1	−1
Hi-Lo	1	1	1	1	1	0	0	0	−1	−1	−1	−1	−1
Hi-Opt I	0	1	1	1	1	0	0	0	−1	−1	−1	−1	0
Hi-Opt II	1	1	2	2	1	1	0	0	−2	−2	−2	−2	0
Zen Count	1	1	2	2	2	1	0	0	−2	−2	−2	−2	−1
Omega II	1	1	2	2	2	1	0	−1	−2	−2	−2	−2	0

The KO Strategy was first introduced in 1992 as the "All Sevens" count in The Book of British Blackjack^[5]

[edit] Running counts versus true counts in balanced counting systems

The running count is the running total of each card's assigned value. When using a balanced count (like the Hi-Lo system), the running count is converted into a "true count," which takes into consideration the number of decks used. With Hi-Lo, the true count is essentially the running count divided by the number of decks that haven't yet been dealt. However, many variations of true count calculation exist.^[6]

[edit] Unbalanced card-counting systems

In an unbalanced card-counting system, conversion to a true count is made unnecessary by the unbalanced nature of the counting system, but the starting number or indices are based on the number of decks being used. Popular unbalanced card counting systems include the K-O system and the Red 7 system. ^[7][8]

[edit] Back-counting

Back-counting, also known as "wonging", consists of standing behind a blackjack table that other players are playing on, and counting the cards as they are dealt. Stanford Wong first proposed the idea of back-counting, and the term "wong" comes from his name.^[9]

The player will enter or "wong in" to the game when the count reaches a point at which the player has an advantage. The player may then raise their bets as their advantage increases, or lower their bets as their advantage goes down. Some back-counters prefer to flat-bet, and only bet the same amount once they have entered the game. Some players will stay at the table until the game is shuffled, or they may "wong out" or leave when the count reaches a level at which they no longer have an advantage.

Back-counting is generally done on shoe games, of 4, 6, or 8 decks, although it can be done on pitch games of 1 or 2 decks. The reason for this is that the count is more stable in a shoe game, so a player will be less likely to sit down for one or two hands and then have to get up. In addition, many casinos do not allow "mid-shoe entry" in single or double deck games which makes wonging impossible. Another reason is that many casinos exhibit more effort to thwart card counters on their pitch games than on their shoe games, as a counter has a smaller advantage on an average shoe game than in a pitch game.^[10]

[edit] Advantages

Back-counting is different from traditional card-counting, in that the player does not play every hand he sees. This offers several advantages. For one, the player does not play hands at which he does not have a statistical advantage. This in turn reduces variance and fluctuations, and increases the total advantage of the player. Another advantage is that the player does not have to change their bet size as much, or at all if they choose. Large variations in bet size are one way that casinos detect card-counters, and this is eliminated with back-counting.

[edit] Disadvantages

There are several disadvantages to back-counting. One is that the player frequently does not stay at the table long enough to earn comps from the casino. Another disadvantage is that some players may become irritated with players who enter in the middle of a game, and superstitiously believe that this interrupts the "flow" of the cards. Lastly, a player who hops in and out of games may attract unwanted attention from casino personnel, and may be detected as a card-counter.

[edit] Group Counting

While a single player can maintain their own advantage with back-counting, card counting is most often used by teams of players to maximize their advantage. In such a team, some players called "counters" will sit at a table and play the game at the table minimum, while keeping a count (basically doing the back "counting". When the count is significantly high, the counter will discreetly signal another player, known as a "big player", that the count is high (the table is "hot"). The big player will then "wong in" and wager vastly higher sums (up to the table maximum) while the count is high. When the count "cools off" or the shoe is shuffled (resetting the count), the big player will "wong out" and look for other counters who are signaling a high count. This was the system used by the MIT Blackjack Team, whose story was in turn the inspiration for the movie "21".

The main advantage of group play is that the team can count several tables while a single back-counting player can usually only track one table. This allows big players to move from table to table, maintaining the high-count advantage without being out of action very long. It also allows redundancy while the big player is seated as both the counter and big player can keep the count (as in the movie "21", the counter can communicate the count to the big player discreetly as he/she sits down). The disadvantages include requiring multiple card-counters who can keep an accurate count, splitting the "take" among all members of the team, requiring counters to play a table regardless of the count (using only basic strategy, these players will lose money long-term), and requiring signals, which can alert pit bosses.

A simple variation removes the loss of having counters play; the counters simply watch the table instead of playing and signal big players to wong in as normal. The disadvantages of this variation are reduced ability of the counter and big player to communicate, and vastly increased suspicion, as blackjack is not generally considered a spectator sport in casinos except among those actually playing (unlike craps, roulette and wheels of fortune which have larger displays and so tend to attract more spectators).

[edit] Ranging bet sizes and the Kelly Criterion

Between 70% and 90% of the player edge when counting cards comes from placing larger bets when the count is favorable to the player. (The rest of the edge comes from changes to basic strategy based on the count.) ^[11] A mathematical principle called the Kelly criterion indicates that bet increases should be proportional to the player advantage. In practice, this means that the higher the count, the more a player should bet on each hand in order to take advantage of the player edge. Taken to its ultimate conclusion, the Kelly criterion would demand that a player not bet anything at all when the deck doesn't offer a positive expectation. "Wonging", as shown above, takes advantage of this.

[edit] Expected profit from card counting

Blackjack played with a perfect basic strategy typically offers a house edge of less than 0.5%, but a typical card counter who ranges his bets appropriately in a game with six decks will have an advantage of approximately 1% over the casino. Advantages of up to 2.5% are possible at normal penetrations from counting 6-deck Spanish 21, for the S17 or H17 with redoubling games.^[12] This amount varies based on the counter's skill level, hands per hour, penetration (1 - fraction of pack cut off), and the number of betting units that the counter is able to spread from. The variance in blackjack is high, so generating a sizeable profit can take hundreds of hours of play. The deck will only have a positive enough count for the player to raise his bets 10%-35% of the time depending on rules, penetration and strategy. ^[13]

At a table where a player makes a $100 average bet, a 1% advantage means a player will win an average $1 per hand. This translates into an average hourly winning of $50 if the player is dealt 50 hands per hour.

With typical bet ranging and typical Las Vegas six-deck rules, a player whose strategy yields an average profit of $50 per hour will likely face a standard deviation in the neighborhood of $1,400 per hour. Therefore, it is highly advisable for counters to set aside a large dedicated bankroll; one popular rule of thumb dictates a bankroll of 100 times the maximum bet per hand. ^[14][15]

Another aspect of the probability of card counting is that, at higher counts, the player's probability of winning a hand is only slightly changed and still below 50%.^[16] The player's edge over the house on such hands does not come from the player's probability of winning the hands. Instead it comes from the increased probability of a blackjack and from the ability to perform certain actions (like doubling down, insuring, and splitting) that are not available to the house.

[edit] Card counting devices

A range of card counting devices are available but are deemed to be illegal in many casinos. In February 2009, the Nevada Gaming Control Board issued a warning that an iPhone card counting application was illegal in that state.^[17] Card counting with your mind is legal and usually more accurate than this application.^[18]

[edit] Legal status of card counting

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A myth some casinos propagate is that card counting is illegal in the United States. Card counting without an outside device is completely legal. There are no provisions in the rules of blackjack or United States law that prohibit card counting. Despite this, casinos still offer blackjack as a game knowing that a skilled player will have an advantage over the house. Casinos believe they avoid losing money by preventing card counters from playing. However, they also inadvertently ban many poor players. In Las Vegas, casinos are allowed to do this because the casino is private property, and the owner can decide who is allowed to enter.

Ken Uston, a man who some consider to be the greatest card-counter who ever lived, took the Atlantic City casinos to court in a famous case called Uston v. Resorts International where he achieved victory as the court ruled that casinos can’t ban skilled players. But this did prompt the casinos to start doing things like adding decks to hinder card counters. Uston wasn’t happy with just playing at Atlantic City casinos though and he chose to still go to places he wasn’t well received such as Vegas. However, he did so under numerous disguises which actually succeeded in fooling casino employees most of the time. One account saw Ken dressed as a Hoover Dam worker where he went on to spread his bet from the table minimum to the table max on a single deck which is usually a tip-off to look into somebody. However, his masterful disguise fooled the workers into thinking he was just a regular dam worker who got extremely lucky.^[19]

[edit] Countermeasures against blackjack card-counters

Casinos have spent a great amount of effort and money in trying to thwart card counters. Countermeasures used to prevent card counters from profiting at blackjack include:

• Harassment of suspected card counters by casino staff. This may be as simple as engaging a suspected card counter in a conversation to break their concentration.
• Adding more decks on the Blackjack table making many more cards to keep track of.
• Card-counter identification, using books of photos and new facial-recognition technologies.
• Computerized scanners in blackjack tables that can identify counting systems when in use.
• Computer systems used in surveillance rooms that surveillance staff use to target suspect players to quantify their threat to the house.
• Shuffling more often or shuffling when a player increases their wager.
• Changing rules for splitting, doubling down, or playing multiple hands. This also includes changing a table's stakes.
• Flat betting a player or making it so they cannot change the amount they bet during a shoe.

Some jurisdictions (e.g. Nevada) have no legal restrictions placed on these countermeasures. Other jurisdictions such as New Jersey limit the countermeasures a casino can take against skilled players. ^[20]

Some of these countermeasures have a downside for the casino as well. Frequent shuffling, for example, reduces the amount of time that the non-counting players are playing and consequently reduces the house's winnings. Some casinos now use automatic shuffling machines to compensate for this, with some models of machines shuffling one set of cards while another is in play. Others, known as Continuous Shuffle Machines (CSMs), allow the dealer to simply return used cards to a single shoe to allow playing with no interruption. Because CSMs essentially force minimal penetration, they remove almost all possible advantage of traditional counting techniques. In most online casinos, the deck is shuffled at the start of each new round, ensuring the house always has the advantage.

A pitboss who determines that a player is a card-counter might either "back off" the player by inviting them to play any game other than blackjack, or will ban them from the casino itself. In jurisdictions where this is not legal, such as Atlantic City, a pitboss can require the player to flat-bet and disallow players from entering in the middle of a shoe. Such countermeasures effectively remove any chance of gaining an advantage from card counting in multi-deck games. The player's name and photo (from surveillance cameras) may also be shared with other casinos and added to a database of card-counters and cheaters (Note: card counting is not cheating, but casinos still associate the two groups together) run for the benefit of casino operators. One such blacklist was known as the Griffin Book, and was maintained by a company called Griffin Investigations. However, Griffin Investigations was forced into bankruptcy in 2005 after losing a libel lawsuit filed by professional gamblers.

[edit] Detecting card counters

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Monitoring player behavior to assist with detecting the card counters falls into the hands of the on-floor casino personnel ("pit bosses") and casino-surveillance personnel, who may use video surveillance ("the eye in the sky") as well as computer analysis, to try to spot playing behavior indicative of card counting; early counter-strategies featured the dealers' learning to count the cards themselves to recognize the patterns in the players. In addition, many casinos employ the services of various agencies, such as Griffin Investigations, who claim to have a catalog of advantage players. If a player is found to be in such a database, he will almost certainly be stopped from play and asked to leave regardless of his table play. For successful card counters, therefore, skill at "cover" behavior, to hide counting and avoid "drawing heat" and possibly being barred, may be just as important as playing skill.

There have been some high-profile lawsuits involving whether the casino is allowed to bar card-counters.^[21] Essentially, card-counting, if done in one's head and with no outside assistance from devices such as blackjack computers, is not illegal. Making calculations within one's own mind is not an arrestable offence. Using an outside device or aid, however, was found illegal in a court case in Nevada. In this case, two individuals were convicted of cheating for using a video device to gain knowledge of a blackjack dealer's hole card.^[22] While this case is clearly distinct from pure card-counting, the precedent could possibly be applied to electronic devices used by players to assist in counting cards. At the time of the trial, however, there was no anti-device law in Nevada, and the law that was written after this case is considered by many attorneys to be unconstitutionally vague.^{[citation needed]} Still, the law has been adopted by most other states with casinos, and no player has yet tried the constitutionality of the law.

Casinos do not tolerate card counters or practitioners of other legal professional gambling techniques willingly and, if permitted by their jurisdiction, may ban counters from their casinos. In Nevada, where the casinos are ruled to be private places, the only prerequisite to a ban is the full reading of the Trespass Act to ban a player for a year. Some skilled counters try to disguise their identities and playing habits; however, some casinos have claimed that facial recognition software can often match a camouflaged face with a banned one. In the experience of most professional gamblers, this is untrue, and a 2004 book by a Las Vegas casino surveillance director, The Card Counter's Guide to Casino Surveillance, also declares this assertion to be an overstatement. Approximately 100 casinos in the United States used the Griffin Investigations consulting firm to help them track down and monitor card counters, before the firm's bankruptcy as a result of a lawsuit for libel filed by professional gamblers.

[edit] Technology for detecting card counters

Several automated systems have been designed to aid detection of card counters. The MindPlay system scans card values for the entire deck after shuffling just prior to play. The ShuffleMaster Intelligent Shoe system^[23] scans card values individually as cards exit the shoe. Software called Bloodhound^[24] and Protec 21^[25] allows voice input of card and bet values, which is used to determine the player edge. A more recent innovation is the use of RFID signatures embedded within the casino chips so that the table can automatically track bet amounts.^[26]

Automated card-reading technology has known abuse potential in that it can be used to simplify the practice of preferential shuffling—having the dealer reshuffle the cards whenever the odds favor the players. To avoid liability concerns, some blackjack protection systems have been designed to refrain from sending data over the network until the shoe has ended.^[27] Other vendors consider real-time notification to surveillance that a shoe is "hot" to be an important product feature.^[28]

With card values, play decisions, and bet decisions conveniently accessible, the casino can analyze bet variation, play accuracy, and play variation.

Bet variation. The simplest way a card-counter makes money is to bet more when he has an edge. While playing back the tapes of a recent session of play, software can generate a scatter plot of the amount bet versus the count at the time the bet was made and find the trendline that best fits the scattered points. If the player is not counting cards, there will be no trend; his bet variation and the count variation will not consistently correlate. If the player is counting and varying bets according to the count, there will be a trend whose slope reflects the player's average edge from this technique.^[29]

Play accuracy. Normal players tend to make basic-strategy errors. Card-counters must accurately know exactly when to hit, stand, split, or double down. Software can verify the rate at which the player makes errors and calculate the resulting house edge.

Play variation. When card-counters vary from basic strategy, they do so in response to the count, to gain an additional edge. Software can verify whether there is a pattern to play variation. Of particular interest is whether the player sometimes (when the count is positive) takes insurance and stands on 16 versus a dealer 10, but plays differently when the count is negative.

[edit] History of card counting

American mathematician Dr. Edward O. Thorp is considered the father of card counting. His 1962 book Beat the Dealer (ISBN 0-394-70310-3) outlined various betting and playing strategies for optimal blackjack play.^[30] Although mathematically sound, some of the techniques described no longer apply, as casinos took counter-measures (such as no longer dealing to the last card). Also, the counting system described (10-count) is harder to use and less profitable than the point-count systems that have been developed since. A history of how counting developed can be seen in David Layton's documentary film, The Hot Shoe.

Even before the publication of Beat the Dealer, however, a small number of professional card counters were beating blackjack games in Las Vegas and casinos elsewhere. One of these early card counters was Jess Marcum, who is described in documents and interviews with professional gamblers of the time as having developed the first full-fledged point-count system. Another documented pre-Thorp card counter was a professional gambler named Joe Bernstein, who is described in the 1961 book I Want To Quit Winners, by Reno casino owner Harold Smith, as an ace counter feared throughout the casinos of Nevada. And in the 1957 book Playing Blackjack to Win, Roger Baldwin, Wilbert Cantey, Herbert Maisel, and James McDermott (known among card counters as "The Four Horsemen") published the first accurate blackjack basic strategy and a rudimentary card-counting system, devised solely with the aid of crude mechanical calculators—what used to be called “adding machines".

From the early days of card-counting, some players have been hugely successful, including Al Francesco, the inventor of blackjack team play and the man who taught Ken Uston how to count cards, and Tommy Hyland, manager of the longest-running blackjack team in history. Ken Uston, though perhaps the most famous card-counter through his 60 Minutes television appearance and his books, tended to overstate his winnings, as documented by players who worked with him, including Al Francesco and team member Darryl Purpose.

In the 1970s and 1980s, as computing power grew, more advanced (and more difficult) card-counting systems came into favor. Many card-counters agree, however, that a simpler and less advantageous system that can be played flawlessly for hours earns an overall higher return than a more complex system prone to user error.

In the 1970s Ken Uston was the first to write about a tactic of card counting he called the Big Player Team. The book was based on his experiences working as a "big player" (BP) on Al Francesco's teams. In big-player blackjack teams a number of card counters, called "spotters", are dispatched to tables around a casino, where their responsibility is to keep track of the count and signal to the big player when the count indicates a player advantage. The big player then joins the game at that table, placing maximum bets at a player advantage. When the spotter indicates that the count has dropped, he again signals the BP to leave the table. By jumping from table to table as called in by spotters, the BP avoids all play at a disadvantage. In addition, since the BP's play appears random and irrational, he avoids detection by the casinos. The spotters, who are doing the actual counting, are not themselves changing their bet size or strategy, so they are relatively inconspicuous.

With this style of play, a number of blackjack teams have cleared millions of dollars through the years. Well-known blackjack teams with documented earnings in the millions include those run by Al Francesco, Ken Uston, Tommy Hyland, various groups from the Massachusetts Institute of Technology (MIT) and, most recently, a team called "The Greeks". Ken Uston wrote about blackjack team play in Million Dollar Blackjack (ISBN 0-89746-068-5), although many of the experiences he represents as his own in his books actually happened to other players, especially Bill Erb, a BP Uston worked with on Al Francesco's team. Ben Mezrich also covers team play in his book Bringing Down The House (ISBN 0-7432-4999-2), which describes how MIT students used it with great success. See also the Canadian movie The Last Casino and more recently the movie 21.

The publication of Ken Uston's books both stimulated the growth of blackjack teams (Hyland's team and the first MIT team were formed in Atlantic City shortly after the publication of Million Dollar Blackjack) and increased casino awareness of the methods of blackjack teams, making it more difficult for such teams to operate. Hyland and Francesco soon switched to a form of shuffle tracking called "ace sequencing." Also referred to as "cutting to the ace," this technique involves various methods designed to spot the bottom card during a shuffle (ideally an ace) and expertly cut the deck and play future hands to force the player to receive the ace. This made it more difficult for casinos to detect when team members were playing with an advantage. In 1994, members of the Hyland team were arrested for ace sequencing and blackjack team play at Casino Windsor in Windsor, Ontario, Canada. It was documented in court that Nevada casinos with ownership stakes in the Windsor casino were instrumental in the decision to prosecute team members on cheating charges. However, the judge ruled that the players' conduct was not cheating, but merely the use of intelligent strategy.^[8]

[edit] References