Card counting

Card counting is a card game strategy used to determine when a player has a probability advantage. Card-counting is a form of advantage gambling, as well as intelligent gameplay. The term is used almost exclusively to refer to the tracking of the ratio of high cards to low cards in blackjack, 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.

Card counting in blackjack

The fundamental principle behind counting cards in blackjack is that a deck of cards with a higher proportion of high cards (tens and aces) to low cards is good for the player, while the reverse is true for the dealer. A deck rich in tens and aces improves the player's odds, because blackjacks (which offer a higher payout than other winning hands) become more common, the dealer is more likely to bust a stiff hand, and double-downs are more successful.

Card counters raise their bets when the ratio of high cards to low cards in the deck is skewed in their favor. Alternatively, they may also watch the game, and enter when the count becomes favorable, a tactic known as back-counting. They also make strategy adjustments based on the ratio of high cards to low cards. These two adjustments to their betting and playing strategy can give players a mathematical advantage over the house.

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".) This myth sprouted from the movie Rain Man, where the savant character Raymond Babbit counts through six decks with ease.

The plus-minus count

Basic card counting assigns a positive, negative, or null value to each card (2 through ace). As each card is dealt, the running count is adjusted by each card's assigned value. There are multiple card-counting systems in use, but a plus-minus count—such as the Hi-Lo system proposed by Harvey Dubner in 1963 and later refined by Julian Braun and Stanford Wong —is one of the more basic and illustrative systems.

In the Hi-Lo system, the cards 2 through 6 are assigned a value of +1. Tens (and face cards) through aces are assigned a value of -1. Cards 7, 8, and 9 have a value of zero (so they can be ignored).

The Hi-Lo system is an example of a balanced card-counting system, in that there are an equal number of +1 and -1 cards in the deck, so a count of all 52 cards would result in an end count of 0.

More advanced counting systems

The Hi-Lo system is considered a single-level or level-one count, because the count never increments or decrements 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 of aces, to deal with situations where the best count for betting accuracy differs from the best count for playing accuracy.

Special-purpose counts are also used when attacking games with nonstandard profitable-play options such as an over/under side bet.

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.

Card Strategy	2	3	4	5	6	7	8	9	10	J	Q	K	A
Ten Count	1	1	1	1	1	1	1	1	-2	-2	-2	-2	1
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

Running counts versus true counts in balanced counting systems

The "running count" is the running total of each card's assigned value. In a multiple-deck game, 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 in play. The true count is the running count divided by the number of decks that haven't yet been dealt. .

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 count begins with something other than 0. The starting number is a value based on the number of decks being used. Popular unbalanced card counting systems include the "K-O" system and the "Red 7" system.

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.) 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. When this is actually done in practice it is called "wonging", after Stanford Wong, who popularised the idea.

Expected profit from card counting

Blackjack played with a perfect basic strategy typically offers a house edge of less than 50%, 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. This amount varies based on the counter's skill level and the playing conditions, and the variance in blackjack is high, so generating an hourly profit can take hundreds of hours of play. The deck will only have a positive enough count for the player to raise his bets 25% of the time.

At a table where a player makes a $1,000 average bet, a 1% advantage means a player will win on average $10 per hand. This translates into an average hourly winning of $500 if the player is dealt 50 hands per hour.

With typical bet ranging, a player's standard deviation per N=100 hands is 1.1*Sqrt(N) x his average bet per hand, meaning that a player whose strategy yields an average profit of $50 per hour will likely face a standard deviation in the neighborhood of $550 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 400 times the average bet per hand at count = 0.

Another interesting aspect of the probability of card counting is the fact that, at higher counts, the player's probability of winning a hand is only slightly changed and still below 50%. The player's edge over the house on such hands comes not from his probability of winning the hands, but from his ability to perform certain actions—like doubling down, insuring, and splitting—that are not available to the house and the increased probability of a blackjack.

Countermeasures against blackjack card-counters

A myth casinos propagate is that card counting is illegal. Card counting 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 avoid losing money by preventing card counters from playing. 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.

Casinos have made a great amount of effort and spent a great deal of money trying to thwart card counters. Among the countermeasures used to prevent card counters from profiting at blackjack:

• 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.
• Card-counter identification, using books of photos and new facial-recognition technologies.
• Computerized scanners in blackjack tables, which 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 his wager size.
• Changing rules for splitting, doubling down, or playing multiple hands. This also includes changing a table's stakes.

Some jurisdictions (like Nevada) have no legal restrictions placed on these countermeasures. Other jurisdictions, like New Jersey, limit the countermeasures a casino can take against "skilled players".

Some of these countermeasures have a downside for the casino as well. Frequent shuffling, for example, reduces the amount of time that the noncounting players are playing and consequently reduces the house's winnings. Some casinos now use automatic shuffling machines to compensate for this. Some models of shuffling machines shuffle 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 him/her to play any game other than blackjack, or will ban him/her 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.

Detecting card counters

Monitoring player behavior to assist in this identification falls to 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 . Essentially, card-counting, if done in one's head and with no outside assistance from devices such as blackjack computers, is not illegal, as 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 . 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. Still, the law has been adopted by most other states with casinos, and no player has yet tried the constitutionality of the law.

Casinos don't 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.

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 scans card values individually as cards exit the shoe. Software called Bloodhound and Protec 21 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.

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.. Other vendors are less scrupulous in this regard and consider real-time notification to surveillance that a shoe is "hot" an important product feature..

Having made the card values, play decisions, and bet decisions conveniently accessible, what can the casino do with this information to spot counters? The casino looks at 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.

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.

History of blackjack 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. 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. The only way such a team can be detected is by their signals.

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.

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.

External links

• Blackjack Forum Online has numerous articles on card counting
• World's Greatest Job by Kevin Blackwood