Card counting - Knowledge

721:. Another disadvantage is that some players may become irritated with players who enter in the middle of a game. They believe that this interrupts the "flow" of the cards. Their resentment may not merely be superstition, though, as this practice will negatively impact the other players at the table; with one fewer player at the table when the card composition becomes unfavorable, the other players will play through more hands under those conditions as they will use up fewer cards per hand. Similarly, they will play fewer hands in the rest of the shoe if the advantage player slips in during the middle of the shoe, when the cards become favorable; with one more player, more of those favorable cards will be used up per hand. This negatively impacts the other players whether they are counting cards or not. Also, a player who hops in and out of games may attract unwanted attention from casino personnel and may be detected as a card-counter. 1217:'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, they again signal the BP to leave the table. By jumping from table to table as called in by spotters, BP avoids all play at a disadvantage. In addition, since BP's play appears random and irrational, they avoid 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. 1275:) 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 1011:. The simplest way a card counter makes money is to bet more when they have an edge. While playing back the tapes of a recent session of play, the 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; their 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. 1157: 730:

doing the back "counting"). When the count is significantly high, the spotter 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

3497: 800:, for the S17 or H17 with redoubling games. This amount varies based on the counter's skill level, penetration (1 – a fraction of pack cut off), and the betting spread (player's maximum bet divided by minimum bet). The variance in blackjack is high, so generating a sizable profit can take hundreds of hours of play. The deck will only have a positive enough count for the player to raise bets 10%-35% of the time depending on rules, penetration, and strategy. 3517: 636: 787:

This creates a "bet ramp" according to the principles of the Kelly criterion. A bet ramp is a betting plan with a specific bet size tied to each true count value in such a way that the player wagers proportionally to the player's advantage to maximize bankroll growth. Taken to its conclusion, the Kelly criterion demands that a player not bet anything when the deck does not offer a positive expectation; "Wonging" implements this.

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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 greatly reduce the 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.

40: 3527: 149:(EOR). The EOR is the estimated effect of removing a given card from play. Counters gauge the effect of removal for all cards dealt and how that affects the current house edge. Larger ratios between point values create better correlations to actual EOR, increasing the efficiency of a system. Such systems are classified as level 1, level 2, level 3, and so on. The level corresponds to the ratio between values. 3507: 758:, the spotter can communicate the count to the big player discreetly as they sit down). The disadvantages include requiring multiple spotters who can keep an accurate count, splitting the "take" among all members of the team, requiring spotters 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. 2812: 910:") 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. Many casino chains keep databases of players that they consider undesirable. Casinos can also subscribe to databases of advantage players offered by agencies like 1017:. When card counters vary from basic strategy, they do so in response to the count, to gain an additional edge. The 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. 927:. If a player is found to be in such a database, they will almost certainly be stopped from play and asked to leave regardless of their 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. 700:

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.

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Some countermeasures result in disadvantages for the casino. Frequent or complex shuffling, for example, reduces the amount of playing time and consequently the house winnings. Some casinos use automatic shuffling machines to counter the loss of time, with some models of machines shuffling one set of

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indicates that bet increases should be proportional to the player's advantage. In practice, this means that the higher the count, the more a player should bet to take advantage of the player's edge. Using this principle, a counter can vary bet sizes in proportion to the advantage dictated by a count.

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Some strategies count the ace (ace-reckoned strategies) and some do not (ace-neutral strategies). Including aces in the count improves betting correlation since the ace is the most valuable card in the deck for betting purposes. However, since the ace can either be counted as one or eleven, including

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shuffle decks, interfere with the shuffle tracking variation of card counting by hiding the shuffle. Continuous shuffling machines (CSMs), that partially shuffle used cards back into the "shoe" during play, interfere with card counting. CSMs result in very shallow penetration (number of seen cards),

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Detection of card counters will be confirmed after a player is first suspected of counting cards; when seeking card counters, casino employees, whatever their position, could be alerted by many things that are most common when related to card counting but not common for other players. These include:

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agreed, ruling that "the state's control of Atlantic City's casinos is so complete that only the New Jersey Casino Control Commission has the power to make rules to exclude skillful players." The commission has made no regulation on card counting, so Atlantic City casinos are not allowed to ban card

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Historically, blackjack played with a perfect basic strategy offered a house edge of less than 0.5%. As more casinos have switched games to dealer hits soft-17 and blackjack pays 6:5, the average house edge in Nevada has increased to 1%. A typical card counter who ranges bets appropriately in a game

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A simple variation removes the loss of having spotters play; the spotters simply watch the table instead of playing and signal big players to Wong in and out as normal. The disadvantages of this variation are reduced ability of the spotter and big player to communicate, reduced comps as the spotters

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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

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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

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A portion of the expected profit comes from modifying playing strategy based on the known altered composition of cards. For this reason, a system's PE gauges how effectively it informs the player to modify strategy according to the actual composition of undealt cards. A system's PE is important when

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Basic card counting systems assign a positive, negative, or zero value to each card. When a card is dealt, the count is adjusted by that card's counting value. Low cards increase the count; they increase the percentage of high cards in the deck. High cards decrease the count for the opposite reason.

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Card counting is not illegal under British law, nor is it under federal, state, or local laws in the United States provided that no external card counting device or person assists the player in counting cards. Still, casinos object to the practice, and try to prevent it, banning players believed to

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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

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The primary goal of a card counting system is to assign point values to each card that roughly correlate to the card's "effect of removal" or EOR (that is, the effect a single card has on the house advantage once removed from play), thus enabling the player to gauge the house advantage based on the

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In the 1970s and 1980s, as computing power grew, more advanced and harder 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

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Back-counting differs from traditional card-counting in that the player does not play every hand they see. This offers several advantages. For one, the player does not play hands without a statistical advantage. This increases the total advantage of the player. Another advantage is that the player

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One way to deal with such tradeoffs is to ignore the ace to yield higher PE while keeping a side count which is used to detect an additional change in EV which the player will use to detect additional betting opportunities that ordinarily would not be indicated by the primary card counting system.

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having the dealer reshuffle the cards whenever the odds favor the players. To comply with licensing regulations, some blackjack protection systems have been designed to delay access to real-time data on the remaining cards in the shoe. Other vendors consider real-time notification to surveillance

889:, the only legal gambling location in China, does not technically prohibit card counting but casinos reserve the right to expel or ban any customers, as is the case in the US and Britain. The use of electronic devices to aid such strategies, however, is strictly prohibited and can lead to arrest. 815:

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%. 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

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The running count is the running total of each card's assigned value. When using a balanced count (such as 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 the running count divided by the

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Since there is the potential to create an overtaxing demand on the human mind while using a card counting system another important design consideration is the ease of use. Higher-level systems and systems with side counts will obviously become more difficult and in an attempt to make them easier,

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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 "spotters" will sit at a table and play the game at the table minimum, while keeping a count (basically

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Under one set of circumstances, a player with a 1-15 unit bet spread with only one-deck cut off of a six-deck game will enjoy an advantage of as much as 1.2% with a Standard Deviation of 3.5 on a 2.1 unit average bet. Therefore, it is highly advisable for counters to set aside a large dedicated

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The most common side counted card is the ace since it is the most important card in terms of achieving a balance of BC and PE. In theory, a player could keep a side count of every card and achieve a near 100% PE, however, methods involving additional side counts for PE become more complex at an

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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

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Card counters do not need unusual mental abilities; they do not track or memorize specific cards. Instead, card counters assign a point score to each card that estimates the value of that card. They track the sum of these values with a running count. The myth that counters track every card was

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composition of cards still to be dealt. Larger ratios between point values can better correlate to actual EOR, but add complexity to the system. Counting systems may be referred to as "level 1", "level 2", etc., corresponding to the number of different point values the system calls for.

1112:, a small number of professional card counters were beating blackjack games in Vegas and elsewhere. One was Jess Marcum, who developed the first full-fledged point-count system. Another pre-Thorp card counter was professional gambler Joe Bernstein. He is described in 1961's 578:

When the sum of all the permutations of the undealt cards offers a positive expectation to a player using optimal playing strategy, there is a positive expectation to a player placing a bet. A system's BC gauges how effective a system is at informing the user of this

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Doubling down increases expected value. The elevated ratio of tens and aces improves the probability that doubling down will succeed. The most common hand values that the player doubles down on are 11, 10, and 9; and drawing a high card to these will make a strong

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Card counters may make unique playing strategy deviations not normally used by non-counters. Plays such as splitting tens, doubling soft 18/19/20, standing on 15/16, and surrendering on 14, when basic strategy says otherwise, may be a sign of a card counter.

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by keeping a running count of high and low valued cards dealt. They generally bet more when they have an advantage and less when the dealer has an advantage. They also change playing decisions based on the composition of the deck and sometimes play in teams.

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Intelligent Shoe system also scans card values as cards exit the shoe. Software called Bloodhound and Protec 21 allows voice input of card and bet values, in an attempt to determine the player edge. A more recent innovation is the use of

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The use of an automatic shuffle machine or in rare cases, a dealer dedicated solely to shuffling a new shoe while another is in play, will eliminate the need for the dealer to shuffle the shoe prior to dealing a new one, increasing game

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The ideal system is a system that is usable by the player and offers the highest average dollar return per period of time when dealt at a fixed rate. With this in mind, systems aim to achieve a balance of efficiency in three categories:

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They also increase the probability the dealer will bust, in the event that the dealer shows a low up-card (i.e. 2-6). This also increases the odds of the player busting, but the player can choose to stand on lower totals based on the

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The publication of Ken Uston's books and of his landmark lawsuits against the casinos, 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

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number of decks that have not yet been dealt; this can be calculated by division or approximated with an average card count per round times the number of rounds dealt. However, many variations of the true count calculation exist.

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On the other hand, low cards benefit the dealer. The rules require the dealer to hit stiff hands (12–16 total), and low cards are less likely to bust these totals. A dealer holding a stiff hand will bust if the next card is a 10.

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

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bankruptcy protection in 2005 after losing a libel lawsuit filed by professional gamblers. In 2008 all Chapter 11 payments were said to be up to date and all requirements met, and information was being supplied using

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count, such as Zen Count, Wong Halves, or Hi-Opt II, further distinguishes card values to increase accuracy. An advanced count includes values such as +2 and −2, or +0.5 and -0.5. Advanced players might also keep a

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The overall efficiency at creating player advantage as a whole; a system may indicate a small advantage when in fact the advantage is much larger – this reduces the overall ROI of the system while in play.

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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.

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A portion of expected gain from counting cards comes from taking the insurance bet, which becomes profitable at high counts. An increase in IC will offer additional value to a card counting system.

1283:, 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 609:

exponential rate as you add more side counts and the ability of the human mind is quickly overtasked and unable to make the necessary computations. Without any side counts, PE can approach 70%.

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Extremely aggressive plays such as splitting tens and doubling soft 19 and 20 are often called out to the pit to notify them because they are telltale signs of not only card counters but

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from the increased probability of blackjacks, increased gain and benefits from doubling, splitting, and surrender, and the insurance side bet, which becomes profitable at high counts.

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For example, the Hi-Lo system subtracts one for each 10, jack, queen, king, or ace and adds one for any card between 2 and 6. 7s, 8s, and 9s count as zero and do not affect the count.

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Keeping track of more data with higher level counts can hurt speed and accuracy. Some counters earn more money playing a simple count quickly than by playing a complex count slowly.

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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

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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.

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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:

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The overall efficiency of a card counting system at detecting player advantage; affects how often the player will actually play a hand at an advantage per period of time

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are not sitting down, and vastly increased suspicion, as blackjack is not generally considered a spectator sport in casinos except among those actually playing (unlike

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unbalanced systems eliminate the need for a player to keep tabs on the number of cards/decks that have already entered play typically at the expense of lowering PE.

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Penetration will almost directly affect the magnitude of player advantage that is exploitable and the rate that hands are dealt with a player at an advantage.

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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

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an ace in the count decreases the accuracy of playing efficiency. Since PE is more important in single- and double-deck games, and BC is more important in

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Many side count techniques exist, including special-purpose counts used for games with nonstandard profitable-play options such as an over/under side bet.

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the 10-count, is harder to use and less profitable than later systems. A history of how counting developed can be seen in David Layton's documentary film

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be counters. In their pursuit to identify card counters, casinos sometimes misidentify and ban players suspected of counting cards even if they do not.

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

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The number of players seated at a table will slow the game pace, and reduce the number of hands a player will be able to play in a given time frame.

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Shuffling when a player increases their wager or when the casino feels the remaining cards are advantageous to the player (preferential shuffling).

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Game speed, table with side bets will be dealt at a slower pace than tables without them which will reduce the number of hands dealt over time.

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They increase the player's probability of hitting a Blackjack, which often pays out at 3 to 2 odds (although some casinos pay at 6 to 5).

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does not have to change their bet size as much (or at all). Large variations in bet size are one way that casinos detect card counters.

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inductee, filed a lawsuit against an Atlantic City casino, claiming that casinos did not have the right to ban skilled players. The

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From the early days, some have been succeeded, including Al Francesco, the inventor of blackjack team play and the man who taught

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Monitoring player behavior to assist with detecting the card counters falls into the hands of the on-floor casino personnel ("

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character Raymond Babbitt counts through six decks with ease, and a casino employee comments that it is impossible to do so.

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Back-counting has disadvantages, too. One is that the player frequently does not stay at the table long enough to earn

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Changing rules for splitting, doubling down, or playing multiple hands. This also includes changing a table's stakes.

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Back-counting, or "Wonging", consists of standing behind a blackjack table and counting the cards as they are dealt.

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counters. As they are unable to ban counters even when identified, Atlantic City casinos have increased the use of

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Decreasing penetration, the number of cards dealt before a shuffle. This reduces the advantage of card counting.

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Automated card-reading technology has known abuse potential in that it can be used to simplify the practice of

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Mathematics in Popular Culture: Essays on Appearances in Film, Fiction, Games, Television and Other Media

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while the big player is seated as both the counter and big player can keep the count (as in the movie

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by Reno casino owner Harold Smith as an ace counter feared throughout Nevada. And in the 1957 book,

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Banning known counters from playing blackjack, all games, or entering casino property (trespassing).

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signatures embedded within the casino chips so that the table can automatically track bet amounts.

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of specific cards like aces. This is done where betting accuracy differs from playing accuracy.

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ruled that the players' conduct was not cheating, but merely the use of intelligent strategy.

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Several semi-automated systems have been designed to aid the detection of card counters. The

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took countermeasures (such as no longer dealing with the last card). The counting system in

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Flat betting a player or making it so they cannot change the amount they bet during a shoe.

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the effect of PE has a large impact on the total gain, as in single- and double-deck games.

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used to determine whether the player or the dealer has an advantage on the next hand.

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Dramatic bet variation especially with larger bets being placed only at the end of a

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The theory of blackjack: the compleat card counter's guide to the casino game of 21

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A card counting system aims to assign point values roughly correlating to a card's

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Repeat until Rich: A Professional Card Counter's Chronicle of the Blackjack Wars

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On the other hand, neither card counting nor ... is illegal under Nevada law.

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Thorp (1966), pp. 24–27, pp. 41–47, pp. 98–99, pp. 102–103, p. 110, p. 115.

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system (now discontinued) scanned card values as the cards were dealt. The

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Not allowing entry into a game until a shuffle occurs (no mid-shoe entry).

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count; the running count never increases or decreases by more than one. A

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Eddie Olsen (18 April 1981). "Ken Uston: Big Player Without a Game".

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limit the countermeasures a casino can take against skilled players.

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which have larger displays and so tend to attract more spectators).

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Uston v. Resorts International Hotel, Inc.; 445 A.2d 370 N.J. 1982

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Card counting is based on statistical evidence that high cards (

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Blackjack strategy used to determine advantage in upcoming hands

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They provide additional splitting opportunities for the player.

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Beat the Dealer: A Winning Strategy for the Game of Twenty-One

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Running counts versus true counts in balanced counting systems

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The Law for Gamblers: A Legal Guide to the Casino Environment

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periodical featured a printout that demonstrated this feature

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Automatic shuffling machines (ASMs or batch shufflers), that

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profitable by increasing the probability of dealer blackjack.

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Sklar, Jessica K.; Sklar, Elizabeth S. (29 February 2012).

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dictates a bankroll of 100 times the maximum bet per hand.

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The Theory of Blackjack: The Complete Card Counter's Guide

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are forbidden from banning card counters as a result of a

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first proposed the idea of back-counting, hence the name.

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Blackjack Blueprint: How to Play Like a Pro ... Part-Time

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that a shoe is "hot" to be an important product feature.

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games, counting the ace is more important in shoe games.

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Casino-ology 2: New Strategies for Managing Casino Games

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This table illustrates some example counting systems.

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greatly reducing the effectiveness of card counting.

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The Pro's Guide to Spanish 21 and Australian Pontoon

2411:"TABLE GAME MYTHS PERSIST AMONG PLAYERS AND DEALERS" 2374:"TABLE GAME MANAGEMENT FOR THE SMALL CASINO, PART 2" 2343:"Dealing With Card-Counters – Gambling and the Law®" 2723:

Blackbelt in Blackjack: Playing 21 as a Martial Art

1775: 1390:(6th ed.). Las Vegas, Nev.: Huntington Press. 949:

Playing only a small number of hands during a shoe.

2725:(Revised ed.). New York: Cardoza Publishing. 561: 32:"Card counter" redirects here. For the film, see 3543: 819:Many factors affect expected profit, including: 2129:The card counter's guide to casino surveillance 1576:"True Count Calculation – The Whole Story" 1087:is the father of card counting. His 1962 book, 2640:(1st ed.). New York: Cardoza Publishing. 2564: 2523: 2293:Casino-ology: The Art of Managing Casino Games 2170:"CNET News story, "Vegas Casino Bets on RFID"" 1353: 3004: 2755: 2602:(1st ed.). Oakland, CA: RGE Publishers. 2572:(4th ed.). Las Vegas: Huntington Press. 1955:"Casino design and why the house always wins" 1124:– what used to be called "adding machines". 2621:(3rd ed.). Las Vegas: RGE Publishing. 2616: 2586: 2013: 1800:: CS1 maint: numeric names: authors list ( 1381: 1379: 1377: 3011: 2997: 2762: 2748: 2598:Rose, I. Nelson; Loeb, Robert A. (1998). 2316:Rose, I. Nelson; Loeb, Robert A. (1998). 2265: 1904: 1871: 1808: 1776:Rose1=I. Nelson; Loeb, Robert A. (1998). 1519: 1517: 1338: 1201:Learn how and when to remove this message 778:Ranging bet sizes and the Kelly criterion 676:Learn how and when to remove this message 2597: 2505:"History of Blackjack and Card Counting" 2476: 2315: 2101: 1984: 1982: 1922:"How Advantage Players Game the Casinos" 1374: 1164:This article includes a list of general 38: 2698:Advantage Play for the Casino Executive 2619:Blackjack Attack: playing the pros' way 2543: 2126: 1886: 1385: 1347: 14: 3544: 2720: 2695: 2676: 2635: 2320:(1st ed.). Oakland, CA: RGE Pub. 2309: 2290: 2241:, diagram 12, "Advantaged Play Server" 2095: 2076: 1988: 1919: 1780:(1st ed.). Oakland, CA: RGE Pub. 1549: 1514: 977:Technology for detecting card counters 2992: 2743: 2654: 2511:from the original on 14 November 2017 2458:from the original on 19 November 2017 2058:from the original on 18 November 2017 1979: 1769: 1696:from the original on 27 December 2011 1362:from the original on 15 November 2011 1290: 1267:, which was based on Mezrich's book. 3506: 2485:from the original on 25 October 2018 2340: 2212:from the original on 8 November 2017 2149:from the original on 15 January 2009 1952: 1887:Sheng, Mingjie; Gu, Chaolin (2018). 1582:from the original on 20 January 2013 1435:from the original on 4 February 2021 1150: 880: 782:A mathematical principle called the 658:adding citations to reliable sources 629: 3526: 2427:from the original on 27 August 2016 2176:from the original on 26 August 2021 2167: 1967:from the original on 26 August 2021 1047:Canceling comps earned by counters. 892: 24: 2714: 2445: 2408: 2390:from the original on 22 April 2014 2371: 1617:from the original on 28 March 2009 1552:The Archer Method of Winning at 21 1531:from the original on 10 March 2013 1502:from the original on 11 March 2009 1241:also covers team play in his book 1170:it lacks sufficient corresponding 1020: 790: 25: 3568: 2353:from the original on 10 July 2018 2014:Liz Benston (13 September 2005). 1953:Sood, Suemedha (17 August 2012). 1826:from the original on 29 June 2020 1757:from the original on 2 March 2009 1731:from the original on 2 April 2009 1670:from the original on 5 March 2009 1467:from the original on 17 July 2014 740:which was later re-made into the 724: 3525: 3515: 3505: 3496: 3495: 2810: 2341:Rose, I. Nelson (27 June 2017). 2022:from the original on 8 June 2010 1934:from the original on 13 May 2020 1920:Kaplan, Michael (29 July 2016). 1714:Schlesinger (2005), pp. 122-146. 1155: 712: 634: 625: 2536: 2497: 2481:. BlackjackApprenticeship.com. 2470: 2439: 2402: 2365: 2334: 2284: 2259: 2244: 2232:Real Time Casino Solution (PDF) 2224: 2188: 2161: 2135: 2120: 2070: 2034: 2007: 1946: 1913: 1880: 1850: 1841: 1743: 1717: 1708: 1682: 1656: 1647: 1638: 1629: 1603: 1594: 1568: 846: 645:needs additional citations for 562:Design and selection of systems 60: 1543: 1488: 1479: 1455:"Rain Man (1988) Plot Summary" 1447: 1404: 13: 1: 2769: 2291:Zender, Bill (October 2013). 1725:"Bankrolls, Goals, Risk Data" 1326: 703: 3018: 2617:Schlesinger, Donald (2005). 2507:. Blackjack Review Network. 2104:Exhibit CAA: beyond counting 1906:10.1016/j.cities.2018.01.003 1644:Axelrad (2010), pp. 258-259. 1635:Axelrad (2010), pp. 19, 259. 1613:. Blackjackforumonline.com. 1354:Wizard of Odds (July 2011). 1331: 897: 554: 551: 548: 545: 542: 539: 536: 533: 530: 527: 524: 516: 513: 510: 507: 504: 501: 498: 495: 492: 489: 486: 478: 475: 472: 469: 466: 463: 460: 457: 454: 451: 448: 440: 437: 434: 431: 428: 425: 422: 419: 416: 413: 410: 402: 399: 396: 393: 390: 387: 384: 381: 378: 375: 372: 364: 361: 358: 355: 352: 349: 346: 343: 340: 337: 334: 326: 323: 320: 317: 314: 311: 308: 305: 302: 299: 296: 288: 285: 282: 279: 276: 273: 270: 267: 264: 261: 258: 250: 247: 244: 241: 238: 235: 232: 229: 226: 223: 220: 43:A blackjack game in progress 7: 2787:Glossary of blackjack terms 2662:. New York: Vintage Books. 2550:. New York: Penguin Press. 2266:Nersesian, Bob (May 2016). 2077:Zender, Bill (April 2011). 1309: 858:casinos in the US state of 123:portrayed in the 1988 film 10: 3573: 2479:"The History of Blackjack" 1525:"Card Counting Strategies" 1386:Griffin, Peter A. (1999). 1294: 1075: 589:Insurance correlation (IC) 136: 31: 3491: 3465: 3432: 3416: 3395: 3344: 3293: 3198: 3172: 3165: 3111: 3098:Mathematics of bookmaking 3085: 3078: 3035: 3026: 2880: 2847:Double Exposure Blackjack 2819: 2808: 2777: 2681:. New York: Maven Press. 2677:Walker, Katarina (2008). 2638:The Big Book of Blackjack 2590:The Philadelphia Inquirer 2347:www.gamblingandthelaw.com 1989:Blaine, Rick (May 2014). 1554:. Henry Regnery Company. 1060:Some jurisdictions (e.g. 83: 2102:Grosjean, James (2007). 1753:. Blackjackincolor.com. 1727:. Blackjackincolor.com. 1666:. Blackjackincolor.com. 1664:"True Count Frequencies" 1273:Million Dollar Blackjack 1227:Million Dollar Blackjack 1146: 1131:how to count cards, and 1118:Playing Blackjack to Win 999:preferential shuffling – 876:New Jersey Supreme Court 864:New Jersey Supreme Court 575:Betting correlation (BC) 72:who try to overcome the 2842:Double Attack Blackjack 2721:Snyder, Arnold (2005). 2636:Snyder, Arnold (2006). 2230:Aventura Technologies, 1496:"Blackjack Side Counts" 1485:Axelrad (2010), p. 256. 1419:McFarland & Company 1356:"How to Play Blackjack" 1261:and the American movie 1244:Bringing Down The House 1185:more precise citations. 958:Playing multiple hands. 582:Playing efficiency (PE) 2893:Blackjack Hall of Fame 2544:Axelrad, Josh (2010). 2127:Cellini, D.V. (2003). 1321:Blackjack Hall of Fame 1122:mechanical calculators 1114:I Want To Quit Winners 1050:Confiscation of chips. 952:Refusal to play rated. 912:Griffin Investigations 872:Blackjack Hall of Fame 829:The rules of the game. 808:bankroll; one popular 152:The Hi-Lo system is a 44: 2852:Elimination Blackjack 2696:Zender, Bill (2006). 2600:Blackjack and the Law 2318:Blackjack and the law 1856:See summary brief of 1778:Blackjack and the law 1550:Archer, John (1973). 42: 3557:Gambling terminology 3483:Video game addiction 3093:Gambling mathematics 3029:Gambling terminology 2295:. Huntington Press. 2270:. Huntington Press. 2081:. Huntington Press. 1993:. Huntington Press. 1751:"Win/Loss/Push Data" 1692:. wizardofodds.com. 1653:Walker (2008), p. 89 1358:. wizardofodds.com. 654:improve this article 2968:Richard W. Munchkin 2131:. Huntington Press. 866:decision. In 1979, 3143:Due Column betting 3121:Advantage gambling 2237:2007-03-06 at the 2143:"Digitace Website" 1927:The New York Times 1865:2021-08-26 at the 1600:Schlesinger (2005) 1316:Advantage gambling 1291:Shuffling machines 961:Lifetime winnings. 732:MIT Blackjack Team 106:They can make the 45: 3539: 3538: 3428: 3427: 3161: 3160: 3148:Labouchère system 3103:Poker probability 2986: 2985: 2862:Malaysian Pontoon 2827:Chinese Blackjack 2688:978-1-4357-1065-8 2628:978-0-910575-20-1 2609:978-0-910575-08-9 2557:978-1-59420-247-6 2302:978-0-929712-56-7 2168:Gilbert, Alorie. 2113:978-0-9790061-4-2 1428:978-0-7864-8994-7 1297:Shuffling machine 1211: 1210: 1203: 772:wheels of fortune 686: 685: 678: 559: 558: 147:effect of removal 70:advantage players 16:(Redirected from 3564: 3529: 3528: 3519: 3509: 3508: 3499: 3498: 3478:Problem gambling 3170: 3169: 3083: 3082: 3070:Riverboat casino 3013: 3006: 2999: 2990: 2989: 2938:Steven L. Heston 2913:Zeljko Ranogajec 2903:Peter A. Griffin 2814: 2764: 2757: 2750: 2741: 2740: 2736: 2709: 2692: 2673: 2656:Thorp, Edward O. 2651: 2632: 2613: 2594: 2583: 2561: 2530: 2527: 2521: 2520: 2518: 2516: 2501: 2495: 2494: 2492: 2490: 2474: 2468: 2467: 2465: 2463: 2452:baltimoresun.com 2443: 2437: 2436: 2434: 2432: 2426: 2415: 2406: 2400: 2399: 2397: 2395: 2389: 2378: 2369: 2363: 2362: 2360: 2358: 2338: 2332: 2331: 2313: 2307: 2306: 2288: 2282: 2281: 2263: 2257: 2250:Arnold Snyder's 2248: 2242: 2228: 2222: 2221: 2219: 2217: 2211: 2200: 2192: 2186: 2185: 2183: 2181: 2172:. News.com.com. 2165: 2159: 2158: 2156: 2154: 2145:. digitace.com. 2139: 2133: 2132: 2124: 2118: 2117: 2099: 2093: 2092: 2074: 2068: 2067: 2065: 2063: 2057: 2046: 2038: 2032: 2031: 2029: 2027: 2011: 2005: 2004: 1986: 1977: 1976: 1974: 1972: 1950: 1944: 1943: 1941: 1939: 1917: 1911: 1910: 1908: 1884: 1878: 1875: 1869: 1854: 1848: 1845: 1839: 1838: 1833: 1831: 1812: 1806: 1805: 1799: 1791: 1773: 1767: 1766: 1764: 1762: 1747: 1741: 1740: 1738: 1736: 1721: 1715: 1712: 1706: 1705: 1703: 1701: 1686: 1680: 1679: 1677: 1675: 1660: 1654: 1651: 1645: 1642: 1636: 1633: 1627: 1626: 1624: 1622: 1607: 1601: 1598: 1592: 1591: 1589: 1587: 1572: 1566: 1565: 1547: 1541: 1540: 1538: 1536: 1521: 1512: 1511: 1509: 1507: 1492: 1486: 1483: 1477: 1476: 1474: 1472: 1451: 1445: 1444: 1442: 1440: 1408: 1402: 1401: 1383: 1372: 1371: 1369: 1367: 1351: 1345: 1342: 1281:Windsor, Ontario 1206: 1199: 1195: 1192: 1186: 1181:this article by 1172:inline citations 1159: 1158: 1151: 1097:Beat the Dealer, 893:Casino reactions 681: 674: 670: 667: 661: 638: 630: 177: 176: 34:The Card Counter 21: 3572: 3571: 3567: 3566: 3565: 3563: 3562: 3561: 3542: 3541: 3540: 3535: 3487: 3461: 3424: 3412: 3391: 3385:Atlantic Canada 3340: 3289: 3194: 3157: 3107: 3074: 3031: 3022: 3017: 2987: 2982: 2973:Don Schlesinger 2958:Lawrence Revere 2923:Edward O. Thorp 2888:Blackjack Forum 2876: 2867:Power blackjack 2815: 2806: 2773: 2768: 2733: 2717: 2715:Further reading 2712: 2689: 2670: 2648: 2629: 2610: 2580: 2558: 2539: 2534: 2533: 2528: 2524: 2514: 2512: 2503: 2502: 2498: 2488: 2486: 2475: 2471: 2461: 2459: 2444: 2440: 2430: 2428: 2424: 2413: 2407: 2403: 2393: 2391: 2387: 2376: 2370: 2366: 2356: 2354: 2339: 2335: 2328: 2314: 2310: 2303: 2289: 2285: 2278: 2264: 2260: 2253:Blackjack Forum 2249: 2245: 2239:Wayback Machine 2229: 2225: 2215: 2213: 2209: 2198: 2194: 2193: 2189: 2179: 2177: 2166: 2162: 2152: 2150: 2141: 2140: 2136: 2125: 2121: 2114: 2100: 2096: 2089: 2075: 2071: 2061: 2059: 2055: 2044: 2040: 2039: 2035: 2025: 2023: 2018:. LasVegasSun. 2012: 2008: 2001: 1987: 1980: 1970: 1968: 1951: 1947: 1937: 1935: 1918: 1914: 1885: 1881: 1876: 1872: 1867:Wayback Machine 1855: 1851: 1846: 1842: 1829: 1827: 1814: 1813: 1809: 1793: 1792: 1788: 1774: 1770: 1760: 1758: 1749: 1748: 1744: 1734: 1732: 1723: 1722: 1718: 1713: 1709: 1699: 1697: 1688: 1687: 1683: 1673: 1671: 1662: 1661: 1657: 1652: 1648: 1643: 1639: 1634: 1630: 1620: 1618: 1609: 1608: 1604: 1599: 1595: 1585: 1583: 1574: 1573: 1569: 1562: 1548: 1544: 1534: 1532: 1523: 1522: 1515: 1505: 1503: 1494: 1493: 1489: 1484: 1480: 1470: 1468: 1453: 1452: 1448: 1438: 1436: 1429: 1421:. p. 151. 1409: 1405: 1398: 1384: 1375: 1365: 1363: 1352: 1348: 1343: 1339: 1334: 1329: 1312: 1299: 1293: 1258:The Last Casino 1207: 1196: 1190: 1187: 1177:Please help to 1176: 1160: 1156: 1149: 1110:Beat the Dealer 1089:Beat the Dealer 1085:Edward O. Thorp 1078: 1056:(back rooming). 1023: 1021:Countermeasures 979: 921:data encryption 900: 895: 881:countermeasures 849: 793: 791:Expected profit 784:Kelly criterion 780: 737:The Last Casino 727: 715: 706: 682: 671: 665: 662: 651: 639: 628: 619: 564: 213:Level of count 139: 129:, in which the 86: 63: 37: 30: 23: 22: 15: 12: 11: 5: 3570: 3560: 3559: 3554: 3537: 3536: 3534: 3533: 3523: 3513: 3503: 3492: 3489: 3488: 3486: 3485: 3480: 3475: 3469: 3467: 3463: 3462: 3460: 3459: 3454: 3449: 3447:Game of chance 3444: 3438: 3436: 3430: 3429: 3426: 3425: 3420: 3418: 3414: 3413: 3411: 3410: 3405: 3399: 3397: 3393: 3392: 3390: 3389: 3388: 3387: 3382: 3380:Western Canada 3377: 3372: 3367: 3359: 3354: 3348: 3346: 3342: 3341: 3339: 3338: 3336:United Kingdom 3333: 3328: 3323: 3318: 3313: 3308: 3303: 3297: 3295: 3291: 3290: 3288: 3287: 3282: 3277: 3272: 3267: 3262: 3257: 3256: 3255: 3245: 3240: 3235: 3230: 3229: 3228: 3223: 3213: 3208: 3202: 3200: 3196: 3195: 3193: 3192: 3187: 3182: 3176: 3174: 3167: 3163: 3162: 3159: 3158: 3156: 3155: 3150: 3145: 3140: 3138:Asian handicap 3135: 3130: 3129: 3128: 3117: 3115: 3109: 3108: 3106: 3105: 3100: 3095: 3089: 3087: 3080: 3076: 3075: 3073: 3072: 3067: 3062: 3057: 3052: 3051: 3050: 3039: 3037: 3033: 3032: 3027: 3024: 3023: 3016: 3015: 3008: 3001: 2993: 2984: 2983: 2981: 2980: 2978:Darryl Purpose 2975: 2970: 2965: 2963:James Grosjean 2960: 2955: 2950: 2945: 2940: 2935: 2930: 2925: 2920: 2915: 2910: 2905: 2900: 2895: 2890: 2884: 2882: 2878: 2877: 2875: 2874: 2869: 2864: 2859: 2854: 2849: 2844: 2839: 2834: 2829: 2823: 2821: 2817: 2816: 2809: 2807: 2805: 2804: 2799: 2794: 2789: 2783: 2781: 2779:Advantage play 2775: 2774: 2767: 2766: 2759: 2752: 2744: 2738: 2737: 2731: 2716: 2713: 2711: 2710: 2693: 2687: 2674: 2668: 2652: 2646: 2633: 2627: 2614: 2608: 2595: 2584: 2578: 2566:Griffin, Peter 2562: 2556: 2540: 2538: 2535: 2532: 2531: 2522: 2496: 2477:Loudon Ofton. 2469: 2446:Barker, Jeff. 2438: 2418:billzender.com 2409:Zender, Bill. 2401: 2381:billzender.com 2372:Zender, Bill. 2364: 2333: 2327:978-0910575089 2326: 2308: 2301: 2283: 2277:978-1935396628 2276: 2258: 2243: 2223: 2187: 2160: 2134: 2119: 2112: 2094: 2087: 2069: 2033: 2006: 2000:978-1935396536 1999: 1978: 1945: 1912: 1879: 1870: 1849: 1840: 1820:Google Scholar 1807: 1787:978-0910575089 1786: 1768: 1742: 1716: 1707: 1681: 1655: 1646: 1637: 1628: 1602: 1593: 1567: 1560: 1542: 1513: 1487: 1478: 1446: 1427: 1403: 1397:978-0929712130 1396: 1373: 1346: 1336: 1335: 1333: 1330: 1328: 1325: 1324: 1323: 1318: 1311: 1308: 1295:Main article: 1292: 1289: 1277:Casino Windsor 1209: 1208: 1163: 1161: 1154: 1148: 1145: 1077: 1074: 1058: 1057: 1051: 1048: 1045: 1042: 1039: 1036: 1033: 1030: 1022: 1019: 1015:Play variation 987:Shuffle Master 978: 975: 963: 962: 959: 956: 955:Table hopping. 953: 950: 947: 940: 925:secure servers 908:eye in the sky 899: 896: 894: 891: 848: 845: 844: 843: 839: 836: 833: 830: 827: 824: 792: 789: 779: 776: 726: 725:Group counting 723: 714: 711: 705: 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3458: 3455: 3453: 3452:Game of skill 3450: 3448: 3445: 3443: 3440: 3439: 3437: 3435: 3431: 3423: 3419: 3417:South America 3415: 3409: 3406: 3404: 3401: 3400: 3398: 3394: 3386: 3383: 3381: 3378: 3376: 3373: 3371: 3368: 3366: 3363: 3362: 3360: 3358: 3357:United States 3355: 3353: 3350: 3349: 3347: 3345:North America 3343: 3337: 3334: 3332: 3329: 3327: 3324: 3322: 3319: 3317: 3314: 3312: 3309: 3307: 3304: 3302: 3299: 3298: 3296: 3292: 3286: 3283: 3281: 3278: 3276: 3273: 3271: 3268: 3266: 3263: 3261: 3258: 3254: 3251: 3250: 3249: 3246: 3244: 3241: 3239: 3236: 3234: 3231: 3227: 3224: 3222: 3219: 3218: 3217: 3214: 3212: 3209: 3207: 3204: 3203: 3201: 3197: 3191: 3188: 3186: 3183: 3181: 3178: 3177: 3175: 3171: 3168: 3164: 3154: 3151: 3149: 3146: 3144: 3141: 3139: 3136: 3134: 3131: 3127: 3126:Card counting 3124: 3123: 3122: 3119: 3118: 3116: 3114: 3110: 3104: 3101: 3099: 3096: 3094: 3091: 3090: 3088: 3084: 3081: 3077: 3071: 3068: 3066: 3063: 3061: 3058: 3056: 3055:Online casino 3053: 3049: 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