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[[Image:Blackjack board.JPG|thumb|300px|A blackjack game in progress]] '''Card counting''' is a strategy that enables the skilled [[Blackjack]] player to make a long-term profit. Blackjack became the most popular casino game in the 1960s and 1970s after the publication of <i>Beat the Dealer</i> by [[Edward Thorp]], which introduced manageable card counting systems. The larger the proportion of aces, face cards, and tens remaining in the deck, the more favorable the odds are for the player. Players take advantage of this by increasing their bet sizes and altering playing strategy. Some casinos consider this cheating and will ban card counters from playing. That the player can win with card counting results from a simple rule: Although the player can stand or hit on any total, the dealer must take a hit until reaching 17. The greater the richness of the deck in ten-value cards than a neutral deck, then, the greater the chance of the dealer busting, leading the player to place larger bets and make less conservative strategy choices in such cases. The converse is true is ten-value card poor decks. Although blackjack dilettantes create an encyclopedia of analysis and manufacture unwieldly jargon to provide a scientific aura around card counting, that rule is the dominant mathematical factor and the basis for all card counting systems. == Basics == The most common variations of card counting are based on theoretical and statistical evidence that high cards (especially aces and 10s) benefit the player more than the dealer, while the low cards, (especially 4s, 5s, and 6s) help the dealer while hurting the player. A high concentration of aces and 10s in the deck increases the player's chances of hitting a natural Blackjack, which pays out 3:2 (unless the dealer also has blackjack). Also, when the [[Shoe (cards)|shoe]] has a high concentration of 10s, players have a better chance of winning when doubling.<ref name="beat-1966">Thorp (1966), pp.24-27, pp. 41-47, pp. 98-99, pp. 102-103, p. 110, p. 115.</ref><!-- A high number of ten-value cards also makes the insurance bet more profitable since that is essentially a bet that the dealer's card is a ten (resulting in a dealer blackjack).--> Low cards benefit the dealer, since according to blackjack rules the dealer must hit ''stiff hands'' (12-16 total) while the player has the option to hit or stand. Thus a dealer holding (12-16) will bust every time if the next card drawn is a 10, making this card essential to track when card counting.<ref name="wiz-bjk">{{cite web |url=http://wizardofodds.com/blackjack |title=How to Play Blackjack |accessdate=2011-11-03 |publisher=wizardofodds.com |author=Wizard of Odds |year=2011 |month=July}}</ref> Contrary to the popular myth, card counters do not need unusual mental abilities in order to count cards, because they are not tracking and memorizing specific cards. Instead, card counters assign a point score to each card they see that estimates the value of that card, and then they track the sum of these values &ndash; a process called keeping a "running count."<ref name="tob-1979">Griffin (1988)</ref> The myth that counters keep track of every card was portrayed in the movie ''[[Rain Man]]'', in which the [[Savant syndrome|savant]] character [[Raymond Babbitt]] counts through six decks with ease and a casino employee erroneously comments that it is impossible to count six decks. === Systems === Basic card counting assigns a positive, negative, or zero value to each card value available. When a card of that value is dealt, the count is adjusted by that card's counting value. Low cards increase the count as they increase the percentage of high cards in the remaining shoe, while high cards decrease it for the opposite reason. For instance, the Hi-Lo system subtracts one for each dealt ten, Jack, Queen, King or Ace, and adds one for any value 2-6. Values 7-9 are assigned a value of zero and therefore do not affect the count.<ref>Axelrad (2010), p. 256.</ref> The goal of a card counting system is to assign point values that roughly correlate to a card's Effect of Removal (EOR). The EOR is the actual effect of removing a given card from play, and the resulting impact on the house advantage. The player may gauge the effect of removal for all cards dealt, and assess the current house advantage of a game based on the remaining cards. As larger ratios between point values are used to create better correlation to actual EOR with the goal of increasing the efficiency of a system, such systems use larger and larger numbers and are broken into classes such as level 1, level 2, level 3, and so on, with regards to the ratio between the highest and lowest assigned point values. The High-Low system is considered a ''single-level'' or ''level-one'' count, because the count never increases or decreases by more than a single, predetermined value. 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 and −2, or +0.5. Advanced players might additionally maintain a ''side count'' (separate 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. 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. Since the 1960’s numerous computer-based systems have been developed. The following table summarizes the values assigned to the cards in the most popular and most powerful systems. References are provided to the published books of computer analyst experts, most holding advanced degrees including the Ph.D or M.A. in mathematics or probability and statistics, who developed the systems. Only authors of reputable, published books, in which the systems have been published, as opposed to any of the hundreds of self-published commercial websites, are referenced. The card value assignments of a comprehensive list of one hundred possible systems, up to level four systems, are provided by [[Blackjack Hall of Fame]] member [[Arnold Snyder]].<ref> http://www.blackjackforumonline.com/content/hundred.htm </ref> {| class="wikitable" border="1" |- style="text-align:center;" !style="background:#B0C4DE"|System Name !style="background:#B0C4DE"|2s !style="background:#B0C4DE"|3s !style="background:#B0C4DE"|4s !style="background:#B0C4DE"|5s !style="background:#B0C4DE"|6s !style="background:#B0C4DE"|7s !style="background:#B0C4DE"|8s !style="background:#B0C4DE"|9s !style="background:#B0C4DE"|10s !style="background:#B0C4DE"|A’s !style="background:#B0C4DE"|Developer |- |Advanced Omega II<ref>Carlson, Bryce (2010) ''Blackjack for Blood'', Gamestar Pr Inc</ref> |1 |1 |2 |2 |2 |1 |0 | -1 | -2 |0 |Bryce Carlson |- |Canfield Expert<ref name="Canfield">{{cite web|url= http://books.google.com/books/about/Blackjack_your_way_to_riches.html?id=6tXtee819p0C |title= Canfield Expert book |publisher= |date= |accessdate=2012-11-24}}</ref> |0 |1 |1 |1 |1 |1 |0 | -1 | -1 |0 |Richard Canfield (John Hinton) |- |Canfield Master<ref name="Canfield"/> |1 |1 |2 |2 |2 |1 |0 | -1 | -2 |0 |Richard Canfield (John Hinton) |- |Complete Point Count or High-Low<ref>Thorp, Edward O.(1962) ''Beat the Dealer: A Winning Strategy for the Game of Twenty-One'', Vintage, New York</ref><ref name=''beat-1966''>Thorp, Edward O.(1966) ''Beat the Dealer: A Winning Strategy for the Game of Twenty-One'', revised edition, Vintage, New York. Although ascribed to Thorp, the system was introduced by mathematician Dr. [[Harvey Dubner]]. The results published by Thorp were programmed by computer analyst Dr. Julian Braun</ref> |1 |1 |1 |1 |1 |0 |0 |0 | -1 | -1 |[[Edward O. Thorp]] |- |Hi-Opt I (High Optimum)<ref name="Humble">Humble, Lance and Cooper, Carl (1987) ''The Worlds Greatest Blackjack Book '', Doubleday, New York</ref> |0 |1 |1 |1 |1 |0 |0 |0 | -1 |0 |Lance Humble and Carl Cooper |- |Hi-Opt II (High Optimum)<ref name="Humble"/> |1 |1 |2 |2 |1 |1 |0 |0 | -2 |0 |Lance Humble and Carl Cooper |- | Keep It Simple 2 (KISS 2)<ref>Renzey, Fred (2006) ''Blackjack Bluebook '', Blackjack Mentor Press</ref> |1 |1 |1 |1 |1 |0 |0 |0 | -1 |0 |Fred Renzey |- | Keep It Simple 3 (KISS 3)<ref>Renzey, Fred (2006) ''Blackjack Bluebook II '', Blackjack Mentor Press</ref> | 0/1 |1 |1 |1 |1 |1 |0 |0 | -1 | -1 |Fred Renzey |- |Knock Out (K-O; All Sevens)<ref>Vancura, Olaf and Fuchs, Ken (1998) ''Knock-Out Blackjack'', Huntington Press</ref><ref name=''british''>Zadehkoochak, M. (1992) ''The Book of British Blackjack'' Medimage. ISBN 1-897728-00-X</ref><ref>Notes: The KO Strategy was first introduced in 1992 as the "All Sevens" count in ''The Book of British Blackjack''</ref> |1 |1 |1 |1 |1 |1 |0 |0 | -1 | -1 |Olaf Vancura and Ken Fuchs |- |Mentor<ref>Renzey, Fred (2006) ''Blackjack Bluebook II '', Blackjack Mentor Press</ref> |1 |2 |2 |2 |2 |1 |0 | -1 | -2 | -1 | Fred Renzey |- |Red Seven<ref>Snyder, Arnold (1983) ''Blackbelt in Blackjack''</ref> |1 |1 |1 |1 |1 | 0/1 |0 |0 | -1 | -1 |[[Arnold Snyder]] |- |Revere 14 Count<ref name="Revere">Revere, Lawrence (1971) ''Playing Blackjack as a Business '', Carol Publishing Group-Lyle Stuart</ref> |2 |2 |3 |4 |2 |1 |0 | -2 | -3 |0 |[[Lawrence Revere]] (G. Owens) |- |Revere Advanced Point Count (RAPC) <ref name="Revere"/> |2 |3 |3 |4 |3 |2 |0 | -1 | -3 | -4 |[[Lawrence Revere]] (G. Owens) |- |Revere Plus-Minus <ref name="Revere"/> |1 |1 |1 |1 |1 |0 |0 | -1 | -1 |0 |[[Lawrence Revere]] (G. Owens) |- |Revere Point Count (RPC) <ref name="Revere"/> |1 |2 |2 |2 |2 |1 |0 | -1 | -2 | -2 |[[Lawrence Revere]] (G. Owens) |- |Silver Fox<ref>Stricker, Ralph, ''Silver Fox Blackjack System'', Gambler’s Book Club, Las Vegas</ref> |1 |1 |1 |1 |1 |1 |0 | -1 | -1 | -1 |Ralph Stricker |- |Unbalanced Zen II (UBZ2)<ref> C., George, ''The Unbalanced Zen II'' in Schlesinger, Don (2008 ) ''Blackjack Attack: Playing the Pros’ Way'', RGE Publishers</ref> |1 |2 |2 |2 |2 |1 |0 |0 | -2 | -1 |George C. |- |Uston Advanced Plus/Minus (APM)<ref name="Uston">Uston, Ken (1998) ''Million Dollar Blackjack'', Carol Publishing Group</ref> |0 |1 |1 |1 |1 |1 |0 |0 | -1 | -1 |[[Ken Uston]] |- |Uston Advanced Point Count (APC)<ref name="Uston"/> |1 |2 |2 |3 |2 |2 |1 | -1 | -3 |0 |[[Ken Uston]] |- |Uston Strongest and Simplest (SS)<ref name="Uston"/> |2 |2 |2 |3 |2 |1 |0 | -1 | -2 | -2 |[[Ken Uston]] |- |Wong Halves<ref>Wong, Stanford (1994) ''Professional Blackjack'', Pi Yee Pr Press</ref> |.5 |1 |1 |1.5 |1 |.5 |0 | -.5 | -1 | -1 |[[Stanford Wong]] (John Ferguson) |- |Zen Count<ref>Synder, Arnold (2005) ''Blackbelt in Blackjack'', Cardoza, Las Vegas</ref> |1 |1 |2 |2 |2 |1 |0 |0 | -2 | -1 |[[Arnold Snyder]] |- |} ==In the Media== <i>Never Split Tens!</i>, a novel based on the life of pioneering card counting theorist [[Edward O. Thorp]], by [[Les Golden]] published in 2017 by Springer, includes numerous examples of card counting in simulated casino play including changing bet sizes, the Kelly criterion, group card counting, and entering the play when the deck is favorable to the player. ==See also== *[[Casino security]] ==References== === Notes === {{Reflist|colwidth=30em}} === Bibliography=== * {{cite book |last = Axelrad |first = Josh |authorlink = |title = Repeat until Rich: A Professional Card Counter's Chronicle of the Blackjack Wars |edition = |publisher = Penguin Press |location = New York |pages = |series = |year = 2010 |doi = |lccn = |oclc = |isbn = 978-1-59420-247-6}} * {{cite book |title=The Theory of Blackjack: The Complete Card Counter's Guide |author=Griffin, Peter |authorlink=Peter_A._Griffin |isbn=0-915141-02-7 |year=1988 |publisher=Huntington Press |location = Las Vegas |edition = 4th}} * {{cite news|author=Eddie Olsen|date=April 18, 1981|publisher=''[[Philadelphia Inquirer]]''|title=Ken Uston: Big Player Without a Game}} * {{cite book |last1 = Rose |first1 = I. Nelson |authorlink1 = |last2 = Loeb |first2 = Robert A. |authorlink2 = |title=Blackjack and the Law |isbn=978-0-910575-08-9 |year=1998 |publisher=RGE Publishers |location=Oakland, CA |edition= 1st}} * {{cite book |last = Schlesinger |first = Donald |authorlink = |title = Blackjack Attack: playing the pros' way |edition = 3rd |publisher = RGE Publishing |location = Las Vegas |pages = |series = |year = 2005 |doi = |lccn = |oclc = |isbn = 978-0-910575-20-1 }} * {{cite book |last = Snyder |first = Arnold |authorlink = |title = The Big Book of Blackjack |edition = 1st |publisher = Cardoza Publishing |location = New York |pages = |series = |year = 2006 |doi = |lccn = |oclc = |isbn = 1-58042-155-5}} * {{cite book |title=Beat the Dealer: A Winning Strategy for the Game of Twenty One | last = Thorp |first = Edward O.|authorlink=Edward O. Thorp|isbn=0394-70310-3 |year=1966 |publisher=Vintage Books |location = New York}} * {{cite book |last = Walker |first = Katarina |authorlink = |title = The Pro's Guide to Spanish 21 and Australian Pontoon |edition = |publisher = Maven Press |location = New York |pages = |series = |year = 2008 |doi = |lccn = |oclc = |isbn = 978-1-4357-1065-8}} * {{cite book |last = Zadehkoochak |first = Mohsen |authorlink = |title = The Book of British Blackjack |edition = |publisher = Medimage |location = Cockfosters, England |pages = |series = |year = 1992 |doi = |lccn = |oclc = |isbn = 1-897728-00-X}} * {{cite book |last = Zender |first = Bill |authorlink = |title = Advantage Play for the Casino Executive |edition = |publisher = |location = |pages = |series = |year = 2006 |doi = |lccn = |oclc = 156916229 |isbn = }} ==Further reading== * {{cite book |last = Snyder |first = Arnold |authorlink = |title = Blackbelt in Blackjack: Playing 21 as a Martial Art |edition = Revised |publisher = Cardoza Publishing |location = New York |pages = |series = |year = 2005 |doi = |lccn = |oclc = |isbn = 1580421431}} {{DEFAULTSORT:Card Counting}} [[Category:Blackjack]] [[Category:Gambling terminology]]

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