Difference between revisions of "Card counting"

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'''Card counting''' is one of the strategies designed to turn the casino game of [[Blackjack]] into a positive result for the players. Blackjack substantially increased in popularity in the 1960s and 1970s once a strategy for beating the game was made public by Eward Thorp in the 1962 publication of Beat the Dealer..
+
[[Image:Blackjack board.JPG|thumb|300px|A blackjack game in progress]]
  
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As the cards are played, the remaining cards can be identified.  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.
+
'''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.
  
−
A skilled card counter can play against the casino at a small mathematical advantage.  Some casinos, in some jurisdictions, falsely consider this cheating and will ban card counters from playing. However, card counting is not illegal in any country.
+
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.
  
−
==Blackjack writers==
+
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.
  
−
These are prominent blackjack writers, whose works are published by reputable non-vanity publishers.  The many self-described "experts"who pay for their own websites are of course excluded.
+
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.
  
−
===John Bukofsky===
+
== Basics ==
−
===Bryce Carlson===
+
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>
−
===Daniel Dravot===
 
−
===Greg Elder===
 
−
===[[Les Golden]]===
 
−
Long-time columnist for [[Bluff Europe]], igamingbusiness, gambling.com, Jackpots Review, and gamblingonline magazines. Author of the biographical novel [[Never Split Tens]] and the adapted screenplay, based on the life of [[Edward Thorp]]. Golden was named as an International Gambling Institute Scholar (University of Nevada, Las Vegas) for 2016.
 
  
−
===Fred Renzey===
+
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.
−
===Chris Statz===
 
−
===[[Edward Thorp]]===
 
−
A pioneering book codifying the methodology by Edward Thorp was published in 1962: ''Beat the Dealer: A Winning Strategy for the Game of Twenty-One''.<ref>Thorp, E. O.  (1966) ''Beat the Dealer: A Winning Strategy for the Game of Twenty-One'', Random House, New York</ref>
 
  
−
===Nathaniel Tilton===
+
=== Systems ===
  
−
===Olaf Vancura and Ken Fuchs===
+
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> 
−
Authors of Knock Out Blackjack.
 
  
−
===Stanford Wong===
 
−
Author of the books Basic Blackjack, Professional Blackjack, and Blackjack Secrets.
 
  
−
===Frank Scoblete===
+
{| class="wikitable" border="1"
−
Author of Golden Touch Blackjack Revolution.
+
|- 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]]
 +
|-
 +
|}
  
−
===Arnold Snyder===
+
==In the Media==
−
Author of books Blackbelt in Blackjack, Big Book of Blackjack, and Blackjack Wisdom..
+
<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.
  
−
===Don Schlesinger===
+
==See also==
−
Author of Blackjack Attack.
+
*[[Casino security]]
  
−
===Barry Meadow===
+
==References==
−
Author of Blackjack Autumn
+
=== Notes ===
−
 
+
{{Reflist|colwidth=30em}}
−
===Rick Blaine===
 
−
Author of Blackjack Blueprint
 
−
 
 
−
===Ian Andersen===
 
−
Author of Burning the Tables in Las Vegas and Turning the Tables in Las Vegas.
 
  
−
===Maverick Sharp===
+
=== Bibliography===
−
Author of the 2013 Dynamic Blackjack.
+
* {{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}}
  
−
===Ken Uston===
+
{{DEFAULTSORT:Card Counting}}
−
Author of Ken Uston on Blackjack and Million Dollar Blackjack..
+
[[Category:Blackjack]]
−
 
+
[[Category:Gambling terminology]]
−
===Lawrence Revere===
 
−
Author of Playing Blackjack as a Business.
 
−
 
 
−
===[[Peter Griffin]]===
 
−
Author of The Theory of Blackjack.
 
−
 
 
−
===Lance Humble and Carl Cooper===
 
−
Authors of The World's Greatest Blacklack Book.
 
−
 
 
−
==See also==
 
−
*[[Blackjack card counting systems]]
 
−
 
 
−
==References==
 
−
<div class="references-small" style="-moz-column-count:1; column-count:1;">
 
−
<references />
 
−
</div>
 

Latest revision as of 15:33, 25 September 2021

File:Blackjack board.JPG
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 Beat the Dealer 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 has a high concentration of 10s, players have a better chance of winning when doubling.[1] 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.[2]

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 – a process called keeping a "running count."[3] The myth that counters keep track of every card was portrayed in the movie Rain Man, in which the 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

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.[4]


System Name 2s 3s 4s 5s 6s 7s 8s 9s 10s A’s Developer
Advanced Omega II[5] 1 1 2 2 2 1 0 -1 -2 0 Bryce Carlson
Canfield Expert[6] 0 1 1 1 1 1 0 -1 -1 0 Richard Canfield (John Hinton)
Canfield Master[6] 1 1 2 2 2 1 0 -1 -2 0 Richard Canfield (John Hinton)
Complete Point Count or High-Low[7][8] 1 1 1 1 1 0 0 0 -1 -1 Edward O. Thorp
Hi-Opt I (High Optimum)[9] 0 1 1 1 1 0 0 0 -1 0 Lance Humble and Carl Cooper
Hi-Opt II (High Optimum)[9] 1 1 2 2 1 1 0 0 -2 0 Lance Humble and Carl Cooper
Keep It Simple 2 (KISS 2)[10] 1 1 1 1 1 0 0 0 -1 0 Fred Renzey
Keep It Simple 3 (KISS 3)[11] 0/1 1 1 1 1 1 0 0 -1 -1 Fred Renzey
Knock Out (K-O; All Sevens)[12][13][14] 1 1 1 1 1 1 0 0 -1 -1 Olaf Vancura and Ken Fuchs
Mentor[15] 1 2 2 2 2 1 0 -1 -2 -1 Fred Renzey
Red Seven[16] 1 1 1 1 1 0/1 0 0 -1 -1 Arnold Snyder
Revere 14 Count[17] 2 2 3 4 2 1 0 -2 -3 0 Lawrence Revere (G. Owens)
Revere Advanced Point Count (RAPC) [17] 2 3 3 4 3 2 0 -1 -3 -4 Lawrence Revere (G. Owens)
Revere Plus-Minus [17] 1 1 1 1 1 0 0 -1 -1 0 Lawrence Revere (G. Owens)
Revere Point Count (RPC) [17] 1 2 2 2 2 1 0 -1 -2 -2 Lawrence Revere (G. Owens)
Silver Fox[18] 1 1 1 1 1 1 0 -1 -1 -1 Ralph Stricker
Unbalanced Zen II (UBZ2)[19] 1 2 2 2 2 1 0 0 -2 -1 George C.
Uston Advanced Plus/Minus (APM)[20] 0 1 1 1 1 1 0 0 -1 -1 Ken Uston
Uston Advanced Point Count (APC)[20] 1 2 2 3 2 2 1 -1 -3 0 Ken Uston
Uston Strongest and Simplest (SS)[20] 2 2 2 3 2 1 0 -1 -2 -2 Ken Uston
Wong Halves[21] .5 1 1 1.5 1 .5 0 -.5 -1 -1 Stanford Wong (John Ferguson)
Zen Count[22] 1 1 2 2 2 1 0 0 -2 -1 Arnold Snyder

In the Media

Never Split Tens!, 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

References

Notes

  1. ^ Thorp (1966), pp.24-27, pp. 41-47, pp. 98-99, pp. 102-103, p. 110, p. 115.
  2. ^ <templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>Wizard of Odds (2011). "How to Play Blackjack". wizardofodds.com. Retrieved 2011-11-03. Unknown parameter |month= ignored (help)
  3. ^ Griffin (1988)
  4. ^ http://www.blackjackforumonline.com/content/hundred.htm
  5. ^ Carlson, Bryce (2010) Blackjack for Blood, Gamestar Pr Inc
  6. ^ a b <templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>"Canfield Expert book". Retrieved 2012-11-24.
  7. ^ Thorp, Edward O.(1962) Beat the Dealer: A Winning Strategy for the Game of Twenty-One, Vintage, New York
  8. ^ 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
  9. ^ a b Humble, Lance and Cooper, Carl (1987) The Worlds Greatest Blackjack Book , Doubleday, New York
  10. ^ Renzey, Fred (2006) Blackjack Bluebook , Blackjack Mentor Press
  11. ^ Renzey, Fred (2006) Blackjack Bluebook II , Blackjack Mentor Press
  12. ^ Vancura, Olaf and Fuchs, Ken (1998) Knock-Out Blackjack, Huntington Press
  13. ^ Zadehkoochak, M. (1992) The Book of British Blackjack Medimage. ISBN 1-897728-00-X
  14. ^ Notes: The KO Strategy was first introduced in 1992 as the "All Sevens" count in The Book of British Blackjack
  15. ^ Renzey, Fred (2006) Blackjack Bluebook II , Blackjack Mentor Press
  16. ^ Snyder, Arnold (1983) Blackbelt in Blackjack
  17. ^ a b c d Revere, Lawrence (1971) Playing Blackjack as a Business , Carol Publishing Group-Lyle Stuart
  18. ^ Stricker, Ralph, Silver Fox Blackjack System, Gambler’s Book Club, Las Vegas
  19. ^ C., George, The Unbalanced Zen II in Schlesinger, Don (2008 ) Blackjack Attack: Playing the Pros’ Way, RGE Publishers
  20. ^ a b c Uston, Ken (1998) Million Dollar Blackjack, Carol Publishing Group
  21. ^ Wong, Stanford (1994) Professional Blackjack, Pi Yee Pr Press
  22. ^ Synder, Arnold (2005) Blackbelt in Blackjack, Cardoza, Las Vegas

Bibliography

Further reading

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