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