Changes

After the publication of Beat the Dealer, gambling casinos reacted to the advantage that a card counter  gains over the house by adopting counter strategies.  These included employing multiple decks rather than the single hand-held deck.  Two-deck games and games employing four and six decks dealt from a so-called shoe became commonplace.

After the publication of Beat the Dealer, gambling casinos reacted to the advantage that a card counter  gains over the house by adopting counter strategies.  These included employing multiple decks rather than the single hand-held deck.  Two-deck games and games employing four and six decks dealt from a so-called shoe became commonplace.

[[File: LesGoldenBiologyET.jpg|thumb|left|175px|<small> Dr. Les Golden, a popular UIC professor of physics and director of the Near Earth Asteroid Reconnaissance Project, delivers a colloquium on the subject of Extraterrestrial Life to the University of Illinois at Chicago Biology Colloquium. </small>]]Players soon realized intuitively that both these changes in the game reduced their probabilities of winning.  In games with a multiple deck, compared to single-deck or double-deck games, players experience frequency, magnitude, and depth (the fraction of the deck which has been dealt in playing previous hands) effects:  1) The deck becomes favorable less frequently at all depths, 2) when the deck does becomes favorable, the magnitude of the advantage is not as great, 3) all decks are favorable infrequently until a significant portion of the deck has been dealt and this occurs at greater depths into the deck in games  using multiple decks.

[[File: LesGoldenBiologyET.jpg|thumb|left|175px|<small> Dr. Les Golden, a popular UIC professor of physics and director of the Near Earth Asteroid Reconnaissance Project, delivers a colloquium on the subject of Extraterrestrial Life to the University of Illinois at Chicago Biology Colloquium. </small>]][[File: DrLeslieMGoldenBlackjackArticle.jpg|thumb|right|125px|<small> The June, 2011, paper in <i>The Mathematical Scientist</i>, a peer-reviewed British scholarly journal, established Prof. Les Golden as a recognized expert in the probability and statistics as well as strategy of the casino game of blackjack. </small>]]Players soon realized intuitively that both these changes in the game reduced their probabilities of winning.  In games with a multiple deck, compared to single-deck or double-deck games, players experience frequency, magnitude, and depth (the fraction of the deck which has been dealt in playing previous hands) effects:  1) The deck becomes favorable less frequently at all depths, 2) when the deck does becomes favorable, the magnitude of the advantage is not as great, 3) all decks are favorable infrequently until a significant portion of the deck has been dealt and this occurs at greater depths into the deck in games  using multiple decks.

Golden, based on a Monte Carlo simulation and theoretical arguments, calculated the magnitude of these effects.  The results of his analysis are displayed as Golden diagrams.<ref>Golden, Les (2010).  “Countering the Casino Countering of Counters:  The Golden Diagram to the Rescue,” ''Bluff Europe'',  June, p. 84-85</ref><ref>Golden, Les (2011). “Trust Me:  An Undetectable Winning System For Blackjack! ,” ''Bluff Europe'', March, p. 94-95</ref>  He also suggested a stepwise betting strategy to reduce the effects.<ref>Golden, Leslie M. (2011). “An Analysis of the Disadvantage to Players of Multiple Decks in the Game of 21.”  ''The Mathematical Scientist'', '''32''', 2,  p. 57-69</ref><ref>Golden, Les (2011). “Stepping Out With My Baby:  The Stepwise Betting Strategy,” ''Bluff Europe'', April, p. 92-93</ref>

Golden, based on a Monte Carlo simulation and theoretical arguments, calculated the magnitude of these effects.  The results of his analysis are displayed as Golden diagrams.<ref>Golden, Les (2010).  “Countering the Casino Countering of Counters:  The Golden Diagram to the Rescue,” ''Bluff Europe'',  June, p. 84-85</ref><ref>Golden, Les (2011). “Trust Me:  An Undetectable Winning System For Blackjack! ,” ''Bluff Europe'', March, p. 94-95</ref>  He also suggested a stepwise betting strategy to reduce the effects.<ref>Golden, Leslie M. (2011). “An Analysis of the Disadvantage to Players of Multiple Decks in the Game of 21.”  ''The Mathematical Scientist'', '''32''', 2,  p. 57-69</ref><ref>Golden, Les (2011). “Stepping Out With My Baby:  The Stepwise Betting Strategy,” ''Bluff Europe'', April, p. 92-93</ref>