An Analysis of the Disadvantage to Players of Multiple Decks in the Game of 21

Players of blackjack recognize that their probabilities of winning are reduced by the casino use of multiple decks in the deck pack as a counter-measure to blackjack card counting systems. When playing blackjack with a deck pack composed of multiple 52-card decks compared to when playing in single-deck or double-deck games, players experience frequency, magnitude, and depth 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, the latter a result of the “fundamental theorem of card counting” (Thorp and Walden, 1973). Here,Monte Carlosimulations and application of a modified central limit theorem quantify these effects with the number of decks in the deck pack and depth as independent variables. The results are displayed graphically in a contour diagram referred to as the Golden Diagram. The numerical results indicate how players can regain much of their lost advantage by variations in strategy and a step-wise betting strategy, leading to an increase in the player’s expected winnings compared to a constant bet, without the need for card counting, by a factor of up to 2.6