Real Valued Card Counting Strategies for the Game of Blackjack

Abstract

Card counting is a family of casino card game advantage gambling strategies, in which a player keeps a mental tally of the cards played in order to calculate whether the next hand is likely to be in the favor of the player or the dealer. A card counting system assigns point values (weights) to the cards. Summing the point values of the already played cards gives a concise numerical estimate of how advantageous the remaining cards are for the player. In theory, any assignment of weights is permissible. Historically, card counting systems used integers and rarely the 1/2 and 3/2 fractions, as computation with these are easier and more tractable for the human memory.

In this paper we investigate how much advantage would a system using real valued weights provide. Using a blackjack simulator and a simple genetic algorithm, we evolved weights vectors for ace-neutral and ace-reckoned balanced strategies with a fitness function that indicates how much a given strategy empirically under or outperforms a simple card counting system. After convergence, we evaluated the systems in the three efficiency categories used to characterize card counting strategies: playing efficiency, betting and insurance correlation. The obtained systems outperform classical integer count techniques, offering a better balance of the efficiency metrics. Finally, by applying rounding and scaling, we transformed some real valued strategies to integer point counts and found that most of the systems’ extra edge is preserved. However, because of the large weight values, it is unlikely that these systems can be played quickly and accurately even by professional card counters.

This project was supported by the Sapientia Foundation Institute for Scientific Research.