Game's statistics: blackjack

Abstract

The main objectives of this article is to understand in depth the mechanism of the blackjack and establish a simple strategy to maximize the chances of winning the hand. First, we make a brief history about blackjack, discussing its origins and evolution. We explain in detail the rules of blackjack (scoring system and game procedures). In order to contextualize the popularity of blackjack, we provide some examples of books, films and video games where it has some role. Next, we present the computer program that we developed to compute the numeric probabilities to obtaining a given score using the blackjack points system, when we randomly draw 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11 cards from a standard 52-card deck. We explain in detail the algorithm of this program, present its results and analyze them. Finally, we simulate several hands of blackjack with just one player and a dealer. In these simulations, we do not allow the player to hit on hands worth more than a certain maximum score (P_max) or to get more than a certain maximum number of cards (N_max). Once again, we present the complete computer program and discuss it line by line. Analyzing the results of 100 simulations, where we sweep the value of  P_max  from 12 to 21 and the value of N_max from 2 to 11, we look for the combination of values of P_max and N_max that bring the best chance of victory. The best situation is the one that the dealer's chances of winning are only 4.7% higher than the player's.