Mathematics Senior Capstone Papers


Hanna Blanchard

Document Type


Publication Date

Spring 2019


In this paper the reader will learn about the math behind the cards in the game of Blackjack. Blackjack or “21” has been played around the world with various rules and regulations in both professional and informal environments. The ultimate objective of the game is to receive a total card value of 21, or as close to 21 as possible without exceeding it, from the cards in a player’s hand in order to beat the dealer’s total. The goal of this project is to calculate the probabilities of various hands to determine the best strategies to win 21. The probabilities of receiving each combination of a two-card pair, as well as the probabilities of a player’s best and worst case of receiving a third card to remain in the game, are calculated. These calculations are done for scenarios involving three players and a dealer using two to six card decks per scenario. The results indicate consistent probabilities of receiving the same two-card pair regardless of the number of decks used, but decreasing probabilities of receiving a third card to remain in the game. Thus, casinos are more likely to administer games with more decks in play. The goal is to determine whether to “hit” or “stand” when dealt certain a pair.



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