Optimal Blackjack Strategy Through Dynamic Programming
Blackjack Blackjack, also known as 21, is a casino banking game where players compete against the dealer rather than each other. The standard version uses one or more 52-card decks, where cards 2-10 count at face value, face cards (J, Q, K) count as 10, and Aces count as either 1 or 11. The game’s mathematical structure makes it particularly amenable to algorithmic analysis. Core Game Rules Objective: Achieve a hand total closer to 21 than the dealer without exceeding it Player Actions: Hit: Take another card Stand: Keep the current hand Dealer Constraints: Must hit until reaching 17 or higher Special Cases: Aces count flexibly as 1 or 11 “Blackjack” (Ace + 10-value card) pays 3:2 Dealer wins ties except when player has blackjack Dealer Probability Analysis The solution calculates exact probabilities for all possible dealer outcomes (17-21 or bust) given their initial card, using dynamic programming with memoization. The infinite deck assumption simplifies probability calculations since card draws remain independent. ...