Common strategies for playing blackjack include basic strategy and card counting. Basic strategy provides guidelines on the optimal decisions to make based on the player's hand and the dealer's upcard, helping to reduce the house edge. It covers actions like hitting, standing, doubling down, and splitting pairs. Card counting is an advanced method that involves tracking the ratio of high to low cards in the deck, allowing players to adjust their bets and strategies accordingly to gain an advantage. Both strategies require practice, quick decision-making, and effective bankroll management to enhance a player's chances of winning.