Players utilize advanced techniques in Blackjack, such as card counting, to make informed decisions about actions like doubling down and splitting. By analyzing the remaining cards in the deck and assessing the dealer's upcard, they can gauge when the odds are in their favor. This strategic approach, combined with a solid understanding of basic strategy, allows players to make calculated moves that optimize their chances of winning, such as choosing to double down on strong hands or splitting pairs when advantageous.