The option to double down influences your strategy by allowing you to increase your risk for the potential of higher rewards. It encourages a more aggressive approach when you feel confident about your hand, particularly when the dealer shows a weak card. This option prompts players to evaluate their hand strength and the dealer's upcard more closely, leading to decisions that could maximize profits in favorable situations while also heightening the stakes. This strategic element can shift the overall gameplay dynamics, making it essential to understand when to leverage doubling down effectively.